Add the ed25519 ref10 code verbatim from supercop-20140622

We might use libsodium or ed25519-donna later on, but for now, let's
see whether this is fast enough.  We should use it in all cases when
performance doesn't matter.

src/ext/ed25519/ref10/Makefile

@@ -0,0 +1,41 @@
+all: d.h d2.h sqrtm1.h base.h base2.h \
+ge_add.h ge_sub.h \
+ge_madd.h ge_msub.h \
+ge_p2_dbl.h \
+pow225521.h pow22523.h
+
+d.h: d.py
+	python d.py > d.h
+
+d2.h: d2.py
+	python d2.py > d2.h
+
+sqrtm1.h: sqrtm1.py
+	python sqrtm1.py > sqrtm1.h
+
+base.h: base.py
+	python base.py > base.h
+
+base2.h: base2.py
+	python base2.py > base2.h
+
+ge_add.h: ge_add.q q2h.sh
+	./q2h.sh < ge_add.q > ge_add.h
+
+ge_sub.h: ge_sub.q q2h.sh
+	./q2h.sh < ge_sub.q > ge_sub.h
+
+ge_madd.h: ge_madd.q q2h.sh
+	./q2h.sh < ge_madd.q > ge_madd.h
+
+ge_msub.h: ge_msub.q q2h.sh
+	./q2h.sh < ge_msub.q > ge_msub.h
+
+ge_p2_dbl.h: ge_p2_dbl.q q2h.sh
+	./q2h.sh < ge_p2_dbl.q > ge_p2_dbl.h
+
+pow22523.h: pow22523.q q2h.sh
+	./q2h.sh < pow22523.q > pow22523.h
+
+pow225521.h: pow225521.q q2h.sh
+	./q2h.sh < pow225521.q > pow225521.h

src/ext/ed25519/ref10/api.h

@@ -0,0 +1,4 @@
+#define CRYPTO_SECRETKEYBYTES 64
+#define CRYPTO_PUBLICKEYBYTES 32
+#define CRYPTO_BYTES 64
+#define CRYPTO_DETERMINISTIC 1

src/ext/ed25519/ref10/base.py

@@ -0,0 +1,65 @@
+b = 256
+q = 2**255 - 19
+l = 2**252 + 27742317777372353535851937790883648493
+
+def expmod(b,e,m):
+  if e == 0: return 1
+  t = expmod(b,e/2,m)**2 % m
+  if e & 1: t = (t*b) % m
+  return t
+
+def inv(x):
+  return expmod(x,q-2,q)
+
+d = -121665 * inv(121666)
+I = expmod(2,(q-1)/4,q)
+
+def xrecover(y):
+  xx = (y*y-1) * inv(d*y*y+1)
+  x = expmod(xx,(q+3)/8,q)
+  if (x*x - xx) % q != 0: x = (x*I) % q
+  if x % 2 != 0: x = q-x
+  return x
+
+By = 4 * inv(5)
+Bx = xrecover(By)
+B = [Bx % q,By % q]
+
+def edwards(P,Q):
+  x1 = P[0]
+  y1 = P[1]
+  x2 = Q[0]
+  y2 = Q[1]
+  x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
+  y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
+  return [x3 % q,y3 % q]
+
+def radix255(x):
+  x = x % q
+  if x + x > q: x -= q
+  x = [x,0,0,0,0,0,0,0,0,0]
+  bits = [26,25,26,25,26,25,26,25,26,25]
+  for i in range(9):
+    carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
+    x[i] -= carry * 2**bits[i]
+    x[i + 1] += carry
+  result = ""
+  for i in range(9):
+    result = result+str(x[i])+","
+  result = result+str(x[9])
+  return result
+
+Bi = B
+for i in range(32):
+  print "{"
+  Bij = Bi
+  for j in range(8):
+    print " {"
+    print "  {",radix255(Bij[1]+Bij[0]),"},"
+    print "  {",radix255(Bij[1]-Bij[0]),"},"
+    print "  {",radix255(2*d*Bij[0]*Bij[1]),"},"
+    Bij = edwards(Bij,Bi)
+    print " },"
+  print "},"
+  for k in range(8):
+    Bi = edwards(Bi,Bi)

src/ext/ed25519/ref10/base2.h

@@ -0,0 +1,40 @@
+ {
+  { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
+  { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
+  { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
+ },
+ {
+  { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
+  { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
+  { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
+ },
+ {
+  { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
+  { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
+  { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
+ },
+ {
+  { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
+  { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
+  { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
+ },
+ {
+  { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 },
+  { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 },
+  { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 },
+ },
+ {
+  { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 },
+  { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 },
+  { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 },
+ },
+ {
+  { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 },
+  { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 },
+  { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 },
+ },
+ {
+  { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 },
+  { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 },
+  { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 },
+ },

src/ext/ed25519/ref10/base2.py

@@ -0,0 +1,60 @@
+b = 256
+q = 2**255 - 19
+l = 2**252 + 27742317777372353535851937790883648493
+
+def expmod(b,e,m):
+  if e == 0: return 1
+  t = expmod(b,e/2,m)**2 % m
+  if e & 1: t = (t*b) % m
+  return t
+
+def inv(x):
+  return expmod(x,q-2,q)
+
+d = -121665 * inv(121666)
+I = expmod(2,(q-1)/4,q)
+
+def xrecover(y):
+  xx = (y*y-1) * inv(d*y*y+1)
+  x = expmod(xx,(q+3)/8,q)
+  if (x*x - xx) % q != 0: x = (x*I) % q
+  if x % 2 != 0: x = q-x
+  return x
+
+By = 4 * inv(5)
+Bx = xrecover(By)
+B = [Bx % q,By % q]
+
+def edwards(P,Q):
+  x1 = P[0]
+  y1 = P[1]
+  x2 = Q[0]
+  y2 = Q[1]
+  x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
+  y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
+  return [x3 % q,y3 % q]
+
+def radix255(x):
+  x = x % q
+  if x + x > q: x -= q
+  x = [x,0,0,0,0,0,0,0,0,0]
+  bits = [26,25,26,25,26,25,26,25,26,25]
+  for i in range(9):
+    carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
+    x[i] -= carry * 2**bits[i]
+    x[i + 1] += carry
+  result = ""
+  for i in range(9):
+    result = result+str(x[i])+","
+  result = result+str(x[9])
+  return result
+
+Bi = B
+
+for i in range(8):
+  print " {"
+  print "  {",radix255(Bi[1]+Bi[0]),"},"
+  print "  {",radix255(Bi[1]-Bi[0]),"},"
+  print "  {",radix255(2*d*Bi[0]*Bi[1]),"},"
+  print " },"
+  Bi = edwards(B,edwards(B,Bi))

src/ext/ed25519/ref10/d.h

@@ -0,0 +1 @@
+-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116

src/ext/ed25519/ref10/d.py

@@ -0,0 +1,28 @@
+q = 2**255 - 19
+
+def expmod(b,e,m):
+  if e == 0: return 1
+  t = expmod(b,e/2,m)**2 % m
+  if e & 1: t = (t*b) % m
+  return t
+
+def inv(x):
+  return expmod(x,q-2,q)
+
+def radix255(x):
+  x = x % q
+  if x + x > q: x -= q
+  x = [x,0,0,0,0,0,0,0,0,0]
+  bits = [26,25,26,25,26,25,26,25,26,25]
+  for i in range(9):
+    carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
+    x[i] -= carry * 2**bits[i]
+    x[i + 1] += carry
+  result = ""
+  for i in range(9):
+    result = result+str(x[i])+","
+  result = result+str(x[9])
+  return result
+
+d = -121665 * inv(121666)
+print radix255(d)

src/ext/ed25519/ref10/d2.h

@@ -0,0 +1 @@
+-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199

src/ext/ed25519/ref10/d2.py

@@ -0,0 +1,28 @@
+q = 2**255 - 19
+
+def expmod(b,e,m):
+  if e == 0: return 1
+  t = expmod(b,e/2,m)**2 % m
+  if e & 1: t = (t*b) % m
+  return t
+
+def inv(x):
+  return expmod(x,q-2,q)
+
+def radix255(x):
+  x = x % q
+  if x + x > q: x -= q
+  x = [x,0,0,0,0,0,0,0,0,0]
+  bits = [26,25,26,25,26,25,26,25,26,25]
+  for i in range(9):
+    carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
+    x[i] -= carry * 2**bits[i]
+    x[i + 1] += carry
+  result = ""
+  for i in range(9):
+    result = result+str(x[i])+","
+  result = result+str(x[9])
+  return result
+
+d = -121665 * inv(121666)
+print radix255(d*2)

src/ext/ed25519/ref10/fe.h

@@ -0,0 +1,56 @@
+#ifndef FE_H
+#define FE_H
+
+#include "crypto_int32.h"
+
+typedef crypto_int32 fe[10];
+
+/*
+fe means field element.
+Here the field is \Z/(2^255-19).
+An element t, entries t[0]...t[9], represents the integer
+t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
+Bounds on each t[i] vary depending on context.
+*/
+
+#define fe_frombytes crypto_sign_ed25519_ref10_fe_frombytes
+#define fe_tobytes crypto_sign_ed25519_ref10_fe_tobytes
+#define fe_copy crypto_sign_ed25519_ref10_fe_copy
+#define fe_isnonzero crypto_sign_ed25519_ref10_fe_isnonzero
+#define fe_isnegative crypto_sign_ed25519_ref10_fe_isnegative
+#define fe_0 crypto_sign_ed25519_ref10_fe_0
+#define fe_1 crypto_sign_ed25519_ref10_fe_1
+#define fe_cswap crypto_sign_ed25519_ref10_fe_cswap
+#define fe_cmov crypto_sign_ed25519_ref10_fe_cmov
+#define fe_add crypto_sign_ed25519_ref10_fe_add
+#define fe_sub crypto_sign_ed25519_ref10_fe_sub
+#define fe_neg crypto_sign_ed25519_ref10_fe_neg
+#define fe_mul crypto_sign_ed25519_ref10_fe_mul
+#define fe_sq crypto_sign_ed25519_ref10_fe_sq
+#define fe_sq2 crypto_sign_ed25519_ref10_fe_sq2
+#define fe_mul121666 crypto_sign_ed25519_ref10_fe_mul121666
+#define fe_invert crypto_sign_ed25519_ref10_fe_invert
+#define fe_pow22523 crypto_sign_ed25519_ref10_fe_pow22523
+
+extern void fe_frombytes(fe,const unsigned char *);
+extern void fe_tobytes(unsigned char *,const fe);
+
+extern void fe_copy(fe,const fe);
+extern int fe_isnonzero(const fe);
+extern int fe_isnegative(const fe);
+extern void fe_0(fe);
+extern void fe_1(fe);
+extern void fe_cswap(fe,fe,unsigned int);
+extern void fe_cmov(fe,const fe,unsigned int);
+
+extern void fe_add(fe,const fe,const fe);
+extern void fe_sub(fe,const fe,const fe);
+extern void fe_neg(fe,const fe);
+extern void fe_mul(fe,const fe,const fe);
+extern void fe_sq(fe,const fe);
+extern void fe_sq2(fe,const fe);
+extern void fe_mul121666(fe,const fe);
+extern void fe_invert(fe,const fe);
+extern void fe_pow22523(fe,const fe);
+
+#endif

src/ext/ed25519/ref10/fe_0.c

@@ -0,0 +1,19 @@
+#include "fe.h"
+
+/*
+h = 0
+*/
+
+void fe_0(fe h)
+{
+  h[0] = 0;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}

src/ext/ed25519/ref10/fe_1.c

@@ -0,0 +1,19 @@
+#include "fe.h"
+
+/*
+h = 1
+*/
+
+void fe_1(fe h)
+{
+  h[0] = 1;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}

src/ext/ed25519/ref10/fe_add.c

@@ -0,0 +1,57 @@
+#include "fe.h"
+
+/*
+h = f + g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h,const fe f,const fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 + g0;
+  crypto_int32 h1 = f1 + g1;
+  crypto_int32 h2 = f2 + g2;
+  crypto_int32 h3 = f3 + g3;
+  crypto_int32 h4 = f4 + g4;
+  crypto_int32 h5 = f5 + g5;
+  crypto_int32 h6 = f6 + g6;
+  crypto_int32 h7 = f7 + g7;
+  crypto_int32 h8 = f8 + g8;
+  crypto_int32 h9 = f9 + g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_cmov.c

@@ -0,0 +1,63 @@
+#include "fe.h"
+
+/*
+Replace (f,g) with (g,g) if b == 1;
+replace (f,g) with (f,g) if b == 0.
+
+Preconditions: b in {0,1}.
+*/
+
+void fe_cmov(fe f,const fe g,unsigned int b)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 x0 = f0 ^ g0;
+  crypto_int32 x1 = f1 ^ g1;
+  crypto_int32 x2 = f2 ^ g2;
+  crypto_int32 x3 = f3 ^ g3;
+  crypto_int32 x4 = f4 ^ g4;
+  crypto_int32 x5 = f5 ^ g5;
+  crypto_int32 x6 = f6 ^ g6;
+  crypto_int32 x7 = f7 ^ g7;
+  crypto_int32 x8 = f8 ^ g8;
+  crypto_int32 x9 = f9 ^ g9;
+  b = -b;
+  x0 &= b;
+  x1 &= b;
+  x2 &= b;
+  x3 &= b;
+  x4 &= b;
+  x5 &= b;
+  x6 &= b;
+  x7 &= b;
+  x8 &= b;
+  x9 &= b;
+  f[0] = f0 ^ x0;
+  f[1] = f1 ^ x1;
+  f[2] = f2 ^ x2;
+  f[3] = f3 ^ x3;
+  f[4] = f4 ^ x4;
+  f[5] = f5 ^ x5;
+  f[6] = f6 ^ x6;
+  f[7] = f7 ^ x7;
+  f[8] = f8 ^ x8;
+  f[9] = f9 ^ x9;
+}

src/ext/ed25519/ref10/fe_copy.c

@@ -0,0 +1,29 @@
+#include "fe.h"
+
+/*
+h = f
+*/
+
+void fe_copy(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  h[0] = f0;
+  h[1] = f1;
+  h[2] = f2;
+  h[3] = f3;
+  h[4] = f4;
+  h[5] = f5;
+  h[6] = f6;
+  h[7] = f7;
+  h[8] = f8;
+  h[9] = f9;
+}

src/ext/ed25519/ref10/fe_frombytes.c

@@ -0,0 +1,73 @@
+#include "fe.h"
+#include "crypto_int64.h"
+#include "crypto_uint64.h"
+
+static crypto_uint64 load_3(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  return result;
+}
+
+static crypto_uint64 load_4(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  result |= ((crypto_uint64) in[3]) << 24;
+  return result;
+}
+
+/*
+Ignores top bit of h.
+*/
+
+void fe_frombytes(fe h,const unsigned char *s)
+{
+  crypto_int64 h0 = load_4(s);
+  crypto_int64 h1 = load_3(s + 4) << 6;
+  crypto_int64 h2 = load_3(s + 7) << 5;
+  crypto_int64 h3 = load_3(s + 10) << 3;
+  crypto_int64 h4 = load_3(s + 13) << 2;
+  crypto_int64 h5 = load_4(s + 16);
+  crypto_int64 h6 = load_3(s + 20) << 7;
+  crypto_int64 h7 = load_3(s + 23) << 5;
+  crypto_int64 h8 = load_3(s + 26) << 4;
+  crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_invert.c

@@ -0,0 +1,14 @@
+#include "fe.h"
+
+void fe_invert(fe out,const fe z)
+{
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+#include "pow225521.h"
+
+  return;
+}

src/ext/ed25519/ref10/fe_isnegative.c

@@ -0,0 +1,16 @@
+#include "fe.h"
+
+/*
+return 1 if f is in {1,3,5,...,q-2}
+return 0 if f is in {0,2,4,...,q-1}
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnegative(const fe f)
+{
+  unsigned char s[32];
+  fe_tobytes(s,f);
+  return s[0] & 1;
+}

src/ext/ed25519/ref10/fe_isnonzero.c

@@ -0,0 +1,19 @@
+#include "fe.h"
+#include "crypto_verify_32.h"
+
+/*
+return 1 if f == 0
+return 0 if f != 0
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static const unsigned char zero[32];
+
+int fe_isnonzero(const fe f)
+{
+  unsigned char s[32];
+  fe_tobytes(s,f);
+  return crypto_verify_32(s,zero);
+}

src/ext/ed25519/ref10/fe_mul.c

@@ -0,0 +1,253 @@
+#include "fe.h"
+#include "crypto_int64.h"
+
+/*
+h = f * g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+   |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+Notes on implementation strategy:
+
+Using schoolbook multiplication.
+Karatsuba would save a little in some cost models.
+
+Most multiplications by 2 and 19 are 32-bit precomputations;
+cheaper than 64-bit postcomputations.
+
+There is one remaining multiplication by 19 in the carry chain;
+one *19 precomputation can be merged into this,
+but the resulting data flow is considerably less clean.
+
+There are 12 carries below.
+10 of them are 2-way parallelizable and vectorizable.
+Can get away with 11 carries, but then data flow is much deeper.
+
+With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+void fe_mul(fe h,const fe f,const fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
+  crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+  crypto_int32 g3_19 = 19 * g3;
+  crypto_int32 g4_19 = 19 * g4;
+  crypto_int32 g5_19 = 19 * g5;
+  crypto_int32 g6_19 = 19 * g6;
+  crypto_int32 g7_19 = 19 * g7;
+  crypto_int32 g8_19 = 19 * g8;
+  crypto_int32 g9_19 = 19 * g9;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f9_2 = 2 * f9;
+  crypto_int64 f0g0    = f0   * (crypto_int64) g0;
+  crypto_int64 f0g1    = f0   * (crypto_int64) g1;
+  crypto_int64 f0g2    = f0   * (crypto_int64) g2;
+  crypto_int64 f0g3    = f0   * (crypto_int64) g3;
+  crypto_int64 f0g4    = f0   * (crypto_int64) g4;
+  crypto_int64 f0g5    = f0   * (crypto_int64) g5;
+  crypto_int64 f0g6    = f0   * (crypto_int64) g6;
+  crypto_int64 f0g7    = f0   * (crypto_int64) g7;
+  crypto_int64 f0g8    = f0   * (crypto_int64) g8;
+  crypto_int64 f0g9    = f0   * (crypto_int64) g9;
+  crypto_int64 f1g0    = f1   * (crypto_int64) g0;
+  crypto_int64 f1g1_2  = f1_2 * (crypto_int64) g1;
+  crypto_int64 f1g2    = f1   * (crypto_int64) g2;
+  crypto_int64 f1g3_2  = f1_2 * (crypto_int64) g3;
+  crypto_int64 f1g4    = f1   * (crypto_int64) g4;
+  crypto_int64 f1g5_2  = f1_2 * (crypto_int64) g5;
+  crypto_int64 f1g6    = f1   * (crypto_int64) g6;
+  crypto_int64 f1g7_2  = f1_2 * (crypto_int64) g7;
+  crypto_int64 f1g8    = f1   * (crypto_int64) g8;
+  crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
+  crypto_int64 f2g0    = f2   * (crypto_int64) g0;
+  crypto_int64 f2g1    = f2   * (crypto_int64) g1;
+  crypto_int64 f2g2    = f2   * (crypto_int64) g2;
+  crypto_int64 f2g3    = f2   * (crypto_int64) g3;
+  crypto_int64 f2g4    = f2   * (crypto_int64) g4;
+  crypto_int64 f2g5    = f2   * (crypto_int64) g5;
+  crypto_int64 f2g6    = f2   * (crypto_int64) g6;
+  crypto_int64 f2g7    = f2   * (crypto_int64) g7;
+  crypto_int64 f2g8_19 = f2   * (crypto_int64) g8_19;
+  crypto_int64 f2g9_19 = f2   * (crypto_int64) g9_19;
+  crypto_int64 f3g0    = f3   * (crypto_int64) g0;
+  crypto_int64 f3g1_2  = f3_2 * (crypto_int64) g1;
+  crypto_int64 f3g2    = f3   * (crypto_int64) g2;
+  crypto_int64 f3g3_2  = f3_2 * (crypto_int64) g3;
+  crypto_int64 f3g4    = f3   * (crypto_int64) g4;
+  crypto_int64 f3g5_2  = f3_2 * (crypto_int64) g5;
+  crypto_int64 f3g6    = f3   * (crypto_int64) g6;
+  crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
+  crypto_int64 f3g8_19 = f3   * (crypto_int64) g8_19;
+  crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
+  crypto_int64 f4g0    = f4   * (crypto_int64) g0;
+  crypto_int64 f4g1    = f4   * (crypto_int64) g1;
+  crypto_int64 f4g2    = f4   * (crypto_int64) g2;
+  crypto_int64 f4g3    = f4   * (crypto_int64) g3;
+  crypto_int64 f4g4    = f4   * (crypto_int64) g4;
+  crypto_int64 f4g5    = f4   * (crypto_int64) g5;
+  crypto_int64 f4g6_19 = f4   * (crypto_int64) g6_19;
+  crypto_int64 f4g7_19 = f4   * (crypto_int64) g7_19;
+  crypto_int64 f4g8_19 = f4   * (crypto_int64) g8_19;
+  crypto_int64 f4g9_19 = f4   * (crypto_int64) g9_19;
+  crypto_int64 f5g0    = f5   * (crypto_int64) g0;
+  crypto_int64 f5g1_2  = f5_2 * (crypto_int64) g1;
+  crypto_int64 f5g2    = f5   * (crypto_int64) g2;
+  crypto_int64 f5g3_2  = f5_2 * (crypto_int64) g3;
+  crypto_int64 f5g4    = f5   * (crypto_int64) g4;
+  crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
+  crypto_int64 f5g6_19 = f5   * (crypto_int64) g6_19;
+  crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
+  crypto_int64 f5g8_19 = f5   * (crypto_int64) g8_19;
+  crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
+  crypto_int64 f6g0    = f6   * (crypto_int64) g0;
+  crypto_int64 f6g1    = f6   * (crypto_int64) g1;
+  crypto_int64 f6g2    = f6   * (crypto_int64) g2;
+  crypto_int64 f6g3    = f6   * (crypto_int64) g3;
+  crypto_int64 f6g4_19 = f6   * (crypto_int64) g4_19;
+  crypto_int64 f6g5_19 = f6   * (crypto_int64) g5_19;
+  crypto_int64 f6g6_19 = f6   * (crypto_int64) g6_19;
+  crypto_int64 f6g7_19 = f6   * (crypto_int64) g7_19;
+  crypto_int64 f6g8_19 = f6   * (crypto_int64) g8_19;
+  crypto_int64 f6g9_19 = f6   * (crypto_int64) g9_19;
+  crypto_int64 f7g0    = f7   * (crypto_int64) g0;
+  crypto_int64 f7g1_2  = f7_2 * (crypto_int64) g1;
+  crypto_int64 f7g2    = f7   * (crypto_int64) g2;
+  crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
+  crypto_int64 f7g4_19 = f7   * (crypto_int64) g4_19;
+  crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
+  crypto_int64 f7g6_19 = f7   * (crypto_int64) g6_19;
+  crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
+  crypto_int64 f7g8_19 = f7   * (crypto_int64) g8_19;
+  crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
+  crypto_int64 f8g0    = f8   * (crypto_int64) g0;
+  crypto_int64 f8g1    = f8   * (crypto_int64) g1;
+  crypto_int64 f8g2_19 = f8   * (crypto_int64) g2_19;
+  crypto_int64 f8g3_19 = f8   * (crypto_int64) g3_19;
+  crypto_int64 f8g4_19 = f8   * (crypto_int64) g4_19;
+  crypto_int64 f8g5_19 = f8   * (crypto_int64) g5_19;
+  crypto_int64 f8g6_19 = f8   * (crypto_int64) g6_19;
+  crypto_int64 f8g7_19 = f8   * (crypto_int64) g7_19;
+  crypto_int64 f8g8_19 = f8   * (crypto_int64) g8_19;
+  crypto_int64 f8g9_19 = f8   * (crypto_int64) g9_19;
+  crypto_int64 f9g0    = f9   * (crypto_int64) g0;
+  crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
+  crypto_int64 f9g2_19 = f9   * (crypto_int64) g2_19;
+  crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
+  crypto_int64 f9g4_19 = f9   * (crypto_int64) g4_19;
+  crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
+  crypto_int64 f9g6_19 = f9   * (crypto_int64) g6_19;
+  crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
+  crypto_int64 f9g8_19 = f9   * (crypto_int64) g8_19;
+  crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
+  crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
+  crypto_int64 h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
+  crypto_int64 h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
+  crypto_int64 h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
+  crypto_int64 h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
+  crypto_int64 h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
+  crypto_int64 h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
+  crypto_int64 h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
+  crypto_int64 h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
+  crypto_int64 h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  /*
+  |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
+    i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
+  |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
+    i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
+  */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  /* |h0| <= 2^25 */
+  /* |h4| <= 2^25 */
+  /* |h1| <= 1.71*2^59 */
+  /* |h5| <= 1.71*2^59 */
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  /* |h1| <= 2^24; from now on fits into int32 */
+  /* |h5| <= 2^24; from now on fits into int32 */
+  /* |h2| <= 1.41*2^60 */
+  /* |h6| <= 1.41*2^60 */
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  /* |h2| <= 2^25; from now on fits into int32 unchanged */
+  /* |h6| <= 2^25; from now on fits into int32 unchanged */
+  /* |h3| <= 1.71*2^59 */
+  /* |h7| <= 1.71*2^59 */
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  /* |h3| <= 2^24; from now on fits into int32 unchanged */
+  /* |h7| <= 2^24; from now on fits into int32 unchanged */
+  /* |h4| <= 1.72*2^34 */
+  /* |h8| <= 1.41*2^60 */
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  /* |h4| <= 2^25; from now on fits into int32 unchanged */
+  /* |h8| <= 2^25; from now on fits into int32 unchanged */
+  /* |h5| <= 1.01*2^24 */
+  /* |h9| <= 1.71*2^59 */
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  /* |h9| <= 2^24; from now on fits into int32 unchanged */
+  /* |h0| <= 1.1*2^39 */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  /* |h0| <= 2^25; from now on fits into int32 unchanged */
+  /* |h1| <= 1.01*2^24 */
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_neg.c

@@ -0,0 +1,45 @@
+#include "fe.h"
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_neg(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 h0 = -f0;
+  crypto_int32 h1 = -f1;
+  crypto_int32 h2 = -f2;
+  crypto_int32 h3 = -f3;
+  crypto_int32 h4 = -f4;
+  crypto_int32 h5 = -f5;
+  crypto_int32 h6 = -f6;
+  crypto_int32 h7 = -f7;
+  crypto_int32 h8 = -f8;
+  crypto_int32 h9 = -f9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_pow22523.c

@@ -0,0 +1,13 @@
+#include "fe.h"
+
+void fe_pow22523(fe out,const fe z)
+{
+  fe t0;
+  fe t1;
+  fe t2;
+  int i;
+
+#include "pow22523.h"
+
+  return;
+}

src/ext/ed25519/ref10/fe_sq.c

@@ -0,0 +1,149 @@
+#include "fe.h"
+#include "crypto_int64.h"
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 f0_2 = 2 * f0;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f2_2 = 2 * f2;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f4_2 = 2 * f4;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f6_2 = 2 * f6;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
+  crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
+  crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
+  crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
+  crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
+  crypto_int64 f0f0    = f0   * (crypto_int64) f0;
+  crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
+  crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
+  crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
+  crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
+  crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
+  crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
+  crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
+  crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
+  crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
+  crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
+  crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
+  crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
+  crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
+  crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
+  crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
+  crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
+  crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
+  crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
+  crypto_int64 f2f2    = f2   * (crypto_int64) f2;
+  crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
+  crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
+  crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
+  crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
+  crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
+  crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
+  crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
+  crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
+  crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
+  crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
+  crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
+  crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
+  crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
+  crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
+  crypto_int64 f4f4    = f4   * (crypto_int64) f4;
+  crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
+  crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
+  crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
+  crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
+  crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
+  crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
+  crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
+  crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
+  crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
+  crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
+  crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
+  crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
+  crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
+  crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
+  crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
+  crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
+  crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
+  crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
+  crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
+  crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
+  crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_sq2.c

@@ -0,0 +1,160 @@
+#include "fe.h"
+#include "crypto_int64.h"
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq2(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 f0_2 = 2 * f0;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f2_2 = 2 * f2;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f4_2 = 2 * f4;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f6_2 = 2 * f6;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
+  crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
+  crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
+  crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
+  crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
+  crypto_int64 f0f0    = f0   * (crypto_int64) f0;
+  crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
+  crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
+  crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
+  crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
+  crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
+  crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
+  crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
+  crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
+  crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
+  crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
+  crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
+  crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
+  crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
+  crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
+  crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
+  crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
+  crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
+  crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
+  crypto_int64 f2f2    = f2   * (crypto_int64) f2;
+  crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
+  crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
+  crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
+  crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
+  crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
+  crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
+  crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
+  crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
+  crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
+  crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
+  crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
+  crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
+  crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
+  crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
+  crypto_int64 f4f4    = f4   * (crypto_int64) f4;
+  crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
+  crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
+  crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
+  crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
+  crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
+  crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
+  crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
+  crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
+  crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
+  crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
+  crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
+  crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
+  crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
+  crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
+  crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
+  crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
+  crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
+  crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
+  crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
+  crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
+  crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  h0 += h0;
+  h1 += h1;
+  h2 += h2;
+  h3 += h3;
+  h4 += h4;
+  h5 += h5;
+  h6 += h6;
+  h7 += h7;
+  h8 += h8;
+  h9 += h9;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_sub.c

@@ -0,0 +1,57 @@
+#include "fe.h"
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h,const fe f,const fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 - g0;
+  crypto_int32 h1 = f1 - g1;
+  crypto_int32 h2 = f2 - g2;
+  crypto_int32 h3 = f3 - g3;
+  crypto_int32 h4 = f4 - g4;
+  crypto_int32 h5 = f5 - g5;
+  crypto_int32 h6 = f6 - g6;
+  crypto_int32 h7 = f7 - g7;
+  crypto_int32 h8 = f8 - g8;
+  crypto_int32 h9 = f9 - g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}

src/ext/ed25519/ref10/fe_tobytes.c

@@ -0,0 +1,119 @@
+#include "fe.h"
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+void fe_tobytes(unsigned char *s,const fe h)
+{
+  crypto_int32 h0 = h[0];
+  crypto_int32 h1 = h[1];
+  crypto_int32 h2 = h[2];
+  crypto_int32 h3 = h[3];
+  crypto_int32 h4 = h[4];
+  crypto_int32 h5 = h[5];
+  crypto_int32 h6 = h[6];
+  crypto_int32 h7 = h[7];
+  crypto_int32 h8 = h[8];
+  crypto_int32 h9 = h[9];
+  crypto_int32 q;
+  crypto_int32 carry0;
+  crypto_int32 carry1;
+  crypto_int32 carry2;
+  crypto_int32 carry3;
+  crypto_int32 carry4;
+  crypto_int32 carry5;
+  crypto_int32 carry6;
+  crypto_int32 carry7;
+  crypto_int32 carry8;
+  crypto_int32 carry9;
+
+  q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25;
+  q = (h0 + q) >> 26;
+  q = (h1 + q) >> 25;
+  q = (h2 + q) >> 26;
+  q = (h3 + q) >> 25;
+  q = (h4 + q) >> 26;
+  q = (h5 + q) >> 25;
+  q = (h6 + q) >> 26;
+  q = (h7 + q) >> 25;
+  q = (h8 + q) >> 26;
+  q = (h9 + q) >> 25;
+
+  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+  h0 += 19 * q;
+  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+
+  carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry9 = h9 >> 25;               h9 -= carry9 << 25;
+                  /* h10 = carry9 */
+
+  /*
+  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+  Have h0+...+2^230 h9 between 0 and 2^255-1;
+  evidently 2^255 h10-2^255 q = 0.
+  Goal: Output h0+...+2^230 h9.
+  */
+
+  s[0] = h0 >> 0;
+  s[1] = h0 >> 8;
+  s[2] = h0 >> 16;
+  s[3] = (h0 >> 24) | (h1 << 2);
+  s[4] = h1 >> 6;
+  s[5] = h1 >> 14;
+  s[6] = (h1 >> 22) | (h2 << 3);
+  s[7] = h2 >> 5;
+  s[8] = h2 >> 13;
+  s[9] = (h2 >> 21) | (h3 << 5);
+  s[10] = h3 >> 3;
+  s[11] = h3 >> 11;
+  s[12] = (h3 >> 19) | (h4 << 6);
+  s[13] = h4 >> 2;
+  s[14] = h4 >> 10;
+  s[15] = h4 >> 18;
+  s[16] = h5 >> 0;
+  s[17] = h5 >> 8;
+  s[18] = h5 >> 16;
+  s[19] = (h5 >> 24) | (h6 << 1);
+  s[20] = h6 >> 7;
+  s[21] = h6 >> 15;
+  s[22] = (h6 >> 23) | (h7 << 3);
+  s[23] = h7 >> 5;
+  s[24] = h7 >> 13;
+  s[25] = (h7 >> 21) | (h8 << 4);
+  s[26] = h8 >> 4;
+  s[27] = h8 >> 12;
+  s[28] = (h8 >> 20) | (h9 << 6);
+  s[29] = h9 >> 2;
+  s[30] = h9 >> 10;
+  s[31] = h9 >> 18;
+}

src/ext/ed25519/ref10/ge.h

@@ -0,0 +1,95 @@
+#ifndef GE_H
+#define GE_H
+
+/*
+ge means group element.
+
+Here the group is the set of pairs (x,y) of field elements (see fe.h)
+satisfying -x^2 + y^2 = 1 + d x^2y^2
+where d = -121665/121666.
+
+Representations:
+  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+  ge_precomp (Duif): (y+x,y-x,2dxy)
+*/
+
+#include "fe.h"
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+#define ge_frombytes_negate_vartime crypto_sign_ed25519_ref10_ge_frombytes_negate_vartime
+#define ge_tobytes crypto_sign_ed25519_ref10_ge_tobytes
+#define ge_p3_tobytes crypto_sign_ed25519_ref10_ge_p3_tobytes
+
+#define ge_p2_0 crypto_sign_ed25519_ref10_ge_p2_0
+#define ge_p3_0 crypto_sign_ed25519_ref10_ge_p3_0
+#define ge_precomp_0 crypto_sign_ed25519_ref10_ge_precomp_0
+#define ge_p3_to_p2 crypto_sign_ed25519_ref10_ge_p3_to_p2
+#define ge_p3_to_cached crypto_sign_ed25519_ref10_ge_p3_to_cached
+#define ge_p1p1_to_p2 crypto_sign_ed25519_ref10_ge_p1p1_to_p2
+#define ge_p1p1_to_p3 crypto_sign_ed25519_ref10_ge_p1p1_to_p3
+#define ge_p2_dbl crypto_sign_ed25519_ref10_ge_p2_dbl
+#define ge_p3_dbl crypto_sign_ed25519_ref10_ge_p3_dbl
+
+#define ge_madd crypto_sign_ed25519_ref10_ge_madd
+#define ge_msub crypto_sign_ed25519_ref10_ge_msub
+#define ge_add crypto_sign_ed25519_ref10_ge_add
+#define ge_sub crypto_sign_ed25519_ref10_ge_sub
+#define ge_scalarmult_base crypto_sign_ed25519_ref10_ge_scalarmult_base
+#define ge_double_scalarmult_vartime crypto_sign_ed25519_ref10_ge_double_scalarmult_vartime
+
+extern void ge_tobytes(unsigned char *,const ge_p2 *);
+extern void ge_p3_tobytes(unsigned char *,const ge_p3 *);
+extern int ge_frombytes_negate_vartime(ge_p3 *,const unsigned char *);
+
+extern void ge_p2_0(ge_p2 *);
+extern void ge_p3_0(ge_p3 *);
+extern void ge_precomp_0(ge_precomp *);
+extern void ge_p3_to_p2(ge_p2 *,const ge_p3 *);
+extern void ge_p3_to_cached(ge_cached *,const ge_p3 *);
+extern void ge_p1p1_to_p2(ge_p2 *,const ge_p1p1 *);
+extern void ge_p1p1_to_p3(ge_p3 *,const ge_p1p1 *);
+extern void ge_p2_dbl(ge_p1p1 *,const ge_p2 *);
+extern void ge_p3_dbl(ge_p1p1 *,const ge_p3 *);
+
+extern void ge_madd(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
+extern void ge_msub(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
+extern void ge_add(ge_p1p1 *,const ge_p3 *,const ge_cached *);
+extern void ge_sub(ge_p1p1 *,const ge_p3 *,const ge_cached *);
+extern void ge_scalarmult_base(ge_p3 *,const unsigned char *);
+extern void ge_double_scalarmult_vartime(ge_p2 *,const unsigned char *,const ge_p3 *,const unsigned char *);
+
+#endif

src/ext/ed25519/ref10/ge_add.c

@@ -0,0 +1,11 @@
+#include "ge.h"
+
+/*
+r = p + q
+*/
+
+void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
+{
+  fe t0;
+#include "ge_add.h"
+}

src/ext/ed25519/ref10/ge_add.h

@@ -0,0 +1,97 @@
+
+/* qhasm: enter ge_add */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe Z2 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ZZ */
+
+/* qhasm: fe YpX2 */
+
+/* qhasm: fe YmX2 */
+
+/* qhasm: fe T2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*YpX2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
+fe_mul(r->Z,r->X,q->YplusX);
+
+/* qhasm: B = YmX1*YmX2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
+fe_mul(r->Y,r->Y,q->YminusX);
+
+/* qhasm: C = T2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
+fe_mul(r->T,q->T2d,p->T);
+
+/* qhasm: ZZ = Z1*Z2 */
+/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
+/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
+fe_mul(r->X,p->Z,q->Z);
+
+/* qhasm: D = 2*ZZ */
+/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
+/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
+fe_add(t0,r->X,r->X);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D+C */
+/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_add(r->Z,t0,r->T);
+
+/* qhasm: T3 = D-C */
+/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
+fe_sub(r->T,t0,r->T);
+
+/* qhasm: return */

src/ext/ed25519/ref10/ge_add.q

@@ -0,0 +1,49 @@
+:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->YplusX:q->YminusX:q->Z:q->T2d:
+fe r:var/r=fe:
+
+enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>YpX2=fe#15:>YmX2=fe#16:>Z2=fe#17:>T2d2=fe#18:
+return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
+
+h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
+h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
+h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
+
+:
+
+enter ge_add
+
+fe X1
+fe Y1
+fe Z1
+fe Z2
+fe T1
+fe ZZ
+fe YpX2
+fe YmX2
+fe T2d2
+fe X3
+fe Y3
+fe Z3
+fe T3
+fe YpX1
+fe YmX1
+fe A
+fe B
+fe C
+fe D
+
+YpX1 = Y1+X1
+YmX1 = Y1-X1
+A = YpX1*YpX2
+B = YmX1*YmX2
+C = T2d2*T1
+ZZ = Z1*Z2
+D = 2*ZZ
+X3 = A-B
+Y3 = A+B
+Z3 = D+C
+T3 = D-C
+
+return

src/ext/ed25519/ref10/ge_double_scalarmult.c

@@ -0,0 +1,96 @@
+#include "ge.h"
+
+static void slide(signed char *r,const unsigned char *a)
+{
+  int i;
+  int b;
+  int k;
+
+  for (i = 0;i < 256;++i)
+    r[i] = 1 & (a[i >> 3] >> (i & 7));
+
+  for (i = 0;i < 256;++i)
+    if (r[i]) {
+      for (b = 1;b <= 6 && i + b < 256;++b) {
+        if (r[i + b]) {
+          if (r[i] + (r[i + b] << b) <= 15) {
+            r[i] += r[i + b] << b; r[i + b] = 0;
+          } else if (r[i] - (r[i + b] << b) >= -15) {
+            r[i] -= r[i + b] << b;
+            for (k = i + b;k < 256;++k) {
+              if (!r[k]) {
+                r[k] = 1;
+                break;
+              }
+              r[k] = 0;
+            }
+          } else
+            break;
+        }
+      }
+    }
+
+}
+
+static ge_precomp Bi[8] = {
+#include "base2.h"
+} ;
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b)
+{
+  signed char aslide[256];
+  signed char bslide[256];
+  ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+  ge_p1p1 t;
+  ge_p3 u;
+  ge_p3 A2;
+  int i;
+
+  slide(aslide,a);
+  slide(bslide,b);
+
+  ge_p3_to_cached(&Ai[0],A);
+  ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
+  ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
+  ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
+  ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
+  ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
+  ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
+  ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
+  ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);
+
+  ge_p2_0(r);
+
+  for (i = 255;i >= 0;--i) {
+    if (aslide[i] || bslide[i]) break;
+  }
+
+  for (;i >= 0;--i) {
+    ge_p2_dbl(&t,r);
+
+    if (aslide[i] > 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_add(&t,&u,&Ai[aslide[i]/2]);
+    } else if (aslide[i] < 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_sub(&t,&u,&Ai[(-aslide[i])/2]);
+    }
+
+    if (bslide[i] > 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_madd(&t,&u,&Bi[bslide[i]/2]);
+    } else if (bslide[i] < 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
+    }
+
+    ge_p1p1_to_p2(r,&t);
+  }
+}

src/ext/ed25519/ref10/ge_frombytes.c

@@ -0,0 +1,50 @@
+#include "ge.h"
+
+static const fe d = {
+#include "d.h"
+} ;
+
+static const fe sqrtm1 = {
+#include "sqrtm1.h"
+} ;
+
+int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
+{
+  fe u;
+  fe v;
+  fe v3;
+  fe vxx;
+  fe check;
+
+  fe_frombytes(h->Y,s);
+  fe_1(h->Z);
+  fe_sq(u,h->Y);
+  fe_mul(v,u,d);
+  fe_sub(u,u,h->Z);       /* u = y^2-1 */
+  fe_add(v,v,h->Z);       /* v = dy^2+1 */
+
+  fe_sq(v3,v);
+  fe_mul(v3,v3,v);        /* v3 = v^3 */
+  fe_sq(h->X,v3);
+  fe_mul(h->X,h->X,v);
+  fe_mul(h->X,h->X,u);    /* x = uv^7 */
+
+  fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
+  fe_mul(h->X,h->X,v3);
+  fe_mul(h->X,h->X,u);    /* x = uv^3(uv^7)^((q-5)/8) */
+
+  fe_sq(vxx,h->X);
+  fe_mul(vxx,vxx,v);
+  fe_sub(check,vxx,u);    /* vx^2-u */
+  if (fe_isnonzero(check)) {
+    fe_add(check,vxx,u);  /* vx^2+u */
+    if (fe_isnonzero(check)) return -1;
+    fe_mul(h->X,h->X,sqrtm1);
+  }
+
+  if (fe_isnegative(h->X) == (s[31] >> 7))
+    fe_neg(h->X,h->X);
+
+  fe_mul(h->T,h->X,h->Y);
+  return 0;
+}

src/ext/ed25519/ref10/ge_madd.c

@@ -0,0 +1,11 @@
+#include "ge.h"
+
+/*
+r = p + q
+*/
+
+void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
+{
+  fe t0;
+#include "ge_madd.h"
+}

src/ext/ed25519/ref10/ge_madd.h

@@ -0,0 +1,88 @@
+
+/* qhasm: enter ge_madd */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ypx2 */
+
+/* qhasm: fe ymx2 */
+
+/* qhasm: fe xy2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*ypx2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ypx2=fe#15); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ypx2=q->yplusx); */
+fe_mul(r->Z,r->X,q->yplusx);
+
+/* qhasm: B = YmX1*ymx2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ymx2=fe#16); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ymx2=q->yminusx); */
+fe_mul(r->Y,r->Y,q->yminusx);
+
+/* qhasm: C = xy2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
+fe_mul(r->T,q->xy2d,p->T);
+
+/* qhasm: D = 2*Z1 */
+/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
+/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
+fe_add(t0,p->Z,p->Z);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D+C */
+/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_add(r->Z,t0,r->T);
+
+/* qhasm: T3 = D-C */
+/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
+fe_sub(r->T,t0,r->T);
+
+/* qhasm: return */

src/ext/ed25519/ref10/ge_madd.q

@@ -0,0 +1,46 @@
+:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->yplusx:q->yminusx:q->xy2d:
+fe r:var/r=fe:
+
+enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>ypx2=fe#15:>ymx2=fe#16:>xy2d2=fe#17:
+return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
+
+h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
+h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
+h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
+
+:
+
+enter ge_madd
+
+fe X1
+fe Y1
+fe Z1
+fe T1
+fe ypx2
+fe ymx2
+fe xy2d2
+fe X3
+fe Y3
+fe Z3
+fe T3
+fe YpX1
+fe YmX1
+fe A
+fe B
+fe C
+fe D
+
+YpX1 = Y1+X1
+YmX1 = Y1-X1
+A = YpX1*ypx2
+B = YmX1*ymx2
+C = xy2d2*T1
+D = 2*Z1
+X3 = A-B
+Y3 = A+B
+Z3 = D+C
+T3 = D-C
+
+return

src/ext/ed25519/ref10/ge_msub.c

@@ -0,0 +1,11 @@
+#include "ge.h"
+
+/*
+r = p - q
+*/
+
+void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
+{
+  fe t0;
+#include "ge_msub.h"
+}

src/ext/ed25519/ref10/ge_msub.h

@@ -0,0 +1,88 @@
+
+/* qhasm: enter ge_msub */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ypx2 */
+
+/* qhasm: fe ymx2 */
+
+/* qhasm: fe xy2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*ymx2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
+fe_mul(r->Z,r->X,q->yminusx);
+
+/* qhasm: B = YmX1*ypx2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
+fe_mul(r->Y,r->Y,q->yplusx);
+
+/* qhasm: C = xy2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
+fe_mul(r->T,q->xy2d,p->T);
+
+/* qhasm: D = 2*Z1 */
+/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
+/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
+fe_add(t0,p->Z,p->Z);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D-C */
+/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_sub(r->Z,t0,r->T);
+
+/* qhasm: T3 = D+C */
+/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
+fe_add(r->T,t0,r->T);
+
+/* qhasm: return */

src/ext/ed25519/ref10/ge_msub.q

@@ -0,0 +1,46 @@
+:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->yplusx:q->yminusx:q->xy2d:
+fe r:var/r=fe:
+
+enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>ypx2=fe#15:>ymx2=fe#16:>xy2d2=fe#17:
+return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
+
+h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
+h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
+h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
+
+:
+
+enter ge_msub
+
+fe X1
+fe Y1
+fe Z1
+fe T1
+fe ypx2
+fe ymx2
+fe xy2d2
+fe X3
+fe Y3
+fe Z3
+fe T3
+fe YpX1
+fe YmX1
+fe A
+fe B
+fe C
+fe D
+
+YpX1 = Y1+X1
+YmX1 = Y1-X1
+A = YpX1*ymx2
+B = YmX1*ypx2
+C = xy2d2*T1
+D = 2*Z1
+X3 = A-B
+Y3 = A+B
+Z3 = D-C
+T3 = D+C
+
+return

src/ext/ed25519/ref10/ge_p1p1_to_p2.c

@@ -0,0 +1,12 @@
+#include "ge.h"
+
+/*
+r = p
+*/
+
+extern void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p)
+{
+  fe_mul(r->X,p->X,p->T);
+  fe_mul(r->Y,p->Y,p->Z);
+  fe_mul(r->Z,p->Z,p->T);
+}

src/ext/ed25519/ref10/ge_p1p1_to_p3.c

@@ -0,0 +1,13 @@
+#include "ge.h"
+
+/*
+r = p
+*/
+
+extern void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p)
+{
+  fe_mul(r->X,p->X,p->T);
+  fe_mul(r->Y,p->Y,p->Z);
+  fe_mul(r->Z,p->Z,p->T);
+  fe_mul(r->T,p->X,p->Y);
+}

src/ext/ed25519/ref10/ge_p2_0.c

@@ -0,0 +1,8 @@
+#include "ge.h"
+
+void ge_p2_0(ge_p2 *h)
+{
+  fe_0(h->X);
+  fe_1(h->Y);
+  fe_1(h->Z);
+}

src/ext/ed25519/ref10/ge_p2_dbl.c

@@ -0,0 +1,11 @@
+#include "ge.h"
+
+/*
+r = 2 * p
+*/
+
+void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
+{
+  fe t0;
+#include "ge_p2_dbl.h"
+}

src/ext/ed25519/ref10/ge_p2_dbl.h

@@ -0,0 +1,73 @@
+
+/* qhasm: enter ge_p2_dbl */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe AA */
+
+/* qhasm: fe XX */
+
+/* qhasm: fe YY */
+
+/* qhasm: fe B */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: XX=X1^2 */
+/* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
+/* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
+fe_sq(r->X,p->X);
+
+/* qhasm: YY=Y1^2 */
+/* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
+/* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
+fe_sq(r->Z,p->Y);
+
+/* qhasm: B=2*Z1^2 */
+/* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
+/* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
+fe_sq2(r->T,p->Z);
+
+/* qhasm: A=X1+Y1 */
+/* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
+/* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
+fe_add(r->Y,p->X,p->Y);
+
+/* qhasm: AA=A^2 */
+/* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
+/* asm 2: fe_sq(>AA=t0,<A=r->Y); */
+fe_sq(t0,r->Y);
+
+/* qhasm: Y3=YY+XX */
+/* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
+/* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
+fe_add(r->Y,r->Z,r->X);
+
+/* qhasm: Z3=YY-XX */
+/* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
+/* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
+fe_sub(r->Z,r->Z,r->X);
+
+/* qhasm: X3=AA-Y3 */
+/* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
+fe_sub(r->X,t0,r->Y);
+
+/* qhasm: T3=B-Z3 */
+/* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
+/* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
+fe_sub(r->T,r->T,r->Z);
+
+/* qhasm: return */

src/ext/ed25519/ref10/ge_p2_dbl.q

@@ -0,0 +1,41 @@
+:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:
+fe r:var/r=fe:
+
+enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:
+return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
+
+h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
+h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
+h=2*f^2:<f=fe:>h=fe:asm/fe_sq2(>h,<f);:
+h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
+
+:
+
+enter ge_p2_dbl
+
+fe X1
+fe Y1
+fe Z1
+fe A
+fe AA
+fe XX
+fe YY
+fe B
+fe X3
+fe Y3
+fe Z3
+fe T3
+
+XX=X1^2
+YY=Y1^2
+B=2*Z1^2
+A=X1+Y1
+AA=A^2
+Y3=YY+XX
+Z3=YY-XX
+X3=AA-Y3
+T3=B-Z3
+
+return

src/ext/ed25519/ref10/ge_p3_0.c

@@ -0,0 +1,9 @@
+#include "ge.h"
+
+void ge_p3_0(ge_p3 *h)
+{
+  fe_0(h->X);
+  fe_1(h->Y);
+  fe_1(h->Z);
+  fe_0(h->T);
+}

src/ext/ed25519/ref10/ge_p3_dbl.c

@@ -0,0 +1,12 @@
+#include "ge.h"
+
+/*
+r = 2 * p
+*/
+
+void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p)
+{
+  ge_p2 q;
+  ge_p3_to_p2(&q,p);
+  ge_p2_dbl(r,&q);
+}

src/ext/ed25519/ref10/ge_p3_to_cached.c

@@ -0,0 +1,17 @@
+#include "ge.h"
+
+/*
+r = p
+*/
+
+static const fe d2 = {
+#include "d2.h"
+} ;
+
+extern void ge_p3_to_cached(ge_cached *r,const ge_p3 *p)
+{
+  fe_add(r->YplusX,p->Y,p->X);
+  fe_sub(r->YminusX,p->Y,p->X);
+  fe_copy(r->Z,p->Z);
+  fe_mul(r->T2d,p->T,d2);
+}

src/ext/ed25519/ref10/ge_p3_to_p2.c

@@ -0,0 +1,12 @@
+#include "ge.h"
+
+/*
+r = p
+*/
+
+extern void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p)
+{
+  fe_copy(r->X,p->X);
+  fe_copy(r->Y,p->Y);
+  fe_copy(r->Z,p->Z);
+}

src/ext/ed25519/ref10/ge_p3_tobytes.c

@@ -0,0 +1,14 @@
+#include "ge.h"
+
+void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
+{
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(recip,h->Z);
+  fe_mul(x,h->X,recip);
+  fe_mul(y,h->Y,recip);
+  fe_tobytes(s,y);
+  s[31] ^= fe_isnegative(x) << 7;
+}

src/ext/ed25519/ref10/ge_precomp_0.c

@@ -0,0 +1,8 @@
+#include "ge.h"
+
+void ge_precomp_0(ge_precomp *h)
+{
+  fe_1(h->yplusx);
+  fe_1(h->yminusx);
+  fe_0(h->xy2d);
+}

src/ext/ed25519/ref10/ge_scalarmult_base.c

@@ -0,0 +1,105 @@
+#include "ge.h"
+#include "crypto_uint32.h"
+
+static unsigned char equal(signed char b,signed char c)
+{
+  unsigned char ub = b;
+  unsigned char uc = c;
+  unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+  crypto_uint32 y = x; /* 0: yes; 1..255: no */
+  y -= 1; /* 4294967295: yes; 0..254: no */
+  y >>= 31; /* 1: yes; 0: no */
+  return y;
+}
+
+static unsigned char negative(signed char b)
+{
+  unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+  x >>= 63; /* 1: yes; 0: no */
+  return x;
+}
+
+static void cmov(ge_precomp *t,ge_precomp *u,unsigned char b)
+{
+  fe_cmov(t->yplusx,u->yplusx,b);
+  fe_cmov(t->yminusx,u->yminusx,b);
+  fe_cmov(t->xy2d,u->xy2d,b);
+}
+
+/* base[i][j] = (j+1)*256^i*B */
+static ge_precomp base[32][8] = {
+#include "base.h"
+} ;
+
+static void select(ge_precomp *t,int pos,signed char b)
+{
+  ge_precomp minust;
+  unsigned char bnegative = negative(b);
+  unsigned char babs = b - (((-bnegative) & b) << 1);
+
+  ge_precomp_0(t);
+  cmov(t,&base[pos][0],equal(babs,1));
+  cmov(t,&base[pos][1],equal(babs,2));
+  cmov(t,&base[pos][2],equal(babs,3));
+  cmov(t,&base[pos][3],equal(babs,4));
+  cmov(t,&base[pos][4],equal(babs,5));
+  cmov(t,&base[pos][5],equal(babs,6));
+  cmov(t,&base[pos][6],equal(babs,7));
+  cmov(t,&base[pos][7],equal(babs,8));
+  fe_copy(minust.yplusx,t->yminusx);
+  fe_copy(minust.yminusx,t->yplusx);
+  fe_neg(minust.xy2d,t->xy2d);
+  cmov(t,&minust,bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+void ge_scalarmult_base(ge_p3 *h,const unsigned char *a)
+{
+  signed char e[64];
+  signed char carry;
+  ge_p1p1 r;
+  ge_p2 s;
+  ge_precomp t;
+  int i;
+
+  for (i = 0;i < 32;++i) {
+    e[2 * i + 0] = (a[i] >> 0) & 15;
+    e[2 * i + 1] = (a[i] >> 4) & 15;
+  }
+  /* each e[i] is between 0 and 15 */
+  /* e[63] is between 0 and 7 */
+
+  carry = 0;
+  for (i = 0;i < 63;++i) {
+    e[i] += carry;
+    carry = e[i] + 8;
+    carry >>= 4;
+    e[i] -= carry << 4;
+  }
+  e[63] += carry;
+  /* each e[i] is between -8 and 8 */
+
+  ge_p3_0(h);
+  for (i = 1;i < 64;i += 2) {
+    select(&t,i / 2,e[i]);
+    ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
+  }
+
+  ge_p3_dbl(&r,h);  ge_p1p1_to_p2(&s,&r);
+  ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
+  ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
+  ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r);
+
+  for (i = 0;i < 64;i += 2) {
+    select(&t,i / 2,e[i]);
+    ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
+  }
+}

src/ext/ed25519/ref10/ge_sub.c

@@ -0,0 +1,11 @@
+#include "ge.h"
+
+/*
+r = p - q
+*/
+
+void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
+{
+  fe t0;
+#include "ge_sub.h"
+}

src/ext/ed25519/ref10/ge_sub.h

@@ -0,0 +1,97 @@
+
+/* qhasm: enter ge_sub */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe Z2 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ZZ */
+
+/* qhasm: fe YpX2 */
+
+/* qhasm: fe YmX2 */
+
+/* qhasm: fe T2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*YmX2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
+fe_mul(r->Z,r->X,q->YminusX);
+
+/* qhasm: B = YmX1*YpX2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
+fe_mul(r->Y,r->Y,q->YplusX);
+
+/* qhasm: C = T2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
+fe_mul(r->T,q->T2d,p->T);
+
+/* qhasm: ZZ = Z1*Z2 */
+/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
+/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
+fe_mul(r->X,p->Z,q->Z);
+
+/* qhasm: D = 2*ZZ */
+/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
+/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
+fe_add(t0,r->X,r->X);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D-C */
+/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_sub(r->Z,t0,r->T);
+
+/* qhasm: T3 = D+C */
+/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
+fe_add(r->T,t0,r->T);
+
+/* qhasm: return */

src/ext/ed25519/ref10/ge_sub.q

@@ -0,0 +1,49 @@
+:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->YplusX:q->YminusX:q->Z:q->T2d:
+fe r:var/r=fe:
+
+enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>YpX2=fe#15:>YmX2=fe#16:>Z2=fe#17:>T2d2=fe#18:
+return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
+
+h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
+h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
+h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
+
+:
+
+enter ge_sub
+
+fe X1
+fe Y1
+fe Z1
+fe Z2
+fe T1
+fe ZZ
+fe YpX2
+fe YmX2
+fe T2d2
+fe X3
+fe Y3
+fe Z3
+fe T3
+fe YpX1
+fe YmX1
+fe A
+fe B
+fe C
+fe D
+
+YpX1 = Y1+X1
+YmX1 = Y1-X1
+A = YpX1*YmX2
+B = YmX1*YpX2
+C = T2d2*T1
+ZZ = Z1*Z2
+D = 2*ZZ
+X3 = A-B
+Y3 = A+B
+Z3 = D-C
+T3 = D+C
+
+return

src/ext/ed25519/ref10/ge_tobytes.c

@@ -0,0 +1,14 @@
+#include "ge.h"
+
+void ge_tobytes(unsigned char *s,const ge_p2 *h)
+{
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(recip,h->Z);
+  fe_mul(x,h->X,recip);
+  fe_mul(y,h->Y,recip);
+  fe_tobytes(s,y);
+  s[31] ^= fe_isnegative(x) << 7;
+}

src/ext/ed25519/ref10/keypair.c

@@ -0,0 +1,23 @@
+#include <string.h>
+#include "randombytes.h"
+#include "crypto_sign.h"
+#include "crypto_hash_sha512.h"
+#include "ge.h"
+
+int crypto_sign_keypair(unsigned char *pk,unsigned char *sk)
+{
+  unsigned char az[64];
+  ge_p3 A;
+
+  randombytes(sk,32);
+  crypto_hash_sha512(az,sk,32);
+  az[0] &= 248;
+  az[31] &= 63;
+  az[31] |= 64;
+
+  ge_scalarmult_base(&A,az);
+  ge_p3_tobytes(pk,&A);
+
+  memmove(sk + 32,pk,32);
+  return 0;
+}

src/ext/ed25519/ref10/open.c

@@ -0,0 +1,48 @@
+#include <string.h>
+#include "crypto_sign.h"
+#include "crypto_hash_sha512.h"
+#include "crypto_verify_32.h"
+#include "ge.h"
+#include "sc.h"
+
+int crypto_sign_open(
+  unsigned char *m,unsigned long long *mlen,
+  const unsigned char *sm,unsigned long long smlen,
+  const unsigned char *pk
+)
+{
+  unsigned char pkcopy[32];
+  unsigned char rcopy[32];
+  unsigned char scopy[32];
+  unsigned char h[64];
+  unsigned char rcheck[32];
+  ge_p3 A;
+  ge_p2 R;
+
+  if (smlen < 64) goto badsig;
+  if (sm[63] & 224) goto badsig;
+  if (ge_frombytes_negate_vartime(&A,pk) != 0) goto badsig;
+
+  memmove(pkcopy,pk,32);
+  memmove(rcopy,sm,32);
+  memmove(scopy,sm + 32,32);
+
+  memmove(m,sm,smlen);
+  memmove(m + 32,pkcopy,32);
+  crypto_hash_sha512(h,m,smlen);
+  sc_reduce(h);
+
+  ge_double_scalarmult_vartime(&R,h,&A,scopy);
+  ge_tobytes(rcheck,&R);
+  if (crypto_verify_32(rcheck,rcopy) == 0) {
+    memmove(m,m + 64,smlen - 64);
+    memset(m + smlen - 64,0,64);
+    *mlen = smlen - 64;
+    return 0;
+  }
+
+badsig:
+  *mlen = -1;
+  memset(m,0,smlen);
+  return -1;
+}

src/ext/ed25519/ref10/pow22523.h

@@ -0,0 +1,160 @@
+
+/* qhasm: fe z1 */
+
+/* qhasm: fe z2 */
+
+/* qhasm: fe z8 */
+
+/* qhasm: fe z9 */
+
+/* qhasm: fe z11 */
+
+/* qhasm: fe z22 */
+
+/* qhasm: fe z_5_0 */
+
+/* qhasm: fe z_10_5 */
+
+/* qhasm: fe z_10_0 */
+
+/* qhasm: fe z_20_10 */
+
+/* qhasm: fe z_20_0 */
+
+/* qhasm: fe z_40_20 */
+
+/* qhasm: fe z_40_0 */
+
+/* qhasm: fe z_50_10 */
+
+/* qhasm: fe z_50_0 */
+
+/* qhasm: fe z_100_50 */
+
+/* qhasm: fe z_100_0 */
+
+/* qhasm: fe z_200_100 */
+
+/* qhasm: fe z_200_0 */
+
+/* qhasm: fe z_250_50 */
+
+/* qhasm: fe z_250_0 */
+
+/* qhasm: fe z_252_2 */
+
+/* qhasm: fe z_252_3 */
+
+/* qhasm: enter pow22523 */
+
+/* qhasm: z2 = z1^2^1 */
+/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
+/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
+fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z8 = z2^2^2 */
+/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
+/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
+fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+
+/* qhasm: z9 = z1*z8 */
+/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
+/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
+fe_mul(t1,z,t1);
+
+/* qhasm: z11 = z2*z9 */
+/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
+/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
+fe_mul(t0,t0,t1);
+
+/* qhasm: z22 = z11^2^1 */
+/* asm 1: fe_sq(>z22=fe#1,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#1,>z22=fe#1); */
+/* asm 2: fe_sq(>z22=t0,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t0,>z22=t0); */
+fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z_5_0 = z9*z22 */
+/* asm 1: fe_mul(>z_5_0=fe#1,<z9=fe#2,<z22=fe#1); */
+/* asm 2: fe_mul(>z_5_0=t0,<z9=t1,<z22=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_10_5 = z_5_0^2^5 */
+/* asm 1: fe_sq(>z_10_5=fe#2,<z_5_0=fe#1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#2,>z_10_5=fe#2); */
+/* asm 2: fe_sq(>z_10_5=t1,<z_5_0=t0); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t1,>z_10_5=t1); */
+fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+
+/* qhasm: z_10_0 = z_10_5*z_5_0 */
+/* asm 1: fe_mul(>z_10_0=fe#1,<z_10_5=fe#2,<z_5_0=fe#1); */
+/* asm 2: fe_mul(>z_10_0=t0,<z_10_5=t1,<z_5_0=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_20_10 = z_10_0^2^10 */
+/* asm 1: fe_sq(>z_20_10=fe#2,<z_10_0=fe#1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#2,>z_20_10=fe#2); */
+/* asm 2: fe_sq(>z_20_10=t1,<z_10_0=t0); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t1,>z_20_10=t1); */
+fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1);
+
+/* qhasm: z_20_0 = z_20_10*z_10_0 */
+/* asm 1: fe_mul(>z_20_0=fe#2,<z_20_10=fe#2,<z_10_0=fe#1); */
+/* asm 2: fe_mul(>z_20_0=t1,<z_20_10=t1,<z_10_0=t0); */
+fe_mul(t1,t1,t0);
+
+/* qhasm: z_40_20 = z_20_0^2^20 */
+/* asm 1: fe_sq(>z_40_20=fe#3,<z_20_0=fe#2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#3,>z_40_20=fe#3); */
+/* asm 2: fe_sq(>z_40_20=t2,<z_20_0=t1); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t2,>z_40_20=t2); */
+fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2);
+
+/* qhasm: z_40_0 = z_40_20*z_20_0 */
+/* asm 1: fe_mul(>z_40_0=fe#2,<z_40_20=fe#3,<z_20_0=fe#2); */
+/* asm 2: fe_mul(>z_40_0=t1,<z_40_20=t2,<z_20_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_50_10 = z_40_0^2^10 */
+/* asm 1: fe_sq(>z_50_10=fe#2,<z_40_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#2,>z_50_10=fe#2); */
+/* asm 2: fe_sq(>z_50_10=t1,<z_40_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t1,>z_50_10=t1); */
+fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1);
+
+/* qhasm: z_50_0 = z_50_10*z_10_0 */
+/* asm 1: fe_mul(>z_50_0=fe#1,<z_50_10=fe#2,<z_10_0=fe#1); */
+/* asm 2: fe_mul(>z_50_0=t0,<z_50_10=t1,<z_10_0=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_100_50 = z_50_0^2^50 */
+/* asm 1: fe_sq(>z_100_50=fe#2,<z_50_0=fe#1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#2,>z_100_50=fe#2); */
+/* asm 2: fe_sq(>z_100_50=t1,<z_50_0=t0); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t1,>z_100_50=t1); */
+fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1);
+
+/* qhasm: z_100_0 = z_100_50*z_50_0 */
+/* asm 1: fe_mul(>z_100_0=fe#2,<z_100_50=fe#2,<z_50_0=fe#1); */
+/* asm 2: fe_mul(>z_100_0=t1,<z_100_50=t1,<z_50_0=t0); */
+fe_mul(t1,t1,t0);
+
+/* qhasm: z_200_100 = z_100_0^2^100 */
+/* asm 1: fe_sq(>z_200_100=fe#3,<z_100_0=fe#2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#3,>z_200_100=fe#3); */
+/* asm 2: fe_sq(>z_200_100=t2,<z_100_0=t1); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t2,>z_200_100=t2); */
+fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2);
+
+/* qhasm: z_200_0 = z_200_100*z_100_0 */
+/* asm 1: fe_mul(>z_200_0=fe#2,<z_200_100=fe#3,<z_100_0=fe#2); */
+/* asm 2: fe_mul(>z_200_0=t1,<z_200_100=t2,<z_100_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_250_50 = z_200_0^2^50 */
+/* asm 1: fe_sq(>z_250_50=fe#2,<z_200_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#2,>z_250_50=fe#2); */
+/* asm 2: fe_sq(>z_250_50=t1,<z_200_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t1,>z_250_50=t1); */
+fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1);
+
+/* qhasm: z_250_0 = z_250_50*z_50_0 */
+/* asm 1: fe_mul(>z_250_0=fe#1,<z_250_50=fe#2,<z_50_0=fe#1); */
+/* asm 2: fe_mul(>z_250_0=t0,<z_250_50=t1,<z_50_0=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_252_2 = z_250_0^2^2 */
+/* asm 1: fe_sq(>z_252_2=fe#1,<z_250_0=fe#1); for (i = 1;i < 2;++i) fe_sq(>z_252_2=fe#1,>z_252_2=fe#1); */
+/* asm 2: fe_sq(>z_252_2=t0,<z_250_0=t0); for (i = 1;i < 2;++i) fe_sq(>z_252_2=t0,>z_252_2=t0); */
+fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0);
+
+/* qhasm: z_252_3 = z_252_2*z1 */
+/* asm 1: fe_mul(>z_252_3=fe#12,<z_252_2=fe#1,<z1=fe#11); */
+/* asm 2: fe_mul(>z_252_3=out,<z_252_2=t0,<z1=z); */
+fe_mul(out,t0,z);
+
+/* qhasm: return */

src/ext/ed25519/ref10/pow22523.q

@@ -0,0 +1,61 @@
+:name:fe:t0:t1:t2:t3:t4:t5:t6:t7:t8:t9:z:out:
+fe r:var/r=fe:
+
+enter f:enter/f:>z1=fe#11:
+return:nofallthrough:<z_252_3=fe#12:leave:
+
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2^k:<f=fe:>h=fe:#k:asm/fe_sq(>h,<f); for (i = 1;i !lt; #k;++i) fe_sq(>h,>h);:
+
+:
+
+fe z1
+fe z2
+fe z8
+fe z9
+fe z11
+fe z22
+fe z_5_0
+fe z_10_5
+fe z_10_0
+fe z_20_10
+fe z_20_0
+fe z_40_20
+fe z_40_0
+fe z_50_10
+fe z_50_0
+fe z_100_50
+fe z_100_0
+fe z_200_100
+fe z_200_0
+fe z_250_50
+fe z_250_0
+fe z_252_2
+fe z_252_3
+
+enter pow22523
+
+z2 = z1^2^1
+z8 = z2^2^2
+z9 = z1*z8
+z11 = z2*z9
+z22 = z11^2^1
+z_5_0 = z9*z22
+z_10_5 = z_5_0^2^5
+z_10_0 = z_10_5*z_5_0
+z_20_10 = z_10_0^2^10
+z_20_0 = z_20_10*z_10_0
+z_40_20 = z_20_0^2^20
+z_40_0 = z_40_20*z_20_0
+z_50_10 = z_40_0^2^10
+z_50_0 = z_50_10*z_10_0
+z_100_50 = z_50_0^2^50
+z_100_0 = z_100_50*z_50_0
+z_200_100 = z_100_0^2^100
+z_200_0 = z_200_100*z_100_0
+z_250_50 = z_200_0^2^50
+z_250_0 = z_250_50*z_50_0
+z_252_2 = z_250_0^2^2
+z_252_3 = z_252_2*z1
+
+return

src/ext/ed25519/ref10/pow225521.h

@@ -0,0 +1,160 @@
+
+/* qhasm: fe z1 */
+
+/* qhasm: fe z2 */
+
+/* qhasm: fe z8 */
+
+/* qhasm: fe z9 */
+
+/* qhasm: fe z11 */
+
+/* qhasm: fe z22 */
+
+/* qhasm: fe z_5_0 */
+
+/* qhasm: fe z_10_5 */
+
+/* qhasm: fe z_10_0 */
+
+/* qhasm: fe z_20_10 */
+
+/* qhasm: fe z_20_0 */
+
+/* qhasm: fe z_40_20 */
+
+/* qhasm: fe z_40_0 */
+
+/* qhasm: fe z_50_10 */
+
+/* qhasm: fe z_50_0 */
+
+/* qhasm: fe z_100_50 */
+
+/* qhasm: fe z_100_0 */
+
+/* qhasm: fe z_200_100 */
+
+/* qhasm: fe z_200_0 */
+
+/* qhasm: fe z_250_50 */
+
+/* qhasm: fe z_250_0 */
+
+/* qhasm: fe z_255_5 */
+
+/* qhasm: fe z_255_21 */
+
+/* qhasm: enter pow225521 */
+
+/* qhasm: z2 = z1^2^1 */
+/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
+/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
+fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z8 = z2^2^2 */
+/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
+/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
+fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+
+/* qhasm: z9 = z1*z8 */
+/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
+/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
+fe_mul(t1,z,t1);
+
+/* qhasm: z11 = z2*z9 */
+/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
+/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
+fe_mul(t0,t0,t1);
+
+/* qhasm: z22 = z11^2^1 */
+/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
+/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
+fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
+
+/* qhasm: z_5_0 = z9*z22 */
+/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
+/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
+fe_mul(t1,t1,t2);
+
+/* qhasm: z_10_5 = z_5_0^2^5 */
+/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
+/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
+fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
+
+/* qhasm: z_10_0 = z_10_5*z_5_0 */
+/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
+/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_20_10 = z_10_0^2^10 */
+/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
+/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
+fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_20_0 = z_20_10*z_10_0 */
+/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_40_20 = z_20_0^2^20 */
+/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
+/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
+fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
+
+/* qhasm: z_40_0 = z_40_20*z_20_0 */
+/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
+/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_50_10 = z_40_0^2^10 */
+/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
+/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
+fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_50_0 = z_50_10*z_10_0 */
+/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_100_50 = z_50_0^2^50 */
+/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
+/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
+fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_100_0 = z_100_50*z_50_0 */
+/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_200_100 = z_100_0^2^100 */
+/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
+/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
+fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
+
+/* qhasm: z_200_0 = z_200_100*z_100_0 */
+/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
+/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_250_50 = z_200_0^2^50 */
+/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
+/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
+fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_250_0 = z_250_50*z_50_0 */
+/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_255_5 = z_250_0^2^5 */
+/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
+/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
+fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+
+/* qhasm: z_255_21 = z_255_5*z11 */
+/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
+/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
+fe_mul(out,t1,t0);
+
+/* qhasm: return */

src/ext/ed25519/ref10/pow225521.q

@@ -0,0 +1,61 @@
+:name:fe:t0:t1:t2:t3:t4:t5:t6:t7:t8:t9:z:out:
+fe r:var/r=fe:
+
+enter f:enter/f:>z1=fe#11:
+return:nofallthrough:<z_255_21=fe#12:leave:
+
+h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
+h=f^2^k:<f=fe:>h=fe:#k:asm/fe_sq(>h,<f); for (i = 1;i !lt; #k;++i) fe_sq(>h,>h);:
+
+:
+
+fe z1
+fe z2
+fe z8
+fe z9
+fe z11
+fe z22
+fe z_5_0
+fe z_10_5
+fe z_10_0
+fe z_20_10
+fe z_20_0
+fe z_40_20
+fe z_40_0
+fe z_50_10
+fe z_50_0
+fe z_100_50
+fe z_100_0
+fe z_200_100
+fe z_200_0
+fe z_250_50
+fe z_250_0
+fe z_255_5
+fe z_255_21
+
+enter pow225521
+
+z2 = z1^2^1
+z8 = z2^2^2
+z9 = z1*z8
+z11 = z2*z9
+z22 = z11^2^1
+z_5_0 = z9*z22
+z_10_5 = z_5_0^2^5
+z_10_0 = z_10_5*z_5_0
+z_20_10 = z_10_0^2^10
+z_20_0 = z_20_10*z_10_0
+z_40_20 = z_20_0^2^20
+z_40_0 = z_40_20*z_20_0
+z_50_10 = z_40_0^2^10
+z_50_0 = z_50_10*z_10_0
+z_100_50 = z_50_0^2^50
+z_100_0 = z_100_50*z_50_0
+z_200_100 = z_100_0^2^100
+z_200_0 = z_200_100*z_100_0
+z_250_50 = z_200_0^2^50
+z_250_0 = z_250_50*z_50_0
+z_255_5 = z_250_0^2^5
+z_255_21 = z_255_5*z11
+
+return

src/ext/ed25519/ref10/q2h.sh

@@ -0,0 +1,4 @@
+#!/bin/sh
+sed 's/^#.*//' \
+| qhasm-generic \
+| sed 's_//\(.*\)$_/*\1 */_'

src/ext/ed25519/ref10/sc.h

@@ -0,0 +1,15 @@
+#ifndef SC_H
+#define SC_H
+
+/*
+The set of scalars is \Z/l
+where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+#define sc_reduce crypto_sign_ed25519_ref10_sc_reduce
+#define sc_muladd crypto_sign_ed25519_ref10_sc_muladd
+
+extern void sc_reduce(unsigned char *);
+extern void sc_muladd(unsigned char *,const unsigned char *,const unsigned char *,const unsigned char *);
+
+#endif

src/ext/ed25519/ref10/sc_muladd.c

@@ -0,0 +1,368 @@
+#include "sc.h"
+#include "crypto_int64.h"
+#include "crypto_uint32.h"
+#include "crypto_uint64.h"
+
+static crypto_uint64 load_3(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  return result;
+}
+
+static crypto_uint64 load_4(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  result |= ((crypto_uint64) in[3]) << 24;
+  return result;
+}
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c)
+{
+  crypto_int64 a0 = 2097151 & load_3(a);
+  crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5);
+  crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2);
+  crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7);
+  crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4);
+  crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1);
+  crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6);
+  crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3);
+  crypto_int64 a8 = 2097151 & load_3(a + 21);
+  crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5);
+  crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2);
+  crypto_int64 a11 = (load_4(a + 28) >> 7);
+  crypto_int64 b0 = 2097151 & load_3(b);
+  crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5);
+  crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2);
+  crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7);
+  crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4);
+  crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1);
+  crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6);
+  crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3);
+  crypto_int64 b8 = 2097151 & load_3(b + 21);
+  crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5);
+  crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2);
+  crypto_int64 b11 = (load_4(b + 28) >> 7);
+  crypto_int64 c0 = 2097151 & load_3(c);
+  crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5);
+  crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2);
+  crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7);
+  crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4);
+  crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1);
+  crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6);
+  crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3);
+  crypto_int64 c8 = 2097151 & load_3(c + 21);
+  crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5);
+  crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2);
+  crypto_int64 c11 = (load_4(c + 28) >> 7);
+  crypto_int64 s0;
+  crypto_int64 s1;
+  crypto_int64 s2;
+  crypto_int64 s3;
+  crypto_int64 s4;
+  crypto_int64 s5;
+  crypto_int64 s6;
+  crypto_int64 s7;
+  crypto_int64 s8;
+  crypto_int64 s9;
+  crypto_int64 s10;
+  crypto_int64 s11;
+  crypto_int64 s12;
+  crypto_int64 s13;
+  crypto_int64 s14;
+  crypto_int64 s15;
+  crypto_int64 s16;
+  crypto_int64 s17;
+  crypto_int64 s18;
+  crypto_int64 s19;
+  crypto_int64 s20;
+  crypto_int64 s21;
+  crypto_int64 s22;
+  crypto_int64 s23;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+  crypto_int64 carry10;
+  crypto_int64 carry11;
+  crypto_int64 carry12;
+  crypto_int64 carry13;
+  crypto_int64 carry14;
+  crypto_int64 carry15;
+  crypto_int64 carry16;
+  crypto_int64 carry17;
+  crypto_int64 carry18;
+  crypto_int64 carry19;
+  crypto_int64 carry20;
+  crypto_int64 carry21;
+  crypto_int64 carry22;
+
+  s0 = c0 + a0*b0;
+  s1 = c1 + a0*b1 + a1*b0;
+  s2 = c2 + a0*b2 + a1*b1 + a2*b0;
+  s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
+  s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
+  s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
+  s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
+  s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
+  s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
+  s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
+  s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
+  s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
+  s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
+  s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
+  s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
+  s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
+  s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
+  s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
+  s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
+  s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
+  s20 = a9*b11 + a10*b10 + a11*b9;
+  s21 = a10*b11 + a11*b10;
+  s22 = a11*b11;
+  s23 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
+  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
+  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
+  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
+  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  s23 = 0;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+  s22 = 0;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+  s21 = 0;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+  s20 = 0;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+  s19 = 0;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+  s18 = 0;
+
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+  s17 = 0;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+  s16 = 0;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+  s15 = 0;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+  s14 = 0;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+  s13 = 0;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}

src/ext/ed25519/ref10/sc_reduce.c

@@ -0,0 +1,275 @@
+#include "sc.h"
+#include "crypto_int64.h"
+#include "crypto_uint32.h"
+#include "crypto_uint64.h"
+
+static crypto_uint64 load_3(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  return result;
+}
+
+static crypto_uint64 load_4(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  result |= ((crypto_uint64) in[3]) << 24;
+  return result;
+}
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+void sc_reduce(unsigned char *s)
+{
+  crypto_int64 s0 = 2097151 & load_3(s);
+  crypto_int64 s1 = 2097151 & (load_4(s + 2) >> 5);
+  crypto_int64 s2 = 2097151 & (load_3(s + 5) >> 2);
+  crypto_int64 s3 = 2097151 & (load_4(s + 7) >> 7);
+  crypto_int64 s4 = 2097151 & (load_4(s + 10) >> 4);
+  crypto_int64 s5 = 2097151 & (load_3(s + 13) >> 1);
+  crypto_int64 s6 = 2097151 & (load_4(s + 15) >> 6);
+  crypto_int64 s7 = 2097151 & (load_3(s + 18) >> 3);
+  crypto_int64 s8 = 2097151 & load_3(s + 21);
+  crypto_int64 s9 = 2097151 & (load_4(s + 23) >> 5);
+  crypto_int64 s10 = 2097151 & (load_3(s + 26) >> 2);
+  crypto_int64 s11 = 2097151 & (load_4(s + 28) >> 7);
+  crypto_int64 s12 = 2097151 & (load_4(s + 31) >> 4);
+  crypto_int64 s13 = 2097151 & (load_3(s + 34) >> 1);
+  crypto_int64 s14 = 2097151 & (load_4(s + 36) >> 6);
+  crypto_int64 s15 = 2097151 & (load_3(s + 39) >> 3);
+  crypto_int64 s16 = 2097151 & load_3(s + 42);
+  crypto_int64 s17 = 2097151 & (load_4(s + 44) >> 5);
+  crypto_int64 s18 = 2097151 & (load_3(s + 47) >> 2);
+  crypto_int64 s19 = 2097151 & (load_4(s + 49) >> 7);
+  crypto_int64 s20 = 2097151 & (load_4(s + 52) >> 4);
+  crypto_int64 s21 = 2097151 & (load_3(s + 55) >> 1);
+  crypto_int64 s22 = 2097151 & (load_4(s + 57) >> 6);
+  crypto_int64 s23 = (load_4(s + 60) >> 3);
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+  crypto_int64 carry10;
+  crypto_int64 carry11;
+  crypto_int64 carry12;
+  crypto_int64 carry13;
+  crypto_int64 carry14;
+  crypto_int64 carry15;
+  crypto_int64 carry16;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  s23 = 0;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+  s22 = 0;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+  s21 = 0;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+  s20 = 0;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+  s19 = 0;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+  s18 = 0;
+
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+  s17 = 0;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+  s16 = 0;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+  s15 = 0;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+  s14 = 0;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+  s13 = 0;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}

src/ext/ed25519/ref10/sign.c

@@ -0,0 +1,41 @@
+#include <string.h>
+#include "crypto_sign.h"
+#include "crypto_hash_sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+int crypto_sign(
+  unsigned char *sm,unsigned long long *smlen,
+  const unsigned char *m,unsigned long long mlen,
+  const unsigned char *sk
+)
+{
+  unsigned char pk[32];
+  unsigned char az[64];
+  unsigned char nonce[64];
+  unsigned char hram[64];
+  ge_p3 R;
+
+  memmove(pk,sk + 32,32);
+
+  crypto_hash_sha512(az,sk,32);
+  az[0] &= 248;
+  az[31] &= 63;
+  az[31] |= 64;
+
+  *smlen = mlen + 64;
+  memmove(sm + 64,m,mlen);
+  memmove(sm + 32,az + 32,32);
+  crypto_hash_sha512(nonce,sm + 32,mlen + 32);
+  memmove(sm + 32,pk,32);
+
+  sc_reduce(nonce);
+  ge_scalarmult_base(&R,nonce);
+  ge_p3_tobytes(sm,&R);
+
+  crypto_hash_sha512(hram,sm,mlen + 64);
+  sc_reduce(hram);
+  sc_muladd(sm + 32,hram,az,nonce);
+
+  return 0;
+}

src/ext/ed25519/ref10/sqrtm1.h

@@ -0,0 +1 @@
+-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482

src/ext/ed25519/ref10/sqrtm1.py

@@ -0,0 +1,28 @@
+q = 2**255 - 19
+
+def expmod(b,e,m):
+  if e == 0: return 1
+  t = expmod(b,e/2,m)**2 % m
+  if e & 1: t = (t*b) % m
+  return t
+
+def inv(x):
+  return expmod(x,q-2,q)
+
+def radix255(x):
+  x = x % q
+  if x + x > q: x -= q
+  x = [x,0,0,0,0,0,0,0,0,0]
+  bits = [26,25,26,25,26,25,26,25,26,25]
+  for i in range(9):
+    carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
+    x[i] -= carry * 2**bits[i]
+    x[i + 1] += carry
+  result = ""
+  for i in range(9):
+    result = result+str(x[i])+","
+  result = result+str(x[9])
+  return result
+
+I = expmod(2,(q-1)/4,q)
+print radix255(I)