sxt: added initial reference implementation of ed25519, btw not all stuff done for this;

include/sxt/fe25519.h

@@ -0,0 +1,65 @@
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/fe25519.h
+ */
+
+#ifndef __SXT_FE25519_H__
+#define __SXT_FE25519_H__
+
+#define fe25519              crypto_sign_ed25519_ref_fe25519
+#define fe25519_freeze       crypto_sign_ed25519_ref_fe25519_freeze
+#define fe25519_unpack       crypto_sign_ed25519_ref_fe25519_unpack
+#define fe25519_pack         crypto_sign_ed25519_ref_fe25519_pack
+#define fe25519_iszero       crypto_sign_ed25519_ref_fe25519_iszero
+#define fe25519_iseq_vartime crypto_sign_ed25519_ref_fe25519_iseq_vartime
+#define fe25519_cmov         crypto_sign_ed25519_ref_fe25519_cmov
+#define fe25519_setone       crypto_sign_ed25519_ref_fe25519_setone
+#define fe25519_setzero      crypto_sign_ed25519_ref_fe25519_setzero
+#define fe25519_neg          crypto_sign_ed25519_ref_fe25519_neg
+#define fe25519_getparity    crypto_sign_ed25519_ref_fe25519_getparity
+#define fe25519_add          crypto_sign_ed25519_ref_fe25519_add
+#define fe25519_sub          crypto_sign_ed25519_ref_fe25519_sub
+#define fe25519_mul          crypto_sign_ed25519_ref_fe25519_mul
+#define fe25519_square       crypto_sign_ed25519_ref_fe25519_square
+#define fe25519_invert       crypto_sign_ed25519_ref_fe25519_invert
+#define fe25519_pow2523      crypto_sign_ed25519_ref_fe25519_pow2523
+
+typedef struct {
+  uint32_t v[32];
+} fe25519;
+
+void fe25519_freeze(fe25519 *r);
+
+void fe25519_unpack(fe25519 *r, const unsigned char x[32]);
+
+void fe25519_pack(unsigned char r[32], const fe25519 *x);
+
+int fe25519_iszero(const fe25519 *x);
+
+int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y);
+
+void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b);
+
+void fe25519_setone(fe25519 *r);
+
+void fe25519_setzero(fe25519 *r);
+
+void fe25519_neg(fe25519 *r, const fe25519 *x);
+
+unsigned char fe25519_getparity(const fe25519 *x);
+
+void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y);
+
+void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y);
+
+void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y);
+
+void fe25519_square(fe25519 *r, const fe25519 *x);
+
+void fe25519_invert(fe25519 *r, const fe25519 *x);
+
+void fe25519_pow2523(fe25519 *r, const fe25519 *x);
+
+
+#endif

include/sxt/ge25519.h

@@ -0,0 +1,42 @@
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519.h
+ */
+
+#ifndef __SXT_GE25519_H__
+#define __SXT_GE25519_H__
+
+#include <sxt/fe25519.h>
+#include <sxt/sc25519.h>
+
+#define ge25519                           crypto_sign_ed25519_ref_ge25519
+#define ge25519_base                      crypto_sign_ed25519_ref_ge25519_base
+#define ge25519_unpackneg_vartime         crypto_sign_ed25519_ref_unpackneg_vartime
+#define ge25519_pack                      crypto_sign_ed25519_ref_pack
+#define ge25519_isneutral_vartime         crypto_sign_ed25519_ref_isneutral_vartime
+#define ge25519_double_scalarmult_vartime crypto_sign_ed25519_ref_double_scalarmult_vartime
+#define ge25519_scalarmult_base           crypto_sign_ed25519_ref_scalarmult_base
+
+typedef struct
+{
+  fe25519 x;
+  fe25519 y;
+  fe25519 z;
+  fe25519 t;
+} ge25519;
+
+const ge25519 ge25519_base;
+
+int ge25519_unpackneg_vartime(ge25519 *r, const unsigned char p[32]);
+
+void ge25519_pack(unsigned char r[32], const ge25519 *p);
+
+int ge25519_isneutral_vartime(const ge25519 *p);
+
+void ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const sc25519 *s1, const ge25519 *p2, const sc25519 *s2);
+
+void ge25519_scalarmult_base(ge25519 *r, const sc25519 *s);
+
+
+#endif

include/sxt/sc25519.h

@@ -0,0 +1,72 @@
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/sc25519.h
+ */
+
+#ifndef __SXT_SC25519_H_
+#define __SXT_SC25519_H_
+
+#define sc25519                  crypto_sign_ed25519_ref_sc25519
+#define shortsc25519             crypto_sign_ed25519_ref_shortsc25519
+#define sc25519_from32bytes      crypto_sign_ed25519_ref_sc25519_from32bytes
+#define shortsc25519_from16bytes crypto_sign_ed25519_ref_shortsc25519_from16bytes
+#define sc25519_from64bytes      crypto_sign_ed25519_ref_sc25519_from64bytes
+#define sc25519_from_shortsc     crypto_sign_ed25519_ref_sc25519_from_shortsc
+#define sc25519_to32bytes        crypto_sign_ed25519_ref_sc25519_to32bytes
+#define sc25519_iszero_vartime   crypto_sign_ed25519_ref_sc25519_iszero_vartime
+#define sc25519_isshort_vartime  crypto_sign_ed25519_ref_sc25519_isshort_vartime
+#define sc25519_lt_vartime       crypto_sign_ed25519_ref_sc25519_lt_vartime
+#define sc25519_add              crypto_sign_ed25519_ref_sc25519_add
+#define sc25519_sub_nored        crypto_sign_ed25519_ref_sc25519_sub_nored
+#define sc25519_mul              crypto_sign_ed25519_ref_sc25519_mul
+#define sc25519_mul_shortsc      crypto_sign_ed25519_ref_sc25519_mul_shortsc
+#define sc25519_window3          crypto_sign_ed25519_ref_sc25519_window3
+#define sc25519_window5          crypto_sign_ed25519_ref_sc25519_window5
+#define sc25519_2interleave2     crypto_sign_ed25519_ref_sc25519_2interleave2
+
+typedef struct {
+  uint32_t v[32];
+} sc25519;
+
+typedef struct {
+  uint32_t v[16];
+} shortsc25519;
+
+void sc25519_from32bytes(sc25519 *r, const unsigned char x[32]);
+
+void shortsc25519_from16bytes(shortsc25519 *r, const unsigned char x[16]);
+
+void sc25519_from64bytes(sc25519 *r, const unsigned char x[64]);
+
+void sc25519_from_shortsc(sc25519 *r, const shortsc25519 *x);
+
+void sc25519_to32bytes(unsigned char r[32], const sc25519 *x);
+
+int sc25519_iszero_vartime(const sc25519 *x);
+
+int sc25519_isshort_vartime(const sc25519 *x);
+
+int sc25519_lt_vartime(const sc25519 *x, const sc25519 *y);
+
+void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y);
+
+void sc25519_sub_nored(sc25519 *r, const sc25519 *x, const sc25519 *y);
+
+void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y);
+
+void sc25519_mul_shortsc(sc25519 *r, const sc25519 *x, const shortsc25519 *y);
+
+/* Convert s into a representation of the form \sum_{i=0}^{84}r[i]2^3
+ * with r[i] in {-4,...,3}
+ */
+void sc25519_window3(signed char r[85], const sc25519 *s);
+
+/* Convert s into a representation of the form \sum_{i=0}^{50}r[i]2^5
+ * with r[i] in {-16,...,15}
+ */
+void sc25519_window5(signed char r[51], const sc25519 *s);
+
+void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2);
+
+#endif

sxt/fe25519.c

@@ -0,0 +1,418 @@
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/fe25519.c
+ */
+
+#define WINDOWSIZE 1 /* Should be 1,2, or 4 */
+#define WINDOWMASK ((1<<WINDOWSIZE)-1)
+
+#include <stdint.h>
+#include <sxt/fe25519.h>
+
+static uint32_t equal(uint32_t a,uint32_t b) /* 16-bit inputs */
+{
+  uint32_t x = a ^ b; /* 0: yes; 1..65535: no */
+  x -= 1; /* 4294967295: yes; 0..65534: no */
+  x >>= 31; /* 1: yes; 0: no */
+  return x;
+}
+
+static uint32_t ge(uint32_t a,uint32_t b) /* 16-bit inputs */
+{
+  unsigned int x = a;
+
+  x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */
+  x >>= 31; /* 0: yes; 1: no */
+  x ^= 1; /* 1: yes; 0: no */
+
+  return x;
+}
+
+static uint32_t times19(uint32_t a)
+{
+  return (a << 4) + (a << 1) + a;
+}
+
+static uint32_t times38(uint32_t a)
+{
+  return (a << 5) + (a << 2) + (a << 1);
+}
+
+static void reduce_add_sub(fe25519 *r)
+{
+  uint32_t t;
+  int i,rep;
+
+  for(rep = 0; rep < 4; rep++) {
+    t = r->v[31] >> 7;
+    r->v[31] &= 127;
+    t = times19(t);
+    r->v[0] += t;
+    for(i = 0; i < 31; i++) {
+      t = r->v[i] >> 8;
+      r->v[i+1] += t;
+      r->v[i] &= 255;
+    }
+  }
+}
+
+static void reduce_mul(fe25519 *r)
+{
+  uint32_t t;
+  int i,rep;
+
+  for(rep = 0; rep < 2; rep++) {
+    t = r->v[31] >> 7;
+    r->v[31] &= 127;
+    t = times19(t);
+    r->v[0] += t;
+    for(i = 0; i < 31; i++) {
+      t = r->v[i] >> 8;
+      r->v[i+1] += t;
+      r->v[i] &= 255;
+    }
+  }
+}
+
+/* reduction modulo 2^255-19 */
+void fe25519_freeze(fe25519 *r)
+{
+  int i;
+  uint32_t m = equal(r->v[31],127);
+
+  for (i = 30; i > 0; i--) {
+    m &= equal(r->v[i],255);
+  }
+  m &= ge(r->v[0],237);
+
+  m = -m;
+
+  r->v[31] -= m&127;
+  for (i = 30; i > 0; i--) {
+    r->v[i] -= m&255;
+  }
+  r->v[0] -= m&237;
+}
+
+void fe25519_unpack(fe25519 *r, const unsigned char x[32])
+{
+  int i;
+
+  for (i = 0;i < 32; i++) {
+    r->v[i] = x[i];
+  }
+
+  r->v[31] &= 127;
+}
+
+/* Assumes input x being reduced below 2^255 */
+void fe25519_pack(unsigned char r[32], const fe25519 *x)
+{
+  int i;
+
+  fe25519 y = *x;
+  fe25519_freeze(&y);
+
+  for (i = 0; i < 32; i++) {
+    r[i] = y.v[i];
+  }
+}
+
+int fe25519_iszero(const fe25519 *x)
+{
+  int i;
+  int r;
+
+  fe25519 t = *x;
+  fe25519_freeze(&t);
+
+  r = equal(t.v[0],0);
+  for (i = 1; i < 32; i++) {
+    r &= equal(t.v[i],0);
+  }
+
+  return r;
+}
+
+int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y)
+{
+  int i;
+
+  fe25519 t1 = *x;
+  fe25519 t2 = *y;
+  fe25519_freeze(&t1);
+  fe25519_freeze(&t2);
+
+  for (i = 0; i < 32; i++) {
+    if(t1.v[i] != t2.v[i]) {
+      return 0;
+    }
+  }
+
+  return 1;
+}
+
+void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
+{
+  int i;
+  uint32_t mask = b;
+
+  mask = -mask;
+
+  for (i = 0; i < 32; i++) {
+    r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
+  }
+}
+
+unsigned char fe25519_getparity(const fe25519 *x)
+{
+  fe25519 t = *x;
+  fe25519_freeze(&t);
+
+  return t.v[0] & 1;
+}
+
+void fe25519_setone(fe25519 *r)
+{
+  int i;
+
+  r->v[0] = 1;
+  for (i = 1; i < 32; i++) {
+    r->v[i]=0;
+  }
+}
+
+void fe25519_setzero(fe25519 *r)
+{
+  int i;
+
+  for (i = 0; i < 32; i++) {
+    r->v[i]=0;
+  }
+}
+
+void fe25519_neg(fe25519 *r, const fe25519 *x)
+{
+  fe25519 t;
+  int i;
+
+  for (i = 0; i < 32; i++) {
+    t.v[i]=x->v[i];
+  }
+
+  fe25519_setzero(r);
+  fe25519_sub(r, r, &t);
+}
+
+void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y)
+{
+  int i;
+
+  for (i = 0; i < 32; i++) {
+    r->v[i] = x->v[i] + y->v[i];
+  }
+
+  reduce_add_sub(r);
+}
+
+void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y)
+{
+  int i;
+  uint32_t t[32];
+
+  t[0] = x->v[0] + 0x1da;
+  t[31] = x->v[31] + 0xfe;
+
+  for (i = 1; i < 31; i++) {
+    t[i] = x->v[i] + 0x1fe;
+  }
+
+  for (i = 0; i < 32; i++) {
+    r->v[i] = t[i] - y->v[i];
+  }
+
+  reduce_add_sub(r);
+}
+
+void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y)
+{
+  int i,j;
+  uint32_t t[63];
+
+  for (i = 0; i < 63; i++) {
+    t[i] = 0;
+  }
+
+  for (i = 0; i < 32; i++) {
+    for (j = 0; j < 32; j++) {
+      t[i+j] += x->v[i] * y->v[j];
+    }
+  }
+
+  for (i = 32; i < 63; i++) {
+    r->v[i-32] = t[i-32] + times38(t[i]);
+  }
+  r->v[31] = t[31]; /* result now in r[0]...r[31] */
+
+  reduce_mul(r);
+}
+
+void fe25519_square(fe25519 *r, const fe25519 *x)
+{
+  fe25519_mul(r, x, x);
+}
+
+void fe25519_invert(fe25519 *r, const fe25519 *x)
+{
+  fe25519 z2;
+  fe25519 z9;
+  fe25519 z11;
+  fe25519 z2_5_0;
+  fe25519 z2_10_0;
+  fe25519 z2_20_0;
+  fe25519 z2_50_0;
+  fe25519 z2_100_0;
+  fe25519 t0;
+  fe25519 t1;
+  int i;
+
+  /* 2 */ fe25519_square(&z2, x);
+  /* 4 */ fe25519_square(&t1, &z2);
+  /* 8 */ fe25519_square(&t0, &t1);
+  /* 9 */ fe25519_mul(&z9, &t0, x);
+  /* 11 */ fe25519_mul(&z11, &z9, &z2);
+  /* 22 */ fe25519_square(&t0, &z11);
+  /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0, &t0, &z9);
+
+  /* 2^6 - 2^1 */ fe25519_square(&t0, &z2_5_0);
+  /* 2^7 - 2^2 */ fe25519_square(&t1, &t0);
+  /* 2^8 - 2^3 */ fe25519_square(&t0, &t1);
+  /* 2^9 - 2^4 */ fe25519_square(&t1, &t0);
+  /* 2^10 - 2^5 */ fe25519_square(&t0, &t1);
+  /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0, &t0, &z2_5_0);
+
+  /* 2^11 - 2^1 */ fe25519_square(&t0, &z2_10_0);
+  /* 2^12 - 2^2 */ fe25519_square(&t1, &t0);
+  /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) {
+    fe25519_square(&t0, &t1);
+    fe25519_square(&t1, &t0);
+  }
+  /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0, &t1, &z2_10_0);
+
+  /* 2^21 - 2^1 */ fe25519_square(&t0, &z2_20_0);
+  /* 2^22 - 2^2 */ fe25519_square(&t1, &t0);
+  /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) {
+    fe25519_square(&t0, &t1);
+    fe25519_square(&t1,&t0);
+  }
+  /* 2^40 - 2^0 */ fe25519_mul(&t0, &t1, &z2_20_0);
+
+  /* 2^41 - 2^1 */ fe25519_square(&t1, &t0);
+  /* 2^42 - 2^2 */ fe25519_square(&t0, &t1);
+  /* 2^50 - 2^10 */ for (i = 2; i < 10;i += 2) {
+    fe25519_square(&t1, &t0);
+    fe25519_square(&t0, &t1);
+  }
+  /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0);
+
+  /* 2^51 - 2^1 */ fe25519_square(&t0, &z2_50_0);
+  /* 2^52 - 2^2 */ fe25519_square(&t1, &t0);
+  /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) {
+    fe25519_square(&t0, &t1);
+    fe25519_square(&t1,&t0);
+  }
+  /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0, &t1, &z2_50_0);
+
+  /* 2^101 - 2^1 */ fe25519_square(&t1, &z2_100_0);
+  /* 2^102 - 2^2 */ fe25519_square(&t0, &t1);
+  /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) {
+    fe25519_square(&t1, &t0);
+    fe25519_square(&t0,&t1);
+  }
+  /* 2^200 - 2^0 */ fe25519_mul(&t1, &t0, &z2_100_0);
+
+  /* 2^201 - 2^1 */ fe25519_square(&t0, &t1);
+  /* 2^202 - 2^2 */ fe25519_square(&t1, &t0);
+  /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) {
+    fe25519_square(&t0, &t1);
+    fe25519_square(&t1,&t0);
+  }
+  /* 2^250 - 2^0 */ fe25519_mul(&t0, &t1, &z2_50_0);
+
+  /* 2^251 - 2^1 */ fe25519_square(&t1, &t0);
+  /* 2^252 - 2^2 */ fe25519_square(&t0, &t1);
+  /* 2^253 - 2^3 */ fe25519_square(&t1, &t0);
+  /* 2^254 - 2^4 */ fe25519_square(&t0, &t1);
+  /* 2^255 - 2^5 */ fe25519_square(&t1, &t0);
+  /* 2^255 - 21 */  fe25519_mul(r, &t1, &z11);
+}
+
+void fe25519_pow2523(fe25519 *r, const fe25519 *x)
+{
+  fe25519 z2;
+  fe25519 z9;
+  fe25519 z11;
+  fe25519 z2_5_0;
+  fe25519 z2_10_0;
+  fe25519 z2_20_0;
+  fe25519 z2_50_0;
+  fe25519 z2_100_0;
+  fe25519 t;
+  int i;
+
+  /* 2 */ fe25519_square(&z2, x);
+  /* 4 */ fe25519_square(&t, &z2);
+  /* 8 */ fe25519_square(&t, &t);
+  /* 9 */ fe25519_mul(&z9, &t, x);
+  /* 11 */ fe25519_mul(&z11, &z9, &z2);
+  /* 22 */ fe25519_square(&t, &z11);
+  /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0, &t, &z9);
+
+  /* 2^6 - 2^1 */ fe25519_square(&t, &z2_5_0);
+  /* 2^10 - 2^5 */ for (i = 1; i < 5; i++) {
+    fe25519_square(&t,&t);
+  }
+  /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0, &t, &z2_5_0);
+
+  /* 2^11 - 2^1 */ fe25519_square(&t, &z2_10_0);
+  /* 2^20 - 2^10 */ for (i = 1; i < 10; i++) {
+    fe25519_square(&t, &t);
+  }
+  /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0, &t, &z2_10_0);
+
+  /* 2^21 - 2^1 */ fe25519_square(&t, &z2_20_0);
+  /* 2^40 - 2^20 */ for (i = 1; i < 20; i++) {
+    fe25519_square(&t,&t);
+  }
+  /* 2^40 - 2^0 */ fe25519_mul(&t, &t, &z2_20_0);
+
+  /* 2^41 - 2^1 */ fe25519_square(&t, &t);
+  /* 2^50 - 2^10 */ for (i = 1; i < 10; i++) {
+    fe25519_square(&t,&t);
+  }
+  /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0, &t, &z2_10_0);
+
+  /* 2^51 - 2^1 */ fe25519_square(&t, &z2_50_0);
+  /* 2^100 - 2^50 */ for (i = 1; i < 50; i++) {
+    fe25519_square(&t, &t);
+  }
+  /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0, &t, &z2_50_0);
+
+  /* 2^101 - 2^1 */ fe25519_square(&t, &z2_100_0);
+  /* 2^200 - 2^100 */ for (i = 1; i < 100; i++) {
+    fe25519_square(&t, &t);
+  }
+  /* 2^200 - 2^0 */ fe25519_mul(&t, &t, &z2_100_0);
+
+  /* 2^201 - 2^1 */ fe25519_square(&t, &t);
+  /* 2^250 - 2^50 */ for (i = 1; i < 50; i++) {
+    fe25519_square(&t, &t);
+  }
+  /* 2^250 - 2^0 */ fe25519_mul(&t, &t, &z2_50_0);
+
+  /* 2^251 - 2^1 */ fe25519_square(&t, &t);
+  /* 2^252 - 2^2 */ fe25519_square(&t, &t);
+  /* 2^252 - 3 */ fe25519_mul(r, &t, x);
+}
+

sxt/ge25519.c

@@ -0,0 +1,367 @@
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519.c
+ */
+
+#include <stdint.h>
+
+#include <sxt/fe25519.h>
+#include <sxt/sc25519.h>
+#include <sxt/ge25519.h>
+
+/*
+ * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2
+ * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555
+ * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);
+ */
+
+/* d */
+static const fe25519 ge25519_ecd = {
+  {0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75,
+   0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00,
+   0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C,
+   0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}
+};
+
+/* 2*d */
+static const fe25519 ge25519_ec2d = {
+  {0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB,
+   0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00,
+   0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19,
+   0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}
+};
+
+/* sqrt(-1) */
+static const fe25519 ge25519_sqrtm1 = {
+  {0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4,
+   0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F,
+   0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B,
+   0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}
+};
+
+#define ge25519_p3 ge25519
+
+typedef struct {
+  fe25519 x;
+  fe25519 z;
+  fe25519 y;
+  fe25519 t;
+} ge25519_p1p1;
+
+typedef struct {
+  fe25519 x;
+  fe25519 y;
+  fe25519 z;
+} ge25519_p2;
+
+typedef struct {
+  fe25519 x;
+  fe25519 y;
+} ge25519_aff;
+
+
+/* Packed coordinates of the base point */
+const ge25519 ge25519_base = {
+  {{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9,
+    0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
+    0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0,
+    0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}},
+  {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
+    0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
+    0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
+    0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}},
+  {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+  {{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D,
+    0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
+    0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66,
+    0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}
+};
+
+/* Multiples of the base point in affine representation */
+static const ge25519_aff ge25519_base_multiples_affine[425] = {
+#include "ge25519_base.data"
+};
+
+static void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
+{
+  fe25519_mul(&r->x, &p->x, &p->t);
+  fe25519_mul(&r->y, &p->y, &p->z);
+  fe25519_mul(&r->z, &p->z, &p->t);
+}
+
+static void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
+{
+  p1p1_to_p2((ge25519_p2 *)r, p);
+  fe25519_mul(&r->t, &p->x, &p->y);
+}
+
+static void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)
+{
+  fe25519 a,b,t1,t2,c,d,e,f,g,h,qt;
+  fe25519_mul(&qt, &q->x, &q->y);
+  fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)*(Y2-X2) */
+  fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */
+  fe25519_sub(&t1, &q->y, &q->x);
+  fe25519_add(&t2, &q->y, &q->x);
+  fe25519_mul(&a, &a, &t1);
+  fe25519_mul(&b, &b, &t2);
+  fe25519_sub(&e, &b, &a); /* E = B-A */
+  fe25519_add(&h, &b, &a); /* H = B+A */
+  fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */
+  fe25519_mul(&c, &c, &ge25519_ec2d);
+  fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */
+  fe25519_sub(&f, &d, &c); /* F = D-C */
+  fe25519_add(&g, &d, &c); /* G = D+C */
+  fe25519_mul(&r->x, &e, &f);
+  fe25519_mul(&r->y, &h, &g);
+  fe25519_mul(&r->z, &g, &f);
+  fe25519_mul(&r->t, &e, &h);
+}
+
+static void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
+{
+  fe25519 a, b, c, d, t;
+
+  fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)*(Y2-X2) */
+  fe25519_sub(&t, &q->y, &q->x);
+  fe25519_mul(&a, &a, &t);
+  fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */
+  fe25519_add(&t, &q->x, &q->y);
+  fe25519_mul(&b, &b, &t);
+  fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */
+  fe25519_mul(&c, &c, &ge25519_ec2d);
+  fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */
+  fe25519_add(&d, &d, &d);
+  fe25519_sub(&r->x, &b, &a); /* E = B-A */
+  fe25519_sub(&r->t, &d, &c); /* F = D-C */
+  fe25519_add(&r->z, &d, &c); /* G = D+C */
+  fe25519_add(&r->y, &b, &a); /* H = B+A */
+}
+
+/* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
+static void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
+{
+  fe25519 a,b,c,d;
+  fe25519_square(&a, &p->x);
+  fe25519_square(&b, &p->y);
+  fe25519_square(&c, &p->z);
+  fe25519_add(&c, &c, &c);
+  fe25519_neg(&d, &a);
+
+  fe25519_add(&r->x, &p->x, &p->y);
+  fe25519_square(&r->x, &r->x);
+  fe25519_sub(&r->x, &r->x, &a);
+  fe25519_sub(&r->x, &r->x, &b);
+  fe25519_add(&r->z, &d, &b);
+  fe25519_sub(&r->t, &r->z, &c);
+  fe25519_sub(&r->y, &d, &b);
+}
+
+/* Constant-time version of: if(b) r = p */
+static void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)
+{
+  fe25519_cmov(&r->x, &p->x, b);
+  fe25519_cmov(&r->y, &p->y, b);
+}
+
+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 */
+  uint32_t 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 choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
+{
+  /* constant time */
+  fe25519 v;
+
+  *t = ge25519_base_multiples_affine[5 * pos + 0];
+
+  cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 1],
+           equal(b,1) | equal(b,-1));
+  cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 2],
+           equal(b,2) | equal(b,-2));
+  cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 3],
+           equal(b,3) | equal(b,-3));
+  cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 4],
+           equal(b,-4));
+
+  fe25519_neg(&v, &t->x);
+  fe25519_cmov(&t->x, &v, negative(b));
+}
+
+static void setneutral(ge25519 *r)
+{
+  fe25519_setzero(&r->x);
+  fe25519_setone(&r->y);
+  fe25519_setone(&r->z);
+  fe25519_setzero(&r->t);
+}
+
+/* ********************************************************************
+ *                    EXPORTED FUNCTIONS
+ ******************************************************************** */
+
+/* return 0 on success, -1 otherwise */
+int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
+{
+  unsigned char par;
+
+  fe25519 t, chk, num, den, den2, den4, den6;
+  fe25519_setone(&r->z);
+  par = p[31] >> 7;
+  fe25519_unpack(&r->y, p);
+  fe25519_square(&num, &r->y); /* x = y^2 */
+  fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */
+  fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
+  fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */
+
+  /* Computation of sqrt(num/den) */
+  /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
+  fe25519_square(&den2, &den);
+  fe25519_square(&den4, &den2);
+  fe25519_mul(&den6, &den4, &den2);
+  fe25519_mul(&t, &den6, &num);
+  fe25519_mul(&t, &t, &den);
+
+  fe25519_pow2523(&t, &t);
+  /* 2. computation of r->x = t * num * den^3 */
+  fe25519_mul(&t, &t, &num);
+  fe25519_mul(&t, &t, &den);
+  fe25519_mul(&t, &t, &den);
+  fe25519_mul(&r->x, &t, &den);
+
+  /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */
+  fe25519_square(&chk, &r->x);
+  fe25519_mul(&chk, &chk, &den);
+  if (!fe25519_iseq_vartime(&chk, &num)) {
+    fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
+  }
+
+  /* 4. Now we have one of the two square roots, except if input was not a square */
+  fe25519_square(&chk, &r->x);
+  fe25519_mul(&chk, &chk, &den);
+  if (!fe25519_iseq_vartime(&chk, &num)) {
+    return -1;
+  }
+
+  /* 5. Choose the desired square root according to parity: */
+  if(fe25519_getparity(&r->x) != (1-par)) {
+    fe25519_neg(&r->x, &r->x);
+  }
+
+  fe25519_mul(&r->t, &r->x, &r->y);
+
+  return 0;
+}
+
+void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
+{
+  fe25519 tx, ty, zi;
+
+  fe25519_invert(&zi, &p->z);
+  fe25519_mul(&tx, &p->x, &zi);
+  fe25519_mul(&ty, &p->y, &zi);
+  fe25519_pack(r, &ty);
+
+  r[31] ^= fe25519_getparity(&tx) << 7;
+}
+
+int ge25519_isneutral_vartime(const ge25519_p3 *p)
+{
+  int ret = 1;
+
+  if (!fe25519_iszero(&p->x)) {
+    ret = 0;
+  }
+
+  if (!fe25519_iseq_vartime(&p->y, &p->z)) {
+    ret = 0;
+  }
+
+  return ret;
+}
+
+/* computes [s1]p1 + [s2]p2 */
+void ge25519_double_scalarmult_vartime(ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)
+{
+  ge25519_p1p1 tp1p1;
+  ge25519_p3 pre[16];
+  unsigned char b[127];
+  int i;
+
+  /* precomputation                                                        s2 s1 */
+  setneutral(pre);                                                      /* 00 00 */
+  pre[1] = *p1;                                                         /* 00 01 */
+  dbl_p1p1(&tp1p1,(ge25519_p2 *)p1);      p1p1_to_p3( &pre[2], &tp1p1); /* 00 10 */
+  add_p1p1(&tp1p1,&pre[1], &pre[2]);      p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */
+  pre[4] = *p2;                                                         /* 01 00 */
+  add_p1p1(&tp1p1,&pre[1], &pre[4]);      p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */
+  add_p1p1(&tp1p1,&pre[2], &pre[4]);      p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */
+  add_p1p1(&tp1p1,&pre[3], &pre[4]);      p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */
+  dbl_p1p1(&tp1p1,(ge25519_p2 *)p2);      p1p1_to_p3( &pre[8], &tp1p1); /* 10 00 */
+  add_p1p1(&tp1p1,&pre[1], &pre[8]);      p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */
+  dbl_p1p1(&tp1p1,(ge25519_p2 *)&pre[5]); p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */
+  add_p1p1(&tp1p1,&pre[3], &pre[8]);      p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
+  add_p1p1(&tp1p1,&pre[4], &pre[8]);      p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
+  add_p1p1(&tp1p1,&pre[1],&pre[12]);      p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
+  add_p1p1(&tp1p1,&pre[2],&pre[12]);      p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
+  add_p1p1(&tp1p1,&pre[3],&pre[12]);      p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */
+
+  sc25519_2interleave2(b,s1,s2);
+
+  /* scalar multiplication */
+  *r = pre[b[126]];
+
+  for (i = 125; i >= 0; i--) {
+    dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
+    p1p1_to_p2((ge25519_p2 *) r, &tp1p1);
+    dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
+    if(b[i] != 0) {
+      p1p1_to_p3(r, &tp1p1);
+      add_p1p1(&tp1p1, r, &pre[b[i]]);
+    }
+    if (i != 0) {
+      p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
+    } else {
+      p1p1_to_p3(r, &tp1p1);
+    }
+  }
+}
+
+void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
+{
+  signed char b[85];
+  int i;
+  ge25519_aff t;
+
+  sc25519_window3(b,s);
+
+  choose_t((ge25519_aff *)r, 0, b[0]);
+  fe25519_setone(&r->z);
+  fe25519_mul(&r->t, &r->x, &r->y);
+  for (i = 1; i < 85; i++) {
+    choose_t(&t, (unsigned long long) i, b[i]);
+    ge25519_mixadd2(r, &t);
+  }
+}

sxt/ge25519_base.data

@@ -0,0 +1,858 @@
+/* $OpenBSD: ge25519_base.data,v 1.3 2013/12/09 11:03:45 markus Exp $ */
+
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519_base.data
+ */
+
+{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}},
+{{{0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21}} ,
+ {{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}}},
+{{{0x0e, 0xce, 0x43, 0x28, 0x4e, 0xa1, 0xc5, 0x83, 0x5f, 0xa4, 0xd7, 0x15, 0x45, 0x8e, 0x0d, 0x08, 0xac, 0xe7, 0x33, 0x18, 0x7d, 0x3b, 0x04, 0x3d, 0x6c, 0x04, 0x5a, 0x9f, 0x4c, 0x38, 0xab, 0x36}} ,
+ {{0xc9, 0xa3, 0xf8, 0x6a, 0xae, 0x46, 0x5f, 0x0e, 0x56, 0x51, 0x38, 0x64, 0x51, 0x0f, 0x39, 0x97, 0x56, 0x1f, 0xa2, 0xc9, 0xe8, 0x5e, 0xa2, 0x1d, 0xc2, 0x29, 0x23, 0x09, 0xf3, 0xcd, 0x60, 0x22}}},
+{{{0x5c, 0xe2, 0xf8, 0xd3, 0x5f, 0x48, 0x62, 0xac, 0x86, 0x48, 0x62, 0x81, 0x19, 0x98, 0x43, 0x63, 0x3a, 0xc8, 0xda, 0x3e, 0x74, 0xae, 0xf4, 0x1f, 0x49, 0x8f, 0x92, 0x22, 0x4a, 0x9c, 0xae, 0x67}} ,
+ {{0xd4, 0xb4, 0xf5, 0x78, 0x48, 0x68, 0xc3, 0x02, 0x04, 0x03, 0x24, 0x67, 0x17, 0xec, 0x16, 0x9f, 0xf7, 0x9e, 0x26, 0x60, 0x8e, 0xa1, 0x26, 0xa1, 0xab, 0x69, 0xee, 0x77, 0xd1, 0xb1, 0x67, 0x12}}},
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+ {{0x65, 0x9c, 0x5d, 0xf0, 0x37, 0x04, 0xf0, 0x34, 0x69, 0x2a, 0xf0, 0xa5, 0x64, 0xca, 0xde, 0x2b, 0x5b, 0x15, 0x10, 0xd2, 0xab, 0x06, 0xdd, 0xc4, 0xb0, 0xb6, 0x5b, 0xc1, 0x17, 0xdf, 0x8f, 0x02}}},
+{{{0xbd, 0x59, 0x3d, 0xbf, 0x5c, 0x31, 0x44, 0x2c, 0x32, 0x94, 0x04, 0x60, 0x84, 0x0f, 0xad, 0x00, 0xb6, 0x8f, 0xc9, 0x1d, 0xcc, 0x5c, 0xa2, 0x49, 0x0e, 0x50, 0x91, 0x08, 0x9a, 0x43, 0x55, 0x05}} ,
+ {{0x5d, 0x93, 0x55, 0xdf, 0x9b, 0x12, 0x19, 0xec, 0x93, 0x85, 0x42, 0x9e, 0x66, 0x0f, 0x9d, 0xaf, 0x99, 0xaf, 0x26, 0x89, 0xbc, 0x61, 0xfd, 0xff, 0xce, 0x4b, 0xf4, 0x33, 0x95, 0xc9, 0x35, 0x58}}},
+{{{0x12, 0x55, 0xf9, 0xda, 0xcb, 0x44, 0xa7, 0xdc, 0x57, 0xe2, 0xf9, 0x9a, 0xe6, 0x07, 0x23, 0x60, 0x54, 0xa7, 0x39, 0xa5, 0x9b, 0x84, 0x56, 0x6e, 0xaa, 0x8b, 0x8f, 0xb0, 0x2c, 0x87, 0xaf, 0x67}} ,
+ {{0x00, 0xa9, 0x4c, 0xb2, 0x12, 0xf8, 0x32, 0xa8, 0x7a, 0x00, 0x4b, 0x49, 0x32, 0xba, 0x1f, 0x5d, 0x44, 0x8e, 0x44, 0x7a, 0xdc, 0x11, 0xfb, 0x39, 0x08, 0x57, 0x87, 0xa5, 0x12, 0x42, 0x93, 0x0e}}},
+{{{0x17, 0xb4, 0xae, 0x72, 0x59, 0xd0, 0xaa, 0xa8, 0x16, 0x8b, 0x63, 0x11, 0xb3, 0x43, 0x04, 0xda, 0x0c, 0xa8, 0xb7, 0x68, 0xdd, 0x4e, 0x54, 0xe7, 0xaf, 0x5d, 0x5d, 0x05, 0x76, 0x36, 0xec, 0x0d}} ,
+ {{0x6d, 0x7c, 0x82, 0x32, 0x38, 0x55, 0x57, 0x74, 0x5b, 0x7d, 0xc3, 0xc4, 0xfb, 0x06, 0x29, 0xf0, 0x13, 0x55, 0x54, 0xc6, 0xa7, 0xdc, 0x4c, 0x9f, 0x98, 0x49, 0x20, 0xa8, 0xc3, 0x8d, 0xfa, 0x48}}},
+{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}},
+{{{0x87, 0x47, 0x9d, 0xe9, 0x25, 0xd5, 0xe3, 0x47, 0x78, 0xdf, 0x85, 0xa7, 0x85, 0x5e, 0x7a, 0x4c, 0x5f, 0x79, 0x1a, 0xf3, 0xa2, 0xb2, 0x28, 0xa0, 0x9c, 0xdd, 0x30, 0x40, 0xd4, 0x38, 0xbd, 0x28}} ,
+ {{0xfc, 0xbb, 0xd5, 0x78, 0x6d, 0x1d, 0xd4, 0x99, 0xb4, 0xaa, 0x44, 0x44, 0x7a, 0x1b, 0xd8, 0xfe, 0xb4, 0x99, 0xb9, 0xcc, 0xe7, 0xc4, 0xd3, 0x3a, 0x73, 0x83, 0x41, 0x5c, 0x40, 0xd7, 0x2d, 0x55}}},
+{{{0x26, 0xe1, 0x7b, 0x5f, 0xe5, 0xdc, 0x3f, 0x7d, 0xa1, 0xa7, 0x26, 0x44, 0x22, 0x23, 0xc0, 0x8f, 0x7d, 0xf1, 0xb5, 0x11, 0x47, 0x7b, 0x19, 0xd4, 0x75, 0x6f, 0x1e, 0xa5, 0x27, 0xfe, 0xc8, 0x0e}} ,
+ {{0xd3, 0x11, 0x3d, 0xab, 0xef, 0x2c, 0xed, 0xb1, 0x3d, 0x7c, 0x32, 0x81, 0x6b, 0xfe, 0xf8, 0x1c, 0x3c, 0x7b, 0xc0, 0x61, 0xdf, 0xb8, 0x75, 0x76, 0x7f, 0xaa, 0xd8, 0x93, 0xaf, 0x3d, 0xe8, 0x3d}}},
+{{{0xfd, 0x5b, 0x4e, 0x8d, 0xb6, 0x7e, 0x82, 0x9b, 0xef, 0xce, 0x04, 0x69, 0x51, 0x52, 0xff, 0xef, 0xa0, 0x52, 0xb5, 0x79, 0x17, 0x5e, 0x2f, 0xde, 0xd6, 0x3c, 0x2d, 0xa0, 0x43, 0xb4, 0x0b, 0x19}} ,
+ {{0xc0, 0x61, 0x48, 0x48, 0x17, 0xf4, 0x9e, 0x18, 0x51, 0x2d, 0xea, 0x2f, 0xf2, 0xf2, 0xe0, 0xa3, 0x14, 0xb7, 0x8b, 0x3a, 0x30, 0xf5, 0x81, 0xc1, 0x5d, 0x71, 0x39, 0x62, 0x55, 0x1f, 0x60, 0x5a}}},
+{{{0xe5, 0x89, 0x8a, 0x76, 0x6c, 0xdb, 0x4d, 0x0a, 0x5b, 0x72, 0x9d, 0x59, 0x6e, 0x63, 0x63, 0x18, 0x7c, 0xe3, 0xfa, 0xe2, 0xdb, 0xa1, 0x8d, 0xf4, 0xa5, 0xd7, 0x16, 0xb2, 0xd0, 0xb3, 0x3f, 0x39}} ,
+ {{0xce, 0x60, 0x09, 0x6c, 0xf5, 0x76, 0x17, 0x24, 0x80, 0x3a, 0x96, 0xc7, 0x94, 0x2e, 0xf7, 0x6b, 0xef, 0xb5, 0x05, 0x96, 0xef, 0xd3, 0x7b, 0x51, 0xda, 0x05, 0x44, 0x67, 0xbc, 0x07, 0x21, 0x4e}}},
+{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}},
+{{{0xe9, 0x73, 0x6f, 0x21, 0xb9, 0xde, 0x22, 0x7d, 0xeb, 0x97, 0x31, 0x10, 0xa3, 0xea, 0xe1, 0xc6, 0x37, 0xeb, 0x8f, 0x43, 0x58, 0xde, 0x41, 0x64, 0x0e, 0x3e, 0x07, 0x99, 0x3d, 0xf1, 0xdf, 0x1e}} ,
+ {{0xf8, 0xad, 0x43, 0xc2, 0x17, 0x06, 0xe2, 0xe4, 0xa9, 0x86, 0xcd, 0x18, 0xd7, 0x78, 0xc8, 0x74, 0x66, 0xd2, 0x09, 0x18, 0xa5, 0xf1, 0xca, 0xa6, 0x62, 0x92, 0xc1, 0xcb, 0x00, 0xeb, 0x42, 0x2e}}},
+{{{0x7b, 0x34, 0x24, 0x4c, 0xcf, 0x38, 0xe5, 0x6c, 0x0a, 0x01, 0x2c, 0x22, 0x0b, 0x24, 0x38, 0xad, 0x24, 0x7e, 0x19, 0xf0, 0x6c, 0xf9, 0x31, 0xf4, 0x35, 0x11, 0xf6, 0x46, 0x33, 0x3a, 0x23, 0x59}} ,
+ {{0x20, 0x0b, 0xa1, 0x08, 0x19, 0xad, 0x39, 0x54, 0xea, 0x3e, 0x23, 0x09, 0xb6, 0xe2, 0xd2, 0xbc, 0x4d, 0xfc, 0x9c, 0xf0, 0x13, 0x16, 0x22, 0x3f, 0xb9, 0xd2, 0x11, 0x86, 0x90, 0x55, 0xce, 0x3c}}},
+{{{0xc4, 0x0b, 0x4b, 0x62, 0x99, 0x37, 0x84, 0x3f, 0x74, 0xa2, 0xf9, 0xce, 0xe2, 0x0b, 0x0f, 0x2a, 0x3d, 0xa3, 0xe3, 0xdb, 0x5a, 0x9d, 0x93, 0xcc, 0xa5, 0xef, 0x82, 0x91, 0x1d, 0xe6, 0x6c, 0x68}} ,
+ {{0xa3, 0x64, 0x17, 0x9b, 0x8b, 0xc8, 0x3a, 0x61, 0xe6, 0x9d, 0xc6, 0xed, 0x7b, 0x03, 0x52, 0x26, 0x9d, 0x3a, 0xb3, 0x13, 0xcc, 0x8a, 0xfd, 0x2c, 0x1a, 0x1d, 0xed, 0x13, 0xd0, 0x55, 0x57, 0x0e}}},
+{{{0x1a, 0xea, 0xbf, 0xfd, 0x4a, 0x3c, 0x8e, 0xec, 0x29, 0x7e, 0x77, 0x77, 0x12, 0x99, 0xd7, 0x84, 0xf9, 0x55, 0x7f, 0xf1, 0x8b, 0xb4, 0xd2, 0x95, 0xa3, 0x8d, 0xf0, 0x8a, 0xa7, 0xeb, 0x82, 0x4b}} ,
+ {{0x2c, 0x28, 0xf4, 0x3a, 0xf6, 0xde, 0x0a, 0xe0, 0x41, 0x44, 0x23, 0xf8, 0x3f, 0x03, 0x64, 0x9f, 0xc3, 0x55, 0x4c, 0xc6, 0xc1, 0x94, 0x1c, 0x24, 0x5d, 0x5f, 0x92, 0x45, 0x96, 0x57, 0x37, 0x14}}},
+{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}},
+{{{0xc1, 0xcd, 0x90, 0x66, 0xb9, 0x76, 0xa0, 0x5b, 0xa5, 0x85, 0x75, 0x23, 0xf9, 0x89, 0xa5, 0x82, 0xb2, 0x6f, 0xb1, 0xeb, 0xc4, 0x69, 0x6f, 0x18, 0x5a, 0xed, 0x94, 0x3d, 0x9d, 0xd9, 0x2c, 0x1a}} ,
+ {{0x35, 0xb0, 0xe6, 0x73, 0x06, 0xb7, 0x37, 0xe0, 0xf8, 0xb0, 0x22, 0xe8, 0xd2, 0xed, 0x0b, 0xef, 0xe6, 0xc6, 0x5a, 0x99, 0x9e, 0x1a, 0x9f, 0x04, 0x97, 0xe4, 0x4d, 0x0b, 0xbe, 0xba, 0x44, 0x40}}},
+{{{0xc1, 0x56, 0x96, 0x91, 0x5f, 0x1f, 0xbb, 0x54, 0x6f, 0x88, 0x89, 0x0a, 0xb2, 0xd6, 0x41, 0x42, 0x6a, 0x82, 0xee, 0x14, 0xaa, 0x76, 0x30, 0x65, 0x0f, 0x67, 0x39, 0xa6, 0x51, 0x7c, 0x49, 0x24}} ,
+ {{0x35, 0xa3, 0x78, 0xd1, 0x11, 0x0f, 0x75, 0xd3, 0x70, 0x46, 0xdb, 0x20, 0x51, 0xcb, 0x92, 0x80, 0x54, 0x10, 0x74, 0x36, 0x86, 0xa9, 0xd7, 0xa3, 0x08, 0x78, 0xf1, 0x01, 0x29, 0xf8, 0x80, 0x3b}}},
+{{{0xdb, 0xa7, 0x9d, 0x9d, 0xbf, 0xa0, 0xcc, 0xed, 0x53, 0xa2, 0xa2, 0x19, 0x39, 0x48, 0x83, 0x19, 0x37, 0x58, 0xd1, 0x04, 0x28, 0x40, 0xf7, 0x8a, 0xc2, 0x08, 0xb7, 0xa5, 0x42, 0xcf, 0x53, 0x4c}} ,
+ {{0xa7, 0xbb, 0xf6, 0x8e, 0xad, 0xdd, 0xf7, 0x90, 0xdd, 0x5f, 0x93, 0x89, 0xae, 0x04, 0x37, 0xe6, 0x9a, 0xb7, 0xe8, 0xc0, 0xdf, 0x16, 0x2a, 0xbf, 0xc4, 0x3a, 0x3c, 0x41, 0xd5, 0x89, 0x72, 0x5a}}},
+{{{0x1f, 0x96, 0xff, 0x34, 0x2c, 0x13, 0x21, 0xcb, 0x0a, 0x89, 0x85, 0xbe, 0xb3, 0x70, 0x9e, 0x1e, 0xde, 0x97, 0xaf, 0x96, 0x30, 0xf7, 0x48, 0x89, 0x40, 0x8d, 0x07, 0xf1, 0x25, 0xf0, 0x30, 0x58}} ,
+ {{0x1e, 0xd4, 0x93, 0x57, 0xe2, 0x17, 0xe7, 0x9d, 0xab, 0x3c, 0x55, 0x03, 0x82, 0x2f, 0x2b, 0xdb, 0x56, 0x1e, 0x30, 0x2e, 0x24, 0x47, 0x6e, 0xe6, 0xff, 0x33, 0x24, 0x2c, 0x75, 0x51, 0xd4, 0x67}}},
+{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}},
+{{{0x2b, 0x06, 0xd9, 0xa1, 0x5d, 0xe1, 0xf4, 0xd1, 0x1e, 0x3c, 0x9a, 0xc6, 0x29, 0x2b, 0x13, 0x13, 0x78, 0xc0, 0xd8, 0x16, 0x17, 0x2d, 0x9e, 0xa9, 0xc9, 0x79, 0x57, 0xab, 0x24, 0x91, 0x92, 0x19}} ,
+ {{0x69, 0xfb, 0xa1, 0x9c, 0xa6, 0x75, 0x49, 0x7d, 0x60, 0x73, 0x40, 0x42, 0xc4, 0x13, 0x0a, 0x95, 0x79, 0x1e, 0x04, 0x83, 0x94, 0x99, 0x9b, 0x1e, 0x0c, 0xe8, 0x1f, 0x54, 0xef, 0xcb, 0xc0, 0x52}}},
+{{{0x14, 0x89, 0x73, 0xa1, 0x37, 0x87, 0x6a, 0x7a, 0xcf, 0x1d, 0xd9, 0x2e, 0x1a, 0x67, 0xed, 0x74, 0xc0, 0xf0, 0x9c, 0x33, 0xdd, 0xdf, 0x08, 0xbf, 0x7b, 0xd1, 0x66, 0xda, 0xe6, 0xc9, 0x49, 0x08}} ,
+ {{0xe9, 0xdd, 0x5e, 0x55, 0xb0, 0x0a, 0xde, 0x21, 0x4c, 0x5a, 0x2e, 0xd4, 0x80, 0x3a, 0x57, 0x92, 0x7a, 0xf1, 0xc4, 0x2c, 0x40, 0xaf, 0x2f, 0xc9, 0x92, 0x03, 0xe5, 0x5a, 0xbc, 0xdc, 0xf4, 0x09}}},
+{{{0xf3, 0xe1, 0x2b, 0x7c, 0x05, 0x86, 0x80, 0x93, 0x4a, 0xad, 0xb4, 0x8f, 0x7e, 0x99, 0x0c, 0xfd, 0xcd, 0xef, 0xd1, 0xff, 0x2c, 0x69, 0x34, 0x13, 0x41, 0x64, 0xcf, 0x3b, 0xd0, 0x90, 0x09, 0x1e}} ,
+ {{0x9d, 0x45, 0xd6, 0x80, 0xe6, 0x45, 0xaa, 0xf4, 0x15, 0xaa, 0x5c, 0x34, 0x87, 0x99, 0xa2, 0x8c, 0x26, 0x84, 0x62, 0x7d, 0xb6, 0x29, 0xc0, 0x52, 0xea, 0xf5, 0x81, 0x18, 0x0f, 0x35, 0xa9, 0x0e}}},
+{{{0xe7, 0x20, 0x72, 0x7c, 0x6d, 0x94, 0x5f, 0x52, 0x44, 0x54, 0xe3, 0xf1, 0xb2, 0xb0, 0x36, 0x46, 0x0f, 0xae, 0x92, 0xe8, 0x70, 0x9d, 0x6e, 0x79, 0xb1, 0xad, 0x37, 0xa9, 0x5f, 0xc0, 0xde, 0x03}} ,
+ {{0x15, 0x55, 0x37, 0xc6, 0x1c, 0x27, 0x1c, 0x6d, 0x14, 0x4f, 0xca, 0xa4, 0xc4, 0x88, 0x25, 0x46, 0x39, 0xfc, 0x5a, 0xe5, 0xfe, 0x29, 0x11, 0x69, 0xf5, 0x72, 0x84, 0x4d, 0x78, 0x9f, 0x94, 0x15}}},
+{{{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
+ {{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}},
+{{{0xec, 0xd3, 0xff, 0x57, 0x0b, 0xb0, 0xb2, 0xdc, 0xf8, 0x4f, 0xe2, 0x12, 0xd5, 0x36, 0xbe, 0x6b, 0x09, 0x43, 0x6d, 0xa3, 0x4d, 0x90, 0x2d, 0xb8, 0x74, 0xe8, 0x71, 0x45, 0x19, 0x8b, 0x0c, 0x6a}} ,
+ {{0xb8, 0x42, 0x1c, 0x03, 0xad, 0x2c, 0x03, 0x8e, 0xac, 0xd7, 0x98, 0x29, 0x13, 0xc6, 0x02, 0x29, 0xb5, 0xd4, 0xe7, 0xcf, 0xcc, 0x8b, 0x83, 0xec, 0x35, 0xc7, 0x9c, 0x74, 0xb7, 0xad, 0x85, 0x5f}}},
+{{{0x78, 0x84, 0xe1, 0x56, 0x45, 0x69, 0x68, 0x5a, 0x4f, 0xb8, 0xb1, 0x29, 0xff, 0x33, 0x03, 0x31, 0xb7, 0xcb, 0x96, 0x25, 0xe6, 0xe6, 0x41, 0x98, 0x1a, 0xbb, 0x03, 0x56, 0xf2, 0xb2, 0x91, 0x34}} ,
+ {{0x2c, 0x6c, 0xf7, 0x66, 0xa4, 0x62, 0x6b, 0x39, 0xb3, 0xba, 0x65, 0xd3, 0x1c, 0xf8, 0x11, 0xaa, 0xbe, 0xdc, 0x80, 0x59, 0x87, 0xf5, 0x7b, 0xe5, 0xe3, 0xb3, 0x3e, 0x39, 0xda, 0xbe, 0x88, 0x09}}},
+{{{0x8b, 0xf1, 0xa0, 0xf5, 0xdc, 0x29, 0xb4, 0xe2, 0x07, 0xc6, 0x7a, 0x00, 0xd0, 0x89, 0x17, 0x51, 0xd4, 0xbb, 0xd4, 0x22, 0xea, 0x7e, 0x7d, 0x7c, 0x24, 0xea, 0xf2, 0xe8, 0x22, 0x12, 0x95, 0x06}} ,
+ {{0xda, 0x7c, 0xa4, 0x0c, 0xf4, 0xba, 0x6e, 0xe1, 0x89, 0xb5, 0x59, 0xca, 0xf1, 0xc0, 0x29, 0x36, 0x09, 0x44, 0xe2, 0x7f, 0xd1, 0x63, 0x15, 0x99, 0xea, 0x25, 0xcf, 0x0c, 0x9d, 0xc0, 0x44, 0x6f}}},
+{{{0x1d, 0x86, 0x4e, 0xcf, 0xf7, 0x37, 0x10, 0x25, 0x8f, 0x12, 0xfb, 0x19, 0xfb, 0xe0, 0xed, 0x10, 0xc8, 0xe2, 0xf5, 0x75, 0xb1, 0x33, 0xc0, 0x96, 0x0d, 0xfb, 0x15, 0x6c, 0x0d, 0x07, 0x5f, 0x05}} ,
+ {{0x69, 0x3e, 0x47, 0x97, 0x2c, 0xaf, 0x52, 0x7c, 0x78, 0x83, 0xad, 0x1b, 0x39, 0x82, 0x2f, 0x02, 0x6f, 0x47, 0xdb, 0x2a, 0xb0, 0xe1, 0x91, 0x99, 0x55, 0xb8, 0x99, 0x3a, 0xa0, 0x44, 0x11, 0x51}}}

sxt/sc25519.c

@@ -0,0 +1,374 @@
+/*
+ * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
+ * Peter Schwabe, Bo-Yin Yang.
+ * Copied from supercop-20130419/crypto_sign/ed25519/ref/sc25519.c
+ */
+
+#include <stdint.h>
+
+#include <sxt/sc25519.h>
+
+/*Arithmetic modulo the group order m = 2^252 +  27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 */
+
+static const uint32_t m[32] = {
+  0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58,
+  0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14,
+  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
+};
+
+static const uint32_t mu[33] = {
+  0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED,
+  0xA7, 0x29, 0x63, 0x08, 0x5D, 0x21, 0x06, 0x21,
+  0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
+  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F
+};
+
+static uint32_t lt(uint32_t a,uint32_t b) /* 16-bit inputs */
+{
+  unsigned int x = a;
+
+  x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */
+  x >>= 31; /* 0: no; 1: yes */
+
+  return x;
+}
+
+/* Reduce coefficients of r before calling reduce_add_sub */
+static void reduce_add_sub(sc25519 *r)
+{
+  uint32_t pb = 0;
+  uint32_t b;
+  uint32_t mask;
+  int i;
+  unsigned char t[32];
+
+  for (i = 0; i < 32; i++) {
+    pb += m[i];
+    b = lt(r->v[i],pb);
+    t[i] = r->v[i]-pb+(b<<8);
+    pb = b;
+  }
+  mask = b - 1;
+  for (i = 0; i < 32; i++) {
+    r->v[i] ^= mask & (r->v[i] ^ t[i]);
+  }
+}
+
+/* Reduce coefficients of x before calling barrett_reduce */
+static void barrett_reduce(sc25519 *r, const uint32_t x[64])
+{
+  /* See HAC, Alg. 14.42 */
+  int i,j;
+  uint32_t q2[66];
+  uint32_t *q3 = q2 + 33;
+  uint32_t r1[33];
+  uint32_t r2[33];
+  uint32_t carry;
+  uint32_t pb = 0;
+  uint32_t b;
+
+  for (i = 0; i < 66; i++) {
+    q2[i] = 0;
+  }
+  for (i = 0; i < 33; i++) {
+    r2[i] = 0;
+  }
+
+  for (i = 0; i < 33; i++) {
+    for (j = 0; j < 33; j++) {
+      if (i + j >= 31) {
+        q2[i+j] += mu[i]*x[j+31];
+      }
+    }
+  }
+
+  carry = q2[31] >> 8;
+  q2[32] += carry;
+  carry = q2[32] >> 8;
+  q2[33] += carry;
+
+  for (i = 0; i < 33; i++) {
+    r1[i] = x[i];
+  }
+
+  for (i = 0; i < 32; i++) {
+    for (j = 0; j < 33; j++) {
+      if (i + j < 33) {
+        r2[i+j] += m[i]*q3[j];
+      }
+    }
+  }
+
+  for (i = 0; i < 32; i++) {
+    carry = r2[i] >> 8;
+    r2[i+1] += carry;
+    r2[i] &= 0xff;
+  }
+
+  for (i = 0; i < 32; i++) {
+    pb += r2[i];
+    b = lt(r1[i],pb);
+    r->v[i] = r1[i]-pb+(b<<8);
+    pb = b;
+  }
+
+  /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3
+   * If so: Handle  it here!
+   */
+
+  reduce_add_sub(r);
+  reduce_add_sub(r);
+}
+
+void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
+{
+  int i;
+  uint32_t t[64];
+
+  for (i = 0; i < 32; i++) {
+    t[i] = x[i];
+  }
+  for (i = 32; i < 64; i++) {
+    t[i] = 0;
+  }
+
+  barrett_reduce(r, t);
+}
+
+void shortsc25519_from16bytes(shortsc25519 *r, const unsigned char x[16])
+{
+  int i;
+
+  for (i = 0; i < 16; i++) {
+    r->v[i] = x[i];
+  }
+}
+
+void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
+{
+  int i;
+  uint32_t t[64];
+
+  for (i = 0; i < 64; i++) {
+    t[i] = x[i];
+  }
+
+  barrett_reduce(r, t);
+}
+
+void sc25519_from_shortsc(sc25519 *r, const shortsc25519 *x)
+{
+  int i;
+
+  for (i = 0; i < 16; i++) {
+    r->v[i] = x->v[i];
+  }
+  for (i = 0; i < 16; i++) {
+    r->v[16+i] = 0;
+  }
+}
+
+void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
+{
+  int i;
+
+  for (i = 0; i < 32; i++) {
+    r[i] = x->v[i];
+  }
+}
+
+int sc25519_iszero_vartime(const sc25519 *x)
+{
+  int i;
+
+  for (i = 0; i < 32; i++) {
+    if(x->v[i] != 0) {
+      return 0;
+    }
+  }
+
+  return 1;
+}
+
+int sc25519_isshort_vartime(const sc25519 *x)
+{
+  int i;
+
+  for (i = 31; i > 15; i--) {
+    if (x->v[i] != 0) {
+      return 0;
+    }
+  }
+
+  return 1;
+}
+
+int sc25519_lt_vartime(const sc25519 *x, const sc25519 *y)
+{
+  int i;
+
+  for (i = 31; i >= 0; i--) {
+    if (x->v[i] < y->v[i]) {
+      return 1;
+    }
+    if (x->v[i] > y->v[i]) {
+      return 0;
+    }
+  }
+
+  return 0;
+}
+
+void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y)
+{
+  int i, carry;
+
+  for (i = 0; i < 32; i++) {
+    r->v[i] = x->v[i] + y->v[i];
+  }
+
+  for (i = 0;i < 31; i++) {
+    carry = r->v[i] >> 8;
+    r->v[i+1] += carry;
+    r->v[i] &= 0xff;
+  }
+
+  reduce_add_sub(r);
+}
+
+void sc25519_sub_nored(sc25519 *r, const sc25519 *x, const sc25519 *y)
+{
+  uint32_t b = 0;
+  uint32_t t;
+  int i;
+
+  for (i = 0; i < 32; i++) {
+    t = x->v[i] - y->v[i] - b;
+    r->v[i] = t & 255;
+    b = (t >> 8) & 1;
+  }
+}
+
+void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
+{
+  int i,j,carry;
+  uint32_t t[64];
+
+  for (i = 0; i < 64; i++) {
+    t[i] = 0;
+  }
+
+  for (i = 0; i < 32; i++) {
+    for (j = 0; j < 32; j++) {
+      t[i+j] += x->v[i] * y->v[j];
+    }
+  }
+
+  /* Reduce coefficients */
+  for (i = 0; i < 63; i++) {
+    carry = t[i] >> 8;
+    t[i+1] += carry;
+    t[i] &= 0xff;
+  }
+
+  barrett_reduce(r, t);
+}
+
+void sc25519_mul_shortsc(sc25519 *r, const sc25519 *x, const shortsc25519 *y)
+{
+  sc25519 t;
+  sc25519_from_shortsc(&t, y);
+  sc25519_mul(r, x, &t);
+}
+
+void sc25519_window3(signed char r[85], const sc25519 *s)
+{
+  char carry;
+  int i;
+
+  for (i = 0; i < 10; i++) {
+    r[8*i+0]  =  s->v[3*i+0]       & 7;
+    r[8*i+1]  = (s->v[3*i+0] >> 3) & 7;
+    r[8*i+2]  = (s->v[3*i+0] >> 6) & 7;
+    r[8*i+2] ^= (s->v[3*i+1] << 2) & 7;
+    r[8*i+3]  = (s->v[3*i+1] >> 1) & 7;
+    r[8*i+4]  = (s->v[3*i+1] >> 4) & 7;
+    r[8*i+5]  = (s->v[3*i+1] >> 7) & 7;
+    r[8*i+5] ^= (s->v[3*i+2] << 1) & 7;
+    r[8*i+6]  = (s->v[3*i+2] >> 2) & 7;
+    r[8*i+7]  = (s->v[3*i+2] >> 5) & 7;
+  }
+  r[8*i+0]  =  s->v[3*i+0]       & 7;
+  r[8*i+1]  = (s->v[3*i+0] >> 3) & 7;
+  r[8*i+2]  = (s->v[3*i+0] >> 6) & 7;
+  r[8*i+2] ^= (s->v[3*i+1] << 2) & 7;
+  r[8*i+3]  = (s->v[3*i+1] >> 1) & 7;
+  r[8*i+4]  = (s->v[3*i+1] >> 4) & 7;
+
+  /* Making it signed */
+  carry = 0;
+  for (i = 0; i < 84; i++) {
+    r[i] += carry;
+    r[i+1] += r[i] >> 3;
+    r[i] &= 7;
+    carry = r[i] >> 2;
+    r[i] -= carry<<3;
+  }
+
+  r[84] += carry;
+}
+
+void sc25519_window5(signed char r[51], const sc25519 *s)
+{
+  char carry;
+  int i;
+
+  for (i = 0; i < 6; i++) {
+    r[8*i+0]  =  s->v[5*i+0]       & 31;
+    r[8*i+1]  = (s->v[5*i+0] >> 5) & 31;
+    r[8*i+1] ^= (s->v[5*i+1] << 3) & 31;
+    r[8*i+2]  = (s->v[5*i+1] >> 2) & 31;
+    r[8*i+3]  = (s->v[5*i+1] >> 7) & 31;
+    r[8*i+3] ^= (s->v[5*i+2] << 1) & 31;
+    r[8*i+4]  = (s->v[5*i+2] >> 4) & 31;
+    r[8*i+4] ^= (s->v[5*i+3] << 4) & 31;
+    r[8*i+5]  = (s->v[5*i+3] >> 1) & 31;
+    r[8*i+6]  = (s->v[5*i+3] >> 6) & 31;
+    r[8*i+6] ^= (s->v[5*i+4] << 2) & 31;
+    r[8*i+7]  = (s->v[5*i+4] >> 3) & 31;
+  }
+  r[8*i+0]  =  s->v[5*i+0]       & 31;
+  r[8*i+1]  = (s->v[5*i+0] >> 5) & 31;
+  r[8*i+1] ^= (s->v[5*i+1] << 3) & 31;
+  r[8*i+2]  = (s->v[5*i+1] >> 2) & 31;
+
+  /* Making it signed */
+  carry = 0;
+  for (i = 0; i < 50; i++) {
+    r[i] += carry;
+    r[i+1] += r[i] >> 5;
+    r[i] &= 31;
+    carry = r[i] >> 4;
+    r[i] -= carry<<5;
+  }
+
+  r[50] += carry;
+}
+
+void sc25519_2interleave2(unsigned char r[127],
+                          const sc25519 *s1,
+                          const sc25519 *s2)
+{
+  int i;
+
+  for (i = 0; i < 31; i++) {
+    r[4*i]   = ( s1->v[i]       & 3) ^ (( s2->v[i]       & 3) << 2);
+    r[4*i+1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2);
+    r[4*i+2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2);
+    r[4*i+3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2);
+  }
+  r[124] = ( s1->v[31]       & 3) ^ (( s2->v[31]       & 3) << 2);
+  r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2);
+  r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2);
+}