upstream: update OpenSSH's Ed25519 code to the last version of SUPERCOP

(20221122) and change the import approach to the same one we use for
Streamlined NTRUPrime: use a shell script to extract the bits we need from
SUPERCOP, make some minor adjustments and squish them all into a single file.

ok tb@ tobhe@

OpenBSD-Commit-ID: 1bc0fd624cb6af440905b8ba74ac7c03311b8e3b

1 files changed, 1967 insertions, 81 deletions

diff --git a/ed25519.c b/ed25519.c
index 767ec24d..0e167ae1 100644
--- a/ed25519.c
+++ b/ed25519.c
@@ -1,52 +1,1935 @@
-/* $OpenBSD: ed25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */
+/*  $OpenBSD: ed25519.c,v 1.4 2023/01/15 23:05:32 djm Exp $ */
 
 /*
- * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
- * Peter Schwabe, Bo-Yin Yang.
- * Copied from supercop-20130419/crypto_sign/ed25519/ref/ed25519.c
+ * Public Domain, Authors:
+ * - Daniel J. Bernstein
+ * - Niels Duif
+ * - Tanja Lange
+ * - lead: Peter Schwabe
+ * - Bo-Yin Yang
  */
 
 #include "includes.h"
+
+#include <string.h>
+
 #include "crypto_api.h"
 
-#include "ge25519.h"
+#define int8 crypto_int8
+#define uint8 crypto_uint8
+#define int16 crypto_int16
+#define uint16 crypto_uint16
+#define int32 crypto_int32
+#define uint32 crypto_uint32
+#define int64 crypto_int64
+#define uint64 crypto_uint64
+
+/* from supercop-20221122/crypto_verify/32/ref/verify.c */
 
-static void get_hram(unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground, unsigned long long smlen)
+static int crypto_verify_32(const unsigned char *x,const unsigned char *y)
 {
-  unsigned long long i;
+  unsigned int differentbits = 0;
+#define F(i) differentbits |= x[i] ^ y[i];
+  F(0)
+  F(1)
+  F(2)
+  F(3)
+  F(4)
+  F(5)
+  F(6)
+  F(7)
+  F(8)
+  F(9)
+  F(10)
+  F(11)
+  F(12)
+  F(13)
+  F(14)
+  F(15)
+  F(16)
+  F(17)
+  F(18)
+  F(19)
+  F(20)
+  F(21)
+  F(22)
+  F(23)
+  F(24)
+  F(25)
+  F(26)
+  F(27)
+  F(28)
+  F(29)
+  F(30)
+  F(31)
+  return (1 & ((differentbits - 1) >> 8)) - 1;
+}
+/* from supercop-20221122/crypto_sign/ed25519/ref/fe25519.h */
+#ifndef FE25519_H
+#define FE25519_H
+
 
-  for (i =  0;i < 32;++i)    playground[i] = sm[i];
-  for (i = 32;i < 64;++i)    playground[i] = pk[i-32];
-  for (i = 64;i < smlen;++i) playground[i] = sm[i];
+#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
 
-  crypto_hash_sha512(hram,playground,smlen);
+typedef struct
+{
+  crypto_uint32 v[32];
 }
+fe25519;
 
+static void fe25519_freeze(fe25519 *r);
 
-int crypto_sign_ed25519_keypair(
-    unsigned char *pk,
-    unsigned char *sk
-    )
+static void fe25519_unpack(fe25519 *r, const unsigned char x[32]);
+
+static void fe25519_pack(unsigned char r[32], const fe25519 *x);
+
+static int fe25519_iszero(const fe25519 *x);
+
+static int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y);
+
+static void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b);
+
+static void fe25519_setone(fe25519 *r);
+
+static void fe25519_setzero(fe25519 *r);
+
+static void fe25519_neg(fe25519 *r, const fe25519 *x);
+
+unsigned char fe25519_getparity(const fe25519 *x);
+
+static void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y);
+
+static void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y);
+
+static void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y);
+
+static void fe25519_square(fe25519 *r, const fe25519 *x);
+
+static void fe25519_invert(fe25519 *r, const fe25519 *x);
+
+static void fe25519_pow2523(fe25519 *r, const fe25519 *x);
+
+#endif
+/* from supercop-20221122/crypto_sign/ed25519/ref/fe25519.c */
+#define WINDOWSIZE 1 /* Should be 1,2, or 4 */
+#define WINDOWMASK ((1<<WINDOWSIZE)-1)
+
+
+static crypto_uint32 fe25519_equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
+{
+  crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */
+  x -= 1; /* 4294967295: yes; 0..65534: no */
+  x >>= 31; /* 1: yes; 0: no */
+  return x;
+}
+
+static crypto_uint32 ge(crypto_uint32 a,crypto_uint32 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 crypto_uint32 times19(crypto_uint32 a)
+{
+  return (a << 4) + (a << 1) + a;
+}
+
+static crypto_uint32 times38(crypto_uint32 a)
+{
+  return (a << 5) + (a << 2) + (a << 1);
+}
+
+static void fe25519_reduce_add_sub(fe25519 *r)
 {
+  crypto_uint32 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)
+{
+  crypto_uint32 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 */
+static void fe25519_freeze(fe25519 *r)
+{
+  int i;
+  crypto_uint32 m = fe25519_equal(r->v[31],127);
+  for(i=30;i>0;i--)
+    m &= fe25519_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;
+}
+
+static 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 */
+static 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];
+}
+
+static int fe25519_iszero(const fe25519 *x)
+{
+  int i;
+  int r;
+  fe25519 t = *x;
+  fe25519_freeze(&t);
+  r = fe25519_equal(t.v[0],0);
+  for(i=1;i<32;i++)
+    r &= fe25519_equal(t.v[i],0);
+  return r;
+}
+
+static 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;
+}
+
+static void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
+{
+  int i;
+  crypto_uint32 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;
+}
+
+static void fe25519_setone(fe25519 *r)
+{
+  int i;
+  r->v[0] = 1;
+  for(i=1;i<32;i++) r->v[i]=0;
+}
+
+static void fe25519_setzero(fe25519 *r)
+{
+  int i;
+  for(i=0;i<32;i++) r->v[i]=0;
+}
+
+static 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);
+}
+
+static 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];
+  fe25519_reduce_add_sub(r);
+}
+
+static void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y)
+{
+  int i;
+  crypto_uint32 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];
+  fe25519_reduce_add_sub(r);
+}
+
+static void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y)
+{
+  int i,j;
+  crypto_uint32 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);
+}
+
+static void fe25519_square(fe25519 *r, const fe25519 *x)
+{
+  fe25519_mul(r, x, x);
+}
+
+static 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);
+}
+
+static 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);
+}
+/* from supercop-20221122/crypto_sign/ed25519/ref/sc25519.h */
+#ifndef SC25519_H
+#define 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 sc25519_from64bytes      crypto_sign_ed25519_ref_sc25519_from64bytes
+#define sc25519_to32bytes        crypto_sign_ed25519_ref_sc25519_to32bytes
+#define sc25519_add              crypto_sign_ed25519_ref_sc25519_add
+#define sc25519_mul              crypto_sign_ed25519_ref_sc25519_mul
+#define sc25519_window3          crypto_sign_ed25519_ref_sc25519_window3
+#define sc25519_2interleave2     crypto_sign_ed25519_ref_sc25519_2interleave2
+
+typedef struct
+{
+  crypto_uint32 v[32];
+}
+sc25519;
+
+typedef struct
+{
+  crypto_uint32 v[16];
+}
+shortsc25519;
+
+static void sc25519_from32bytes(sc25519 *r, const unsigned char x[32]);
+
+
+static void sc25519_from64bytes(sc25519 *r, const unsigned char x[64]);
+
+
+static void sc25519_to32bytes(unsigned char r[32], const sc25519 *x);
+
+
+
+
+static void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y);
+
+
+static void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y);
+
+
+/* Convert s into a representation of the form \sum_{i=0}^{84}r[i]2^3
+ * with r[i] in {-4,...,3}
+ */
+static 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}
+ */
+
+static void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2);
+
+#endif
+/* from supercop-20221122/crypto_sign/ed25519/ref/sc25519.c */
+
+/*Arithmetic modulo the group order m = 2^252 +  27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989 */
+
+static const crypto_uint32 sc25519_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 crypto_uint32 sc25519_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 crypto_uint32 lt(crypto_uint32 a,crypto_uint32 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 sc25519_reduce_add_sub */
+static void sc25519_reduce_add_sub(sc25519 *r)
+{
+  crypto_uint32 pb = 0;
+  crypto_uint32 b;
+  crypto_uint32 mask;
+  int i;
+  unsigned char t[32];
+
+  for(i=0;i<32;i++)
+  {
+    pb += sc25519_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 crypto_uint32 x[64])
+{
+  /* See HAC, Alg. 14.42 */
+  int i,j;
+  crypto_uint32 q2[66];
+  crypto_uint32 *q3 = q2 + 33;
+  crypto_uint32 r1[33];
+  crypto_uint32 r2[33];
+  crypto_uint32 carry;
+  crypto_uint32 pb = 0;
+  crypto_uint32 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] += sc25519_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] += sc25519_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!
+   */
+
+  sc25519_reduce_add_sub(r);
+  sc25519_reduce_add_sub(r);
+}
+
+static void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
+{
+  int i;
+  crypto_uint32 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);
+}
+
+
+static void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
+{
+  int i;
+  crypto_uint32 t[64];
+  for(i=0;i<64;i++) t[i] = x[i];
+  barrett_reduce(r, t);
+}
+
+
+static void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
+{
+  int i;
+  for(i=0;i<32;i++) r[i] = x->v[i];
+}
+
+
+
+
+static 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;
+  }
+  sc25519_reduce_add_sub(r);
+}
+
+
+static void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
+{
+  int i,j,carry;
+  crypto_uint32 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);
+}
+
+
+static 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;
+}
+
+
+static 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);
+}
+/* from supercop-20221122/crypto_sign/ed25519/ref/ge25519.h */
+#ifndef GE25519_H
+#define GE25519_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]);
+
+static void ge25519_pack(unsigned char r[32], const ge25519 *p);
+
+int ge25519_isneutral_vartime(const ge25519 *p);
+
+static void ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const sc25519 *s1, const ge25519 *p2, const sc25519 *s2);
+
+static void ge25519_scalarmult_base(ge25519 *r, const sc25519 *s);
+
+#endif
+/* from supercop-20221122/crypto_sign/ed25519/ref/ge25519.c */
+
+/*
+ * 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] = {
+{{{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}}},
+{{{0x70, 0xf8, 0xc9, 0xc4, 0x57, 0xa6, 0x3a, 0x49, 0x47, 0x15, 0xce, 0x93, 0xc1, 0x9e, 0x73, 0x1a, 0xf9, 0x20, 0x35, 0x7a, 0xb8, 0xd4, 0x25, 0x83, 0x46, 0xf1, 0xcf, 0x56, 0xdb, 0xa8, 0x3d, 0x20}} ,
+ {{0x2f, 0x11, 0x32, 0xca, 0x61, 0xab, 0x38, 0xdf, 0xf0, 0x0f, 0x2f, 0xea, 0x32, 0x28, 0xf2, 0x4c, 0x6c, 0x71, 0xd5, 0x80, 0x85, 0xb8, 0x0e, 0x47, 0xe1, 0x95, 0x15, 0xcb, 0x27, 0xe8, 0xd0, 0x47}}},
+{{{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}}},
+{{{0xc8, 0x84, 0xa5, 0x08, 0xbc, 0xfd, 0x87, 0x3b, 0x99, 0x8b, 0x69, 0x80, 0x7b, 0xc6, 0x3a, 0xeb, 0x93, 0xcf, 0x4e, 0xf8, 0x5c, 0x2d, 0x86, 0x42, 0xb6, 0x71, 0xd7, 0x97, 0x5f, 0xe1, 0x42, 0x67}} ,
+ {{0xb4, 0xb9, 0x37, 0xfc, 0xa9, 0x5b, 0x2f, 0x1e, 0x93, 0xe4, 0x1e, 0x62, 0xfc, 0x3c, 0x78, 0x81, 0x8f, 0xf3, 0x8a, 0x66, 0x09, 0x6f, 0xad, 0x6e, 0x79, 0x73, 0xe5, 0xc9, 0x00, 0x06, 0xd3, 0x21}}},
+{{{0xf8, 0xf9, 0x28, 0x6c, 0x6d, 0x59, 0xb2, 0x59, 0x74, 0x23, 0xbf, 0xe7, 0x33, 0x8d, 0x57, 0x09, 0x91, 0x9c, 0x24, 0x08, 0x15, 0x2b, 0xe2, 0xb8, 0xee, 0x3a, 0xe5, 0x27, 0x06, 0x86, 0xa4, 0x23}} ,
+ {{0xeb, 0x27, 0x67, 0xc1, 0x37, 0xab, 0x7a, 0xd8, 0x27, 0x9c, 0x07, 0x8e, 0xff, 0x11, 0x6a, 0xb0, 0x78, 0x6e, 0xad, 0x3a, 0x2e, 0x0f, 0x98, 0x9f, 0x72, 0xc3, 0x7f, 0x82, 0xf2, 0x96, 0x96, 0x70}}},
+{{{0x81, 0x6b, 0x88, 0xe8, 0x1e, 0xc7, 0x77, 0x96, 0x0e, 0xa1, 0xa9, 0x52, 0xe0, 0xd8, 0x0e, 0x61, 0x9e, 0x79, 0x2d, 0x95, 0x9c, 0x8d, 0x96, 0xe0, 0x06, 0x40, 0x5d, 0x87, 0x28, 0x5f, 0x98, 0x70}} ,
+ {{0xf1, 0x79, 0x7b, 0xed, 0x4f, 0x44, 0xb2, 0xe7, 0x08, 0x0d, 0xc2, 0x08, 0x12, 0xd2, 0x9f, 0xdf, 0xcd, 0x93, 0x20, 0x8a, 0xcf, 0x33, 0xca, 0x6d, 0x89, 0xb9, 0x77, 0xc8, 0x93, 0x1b, 0x4e, 0x60}}},
+{{{0x26, 0x4f, 0x7e, 0x97, 0xf6, 0x40, 0xdd, 0x4f, 0xfc, 0x52, 0x78, 0xf9, 0x90, 0x31, 0x03, 0xe6, 0x7d, 0x56, 0x39, 0x0b, 0x1d, 0x56, 0x82, 0x85, 0xf9, 0x1a, 0x42, 0x17, 0x69, 0x6c, 0xcf, 0x39}} ,
+ {{0x69, 0xd2, 0x06, 0x3a, 0x4f, 0x39, 0x2d, 0xf9, 0x38, 0x40, 0x8c, 0x4c, 0xe7, 0x05, 0x12, 0xb4, 0x78, 0x8b, 0xf8, 0xc0, 0xec, 0x93, 0xde, 0x7a, 0x6b, 0xce, 0x2c, 0xe1, 0x0e, 0xa9, 0x34, 0x44}}},
+{{{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}}},
+{{{0x0b, 0xa4, 0x3c, 0xb0, 0x0f, 0x7a, 0x51, 0xf1, 0x78, 0xd6, 0xd9, 0x6a, 0xfd, 0x46, 0xe8, 0xb8, 0xa8, 0x79, 0x1d, 0x87, 0xf9, 0x90, 0xf2, 0x9c, 0x13, 0x29, 0xf8, 0x0b, 0x20, 0x64, 0xfa, 0x05}} ,
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