xref: /freebsd/crypto/openssh/ed25519.c (revision bdd1243df58e60e85101c09001d9812a789b6bc4)

/*  $OpenBSD: ed25519.c,v 1.4 2023/01/15 23:05:32 djm Exp $ */

/*
 * 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"

#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 int crypto_verify_32(const unsigned char *x,const unsigned char *y)
{
  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


#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
{
  crypto_uint32 v[32];
}
fe25519;

static void fe25519_freeze(fe25519 *r);

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}} ,
 {{0x26, 0x09, 0xda, 0x17, 0xaf, 0x95, 0xd6, 0xfb, 0x6a, 0x19, 0x0d, 0x6e, 0x5e, 0x12, 0xf1, 0x99, 0x4c, 0xaa, 0xa8, 0x6f, 0x79, 0x86, 0xf4, 0x72, 0x28, 0x00, 0x26, 0xf9, 0xea, 0x9e, 0x19, 0x3d}}},
{{{0x87, 0xdd, 0xcf, 0xf0, 0x5b, 0x49, 0xa2, 0x5d, 0x40, 0x7a, 0x23, 0x26, 0xa4, 0x7a, 0x83, 0x8a, 0xb7, 0x8b, 0xd2, 0x1a, 0xbf, 0xea, 0x02, 0x24, 0x08, 0x5f, 0x7b, 0xa9, 0xb1, 0xbe, 0x9d, 0x37}} ,
 {{0xfc, 0x86, 0x4b, 0x08, 0xee, 0xe7, 0xa0, 0xfd, 0x21, 0x45, 0x09, 0x34, 0xc1, 0x61, 0x32, 0x23, 0xfc, 0x9b, 0x55, 0x48, 0x53, 0x99, 0xf7, 0x63, 0xd0, 0x99, 0xce, 0x01, 0xe0, 0x9f, 0xeb, 0x28}}},
{{{0x47, 0xfc, 0xab, 0x5a, 0x17, 0xf0, 0x85, 0x56, 0x3a, 0x30, 0x86, 0x20, 0x28, 0x4b, 0x8e, 0x44, 0x74, 0x3a, 0x6e, 0x02, 0xf1, 0x32, 0x8f, 0x9f, 0x3f, 0x08, 0x35, 0xe9, 0xca, 0x16, 0x5f, 0x6e}} ,
 {{0x1c, 0x59, 0x1c, 0x65, 0x5d, 0x34, 0xa4, 0x09, 0xcd, 0x13, 0x9c, 0x70, 0x7d, 0xb1, 0x2a, 0xc5, 0x88, 0xaf, 0x0b, 0x60, 0xc7, 0x9f, 0x34, 0x8d, 0xd6, 0xb7, 0x7f, 0xea, 0x78, 0x65, 0x8d, 0x77}}},
{{{0x56, 0xa5, 0xc2, 0x0c, 0xdd, 0xbc, 0xb8, 0x20, 0x6d, 0x57, 0x61, 0xb5, 0xfb, 0x78, 0xb5, 0xd4, 0x49, 0x54, 0x90, 0x26, 0xc1, 0xcb, 0xe9, 0xe6, 0xbf, 0xec, 0x1d, 0x4e, 0xed, 0x07, 0x7e, 0x5e}} ,
 {{0xc7, 0xf6, 0x6c, 0x56, 0x31, 0x20, 0x14, 0x0e, 0xa8, 0xd9, 0x27, 0xc1, 0x9a, 0x3d, 0x1b, 0x7d, 0x0e, 0x26, 0xd3, 0x81, 0xaa, 0xeb, 0xf5, 0x6b, 0x79, 0x02, 0xf1, 0x51, 0x5c, 0x75, 0x55, 0x0f}}},
{{{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}}},
{{{0x0a, 0x34, 0xcd, 0x82, 0x3c, 0x33, 0x09, 0x54, 0xd2, 0x61, 0x39, 0x30, 0x9b, 0xfd, 0xef, 0x21, 0x26, 0xd4, 0x70, 0xfa, 0xee, 0xf9, 0x31, 0x33, 0x73, 0x84, 0xd0, 0xb3, 0x81, 0xbf, 0xec, 0x2e}} ,
 {{0xe8, 0x93, 0x8b, 0x00, 0x64, 0xf7, 0x9c, 0xb8, 0x74, 0xe0, 0xe6, 0x49, 0x48, 0x4d, 0x4d, 0x48, 0xb6, 0x19, 0xa1, 0x40, 0xb7, 0xd9, 0x32, 0x41, 0x7c, 0x82, 0x37, 0xa1, 0x2d, 0xdc, 0xd2, 0x54}}},
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{{{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}}}
};

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 */
  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 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;
}

static 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 */
static 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);
  }
}

static 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);
  }
}
/* from supercop-20221122/crypto_sign/ed25519/ref/keypair.c */

int crypto_sign_ed25519_keypair(unsigned char *pk,unsigned char *sk)
{
  unsigned char az[64];
  sc25519 scsk;
  ge25519 gepk;

  randombytes(sk,32);
  crypto_hash_sha512(az,sk,32);
  az[0] &= 248;
  az[31] &= 127;
  az[31] |= 64;

  sc25519_from32bytes(&scsk,az);

  ge25519_scalarmult_base(&gepk, &scsk);
  ge25519_pack(pk, &gepk);
  memmove(sk + 32,pk,32);
  return 0;
}
/* from supercop-20221122/crypto_sign/ed25519/ref/sign.c */

int crypto_sign_ed25519(
    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];
  sc25519 sck, scs, scsk;
  ge25519 ger;

  memmove(pk,sk + 32,32);
  /* pk: 32-byte public key A */

  crypto_hash_sha512(az,sk,32);
  az[0] &= 248;
  az[31] &= 127;
  az[31] |= 64;
  /* az: 32-byte scalar a, 32-byte randomizer z */

  *smlen = mlen + 64;
  memmove(sm + 64,m,mlen);
  memmove(sm + 32,az + 32,32);
  /* sm: 32-byte uninit, 32-byte z, mlen-byte m */

  crypto_hash_sha512(nonce, sm+32, mlen+32);
  /* nonce: 64-byte H(z,m) */

  sc25519_from64bytes(&sck, nonce);
  ge25519_scalarmult_base(&ger, &sck);
  ge25519_pack(sm, &ger);
  /* sm: 32-byte R, 32-byte z, mlen-byte m */

  memmove(sm + 32,pk,32);
  /* sm: 32-byte R, 32-byte A, mlen-byte m */

  crypto_hash_sha512(hram,sm,mlen + 64);
  /* hram: 64-byte H(R,A,m) */

  sc25519_from64bytes(&scs, hram);
  sc25519_from32bytes(&scsk, az);
  sc25519_mul(&scs, &scs, &scsk);
  sc25519_add(&scs, &scs, &sck);
  /* scs: S = nonce + H(R,A,m)a */

  sc25519_to32bytes(sm + 32,&scs);
  /* sm: 32-byte R, 32-byte S, mlen-byte m */

  return 0;
}
/* from supercop-20221122/crypto_sign/ed25519/ref/open.c */

int crypto_sign_ed25519_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 hram[64];
  unsigned char rcheck[32];
  ge25519 get1, get2;
  sc25519 schram, scs;

  if (smlen < 64) goto badsig;
  if (sm[63] & 224) goto badsig;
  if (ge25519_unpackneg_vartime(&get1,pk)) goto badsig;

  memmove(pkcopy,pk,32);
  memmove(rcopy,sm,32);

  sc25519_from32bytes(&scs, sm+32);

  memmove(m,sm,smlen);
  memmove(m + 32,pkcopy,32);
  crypto_hash_sha512(hram,m,smlen);

  sc25519_from64bytes(&schram, hram);

  ge25519_double_scalarmult_vartime(&get2, &get1, &schram, &ge25519_base, &scs);
  ge25519_pack(rcheck, &get2);

  if (crypto_verify_32(rcopy,rcheck) == 0) {
    memmove(m,m + 64,smlen - 64);
    memset(m + smlen - 64,0,64);
    *mlen = smlen - 64;
    return 0;
  }

badsig:
  *mlen = (unsigned long long) -1;
  memset(m,0,smlen);
  return -1;
}