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GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	usr.bin/ssh/lib/../ge25519.c	Lines:	57	157	36.3 %
Date:	2017-11-07	Branches:	2	18	11.1 %


/* $OpenBSD: ge25519.c,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.c
 */

#include "fe25519.h"
#include "sc25519.h"
#include "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 */
  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;
}

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);
  }
}


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: ge25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */
2
3			/*
4			* Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange,
5			* Peter Schwabe, Bo-Yin Yang.
6			* Copied from supercop-20130419/crypto_sign/ed25519/ref/ge25519.c
7			*/
8
9			#include "fe25519.h"
10			#include "sc25519.h"
11			#include "ge25519.h"
12
13			/*
14			* Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2
15			* with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555
16			* Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);
17			*/
18
19			/* d */
20			static const fe25519 ge25519_ecd = {{0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41, 0x41, 0x4D, 0x0A, 0x70, 0x00,
21			0x98, 0xE8, 0x79, 0x77, 0x79, 0x40, 0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52}};
22			/* 2d /
23			static const fe25519 ge25519_ec2d = {{0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83, 0x82, 0x9A, 0x14, 0xE0, 0x00,
24			0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80, 0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24}};
25			/* sqrt(-1) */
26			static const fe25519 ge25519_sqrtm1 = {{0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F, 0xAD, 0x06, 0x18, 0x43, 0x2F,
27			0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00, 0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B}};
28
29			#define ge25519_p3 ge25519
30
31			typedef struct
32			{
33			fe25519 x;
34			fe25519 z;
35			fe25519 y;
36			fe25519 t;
37			} ge25519_p1p1;
38
39			typedef struct
40			{
41			fe25519 x;
42			fe25519 y;
43			fe25519 z;
44			} ge25519_p2;
45
46			typedef struct
47			{
48			fe25519 x;
49			fe25519 y;
50			} ge25519_aff;
51
52
53			/* Packed coordinates of the base point */
54			const ge25519 ge25519_base = {{{0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
55			0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21}},
56			{{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
57			0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66}},
58			{{0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
59			0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}},
60			{{0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
61			0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67}}};
62
63			/* Multiples of the base point in affine representation */
64			static const ge25519_aff ge25519_base_multiples_affine[425] = {
65			#include "ge25519_base.data"
66			};
67
68			static void p1p1_to_p2(ge25519_p2 r, const ge25519_p1p1 p)
69			{
70			fe25519_mul(&r->x, &p->x, &p->t);
71			fe25519_mul(&r->y, &p->y, &p->z);
72			fe25519_mul(&r->z, &p->z, &p->t);
73			}
74
75			static void p1p1_to_p3(ge25519_p3 r, const ge25519_p1p1 p)
76			{
77			p1p1_to_p2((ge25519_p2 *)r, p);
78			fe25519_mul(&r->t, &p->x, &p->y);
79			}
80
81			static void ge25519_mixadd2(ge25519_p3 r, const ge25519_aff q)
82			{
83		840	fe25519 a,b,t1,t2,c,d,e,f,g,h,qt;
84		420	fe25519_mul(&qt, &q->x, &q->y);
85		420	fe25519_sub(&a, &r->y, &r->x); /* A = (Y1-X1)(Y2-X2) /
86		420	fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)(Y2+X2) /
87		420	fe25519_sub(&t1, &q->y, &q->x);
88		420	fe25519_add(&t2, &q->y, &q->x);
89		420	fe25519_mul(&a, &a, &t1);
90		420	fe25519_mul(&b, &b, &t2);
91		420	fe25519_sub(&e, &b, &a); /* E = B-A */
92		420	fe25519_add(&h, &b, &a); /* H = B+A */
93		420	fe25519_mul(&c, &r->t, &qt); /* C = T1kT2 */
94		420	fe25519_mul(&c, &c, &ge25519_ec2d);
95		420	fe25519_add(&d, &r->z, &r->z); /* D = Z12 /
96		420	fe25519_sub(&f, &d, &c); /* F = D-C */
97		420	fe25519_add(&g, &d, &c); /* G = D+C */
98		420	fe25519_mul(&r->x, &e, &f);
99		420	fe25519_mul(&r->y, &h, &g);
100		420	fe25519_mul(&r->z, &g, &f);
101		420	fe25519_mul(&r->t, &e, &h);
102		420	}
103
104			static void add_p1p1(ge25519_p1p1 r, const ge25519_p3 p, const ge25519_p3 *q)
105			{
106			fe25519 a, b, c, d, t;
107
108			fe25519_sub(&a, &p->y, &p->x); /* A = (Y1-X1)(Y2-X2) /
109			fe25519_sub(&t, &q->y, &q->x);
110			fe25519_mul(&a, &a, &t);
111			fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)(Y2+X2) /
112			fe25519_add(&t, &q->x, &q->y);
113			fe25519_mul(&b, &b, &t);
114			fe25519_mul(&c, &p->t, &q->t); /* C = T1kT2 */
115			fe25519_mul(&c, &c, &ge25519_ec2d);
116			fe25519_mul(&d, &p->z, &q->z); /* D = Z12Z2 */
117			fe25519_add(&d, &d, &d);
118			fe25519_sub(&r->x, &b, &a); /* E = B-A */
119			fe25519_sub(&r->t, &d, &c); /* F = D-C */
120			fe25519_add(&r->z, &d, &c); /* G = D+C */
121			fe25519_add(&r->y, &b, &a); /* H = B+A */
122			}
123
124			/* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
125			static void dbl_p1p1(ge25519_p1p1 r, const ge25519_p2 p)
126			{
127			fe25519 a,b,c,d;
128			fe25519_square(&a, &p->x);
129			fe25519_square(&b, &p->y);
130			fe25519_square(&c, &p->z);
131			fe25519_add(&c, &c, &c);
132			fe25519_neg(&d, &a);
133
134			fe25519_add(&r->x, &p->x, &p->y);
135			fe25519_square(&r->x, &r->x);
136			fe25519_sub(&r->x, &r->x, &a);
137			fe25519_sub(&r->x, &r->x, &b);
138			fe25519_add(&r->z, &d, &b);
139			fe25519_sub(&r->t, &r->z, &c);
140			fe25519_sub(&r->y, &d, &b);
141			}
142
143			/* Constant-time version of: if(b) r = p */
144			static void cmov_aff(ge25519_aff r, const ge25519_aff p, unsigned char b)
145			{
146		3400	fe25519_cmov(&r->x, &p->x, b);
147		1700	fe25519_cmov(&r->y, &p->y, b);
148		1700	}
149
150			static unsigned char equal(signed char b,signed char c)
151			{
152			unsigned char ub = b;
153			unsigned char uc = c;
154		5950	unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
155		2975	crypto_uint32 y = x; /* 0: yes; 1..255: no */
156		2975	y -= 1; /* 4294967295: yes; 0..254: no */
157		2975	y >>= 31; /* 1: yes; 0: no */
158		2975	return y;
159			}
160
161			static unsigned char negative(signed char b)
162			{
163		850	unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
164		425	x >>= 63; /* 1: yes; 0: no */
165		425	return x;
166			}
167
168			static void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
169			{
170			/* constant time */
171		850	fe25519 v;
172		425	t = ge25519_base_multiples_affine[5pos+0];
173		425	cmov_aff(t, &ge25519_base_multiples_affine[5*pos+1],equal(b,1) \| equal(b,-1));
174		425	cmov_aff(t, &ge25519_base_multiples_affine[5*pos+2],equal(b,2) \| equal(b,-2));
175		425	cmov_aff(t, &ge25519_base_multiples_affine[5*pos+3],equal(b,3) \| equal(b,-3));
176		425	cmov_aff(t, &ge25519_base_multiples_affine[5*pos+4],equal(b,-4));
177		425	fe25519_neg(&v, &t->x);
178		425	fe25519_cmov(&t->x, &v, negative(b));
179		425	}
180
181			static void setneutral(ge25519 *r)
182			{
183			fe25519_setzero(&r->x);
184			fe25519_setone(&r->y);
185			fe25519_setone(&r->z);
186			fe25519_setzero(&r->t);
187			}
188
189			/* ********************************************************************
190			* EXPORTED FUNCTIONS
191			******************************************************************** */
192
193			/* return 0 on success, -1 otherwise */
194			int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
195			{
196			unsigned char par;
197			fe25519 t, chk, num, den, den2, den4, den6;
198			fe25519_setone(&r->z);
199			par = p[31] >> 7;
200			fe25519_unpack(&r->y, p);
201			fe25519_square(&num, &r->y); /* x = y^2 */
202			fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */
203			fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
204			fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */
205
206			/* Computation of sqrt(num/den) */
207			/* 1.: computation of num^((p-5)/8)den^((7p-35)/8) = (numden^7)^((p-5)/8) */
208			fe25519_square(&den2, &den);
209			fe25519_square(&den4, &den2);
210			fe25519_mul(&den6, &den4, &den2);
211			fe25519_mul(&t, &den6, &num);
212			fe25519_mul(&t, &t, &den);
213
214			fe25519_pow2523(&t, &t);
215			/* 2. computation of r->x = t * num * den^3 */
216			fe25519_mul(&t, &t, &num);
217			fe25519_mul(&t, &t, &den);
218			fe25519_mul(&t, &t, &den);
219			fe25519_mul(&r->x, &t, &den);
220
221			/* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */
222			fe25519_square(&chk, &r->x);
223			fe25519_mul(&chk, &chk, &den);
224			if (!fe25519_iseq_vartime(&chk, &num))
225			fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
226
227			/* 4. Now we have one of the two square roots, except if input was not a square */
228			fe25519_square(&chk, &r->x);
229			fe25519_mul(&chk, &chk, &den);
230			if (!fe25519_iseq_vartime(&chk, &num))
231			return -1;
232
233			/* 5. Choose the desired square root according to parity: */
234			if(fe25519_getparity(&r->x) != (1-par))
235			fe25519_neg(&r->x, &r->x);
236
237			fe25519_mul(&r->t, &r->x, &r->y);
238			return 0;
239			}
240
241			void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
242			{
243		10	fe25519 tx, ty, zi;
244		5	fe25519_invert(&zi, &p->z);
245		5	fe25519_mul(&tx, &p->x, &zi);
246		5	fe25519_mul(&ty, &p->y, &zi);
247		5	fe25519_pack(r, &ty);
248		5	r[31] ^= fe25519_getparity(&tx) << 7;
249		5	}
250
251			int ge25519_isneutral_vartime(const ge25519_p3 *p)
252			{
253			int ret = 1;
254			if(!fe25519_iszero(&p->x)) ret = 0;
255			if(!fe25519_iseq_vartime(&p->y, &p->z)) ret = 0;
256			return ret;
257			}
258
259			/* computes [s1]p1 + [s2]p2 */
260			void ge25519_double_scalarmult_vartime(ge25519_p3 r, const ge25519_p3 p1, const sc25519 s1, const ge25519_p3 p2, const sc25519 *s2)
261			{
262			ge25519_p1p1 tp1p1;
263			ge25519_p3 pre[16];
264			unsigned char b[127];
265			int i;
266
267			/* precomputation s2 s1 */
268			setneutral(pre); /* 00 00 */
269			pre[1] = p1; / 00 01 */
270			dbl_p1p1(&tp1p1,(ge25519_p2 )p1); p1p1_to_p3( &pre[2], &tp1p1); / 00 10 */
271			add_p1p1(&tp1p1,&pre[1], &pre[2]); p1p1_to_p3( &pre[3], &tp1p1); /* 00 11 */
272			pre[4] = p2; / 01 00 */
273			add_p1p1(&tp1p1,&pre[1], &pre[4]); p1p1_to_p3( &pre[5], &tp1p1); /* 01 01 */
274			add_p1p1(&tp1p1,&pre[2], &pre[4]); p1p1_to_p3( &pre[6], &tp1p1); /* 01 10 */
275			add_p1p1(&tp1p1,&pre[3], &pre[4]); p1p1_to_p3( &pre[7], &tp1p1); /* 01 11 */
276			dbl_p1p1(&tp1p1,(ge25519_p2 )p2); p1p1_to_p3( &pre[8], &tp1p1); / 10 00 */
277			add_p1p1(&tp1p1,&pre[1], &pre[8]); p1p1_to_p3( &pre[9], &tp1p1); /* 10 01 */
278			dbl_p1p1(&tp1p1,(ge25519_p2 )&pre[5]); p1p1_to_p3(&pre[10], &tp1p1); / 10 10 */
279			add_p1p1(&tp1p1,&pre[3], &pre[8]); p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
280			add_p1p1(&tp1p1,&pre[4], &pre[8]); p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
281			add_p1p1(&tp1p1,&pre[1],&pre[12]); p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
282			add_p1p1(&tp1p1,&pre[2],&pre[12]); p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
283			add_p1p1(&tp1p1,&pre[3],&pre[12]); p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */
284
285			sc25519_2interleave2(b,s1,s2);
286
287			/* scalar multiplication */
288			*r = pre[b[126]];
289			for(i=125;i>=0;i--)
290			{
291			dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
292			p1p1_to_p2((ge25519_p2 *) r, &tp1p1);
293			dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
294			if(b[i]!=0)
295			{
296			p1p1_to_p3(r, &tp1p1);
297			add_p1p1(&tp1p1, r, &pre[b[i]]);
298			}
299			if(i != 0) p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
300			else p1p1_to_p3(r, &tp1p1);
301			}
302			}
303
304			void ge25519_scalarmult_base(ge25519_p3 r, const sc25519 s)
305			{
306		10	signed char b[85];
307			int i;
308		5	ge25519_aff t;
309		5	sc25519_window3(b,s);
310
311		5	choose_t((ge25519_aff *)r, 0, b[0]);
312		5	fe25519_setone(&r->z);
313		5	fe25519_mul(&r->t, &r->x, &r->y);
314	✓✓	850	for(i=1;i<85;i++)
315			{
316		420	choose_t(&t, (unsigned long long) i, b[i]);
317		420	ge25519_mixadd2(r, &t);
318			}
319		5	}