cryptonite-0.30: cbits/decaf/ed448goldilocks/decaf.c
/**
* @file ed448goldilocks/decaf.c
* @author Mike Hamburg
*
* @copyright
* Copyright (c) 2015-2016 Cryptography Research, Inc. \n
* Released under the MIT License. See LICENSE.txt for license information.
*
* @brief Decaf high-level functions.
*
* @warning This file was automatically generated in Python.
* Please do not edit it.
*/
#define _XOPEN_SOURCE 600 /* for posix_memalign */
#include "word.h"
#include "field.h"
#include <decaf.h>
#include <decaf/ed448.h>
/* Template stuff */
#define API_NS(_id) cryptonite_decaf_448_##_id
#define SCALAR_BITS CRYPTONITE_DECAF_448_SCALAR_BITS
#define SCALAR_SER_BYTES CRYPTONITE_DECAF_448_SCALAR_BYTES
#define SCALAR_LIMBS CRYPTONITE_DECAF_448_SCALAR_LIMBS
#define scalar_t API_NS(scalar_t)
#define point_t API_NS(point_t)
#define precomputed_s API_NS(precomputed_s)
#define IMAGINE_TWIST 0
#define COFACTOR 4
/* Comb config: number of combs, n, t, s. */
#define COMBS_N 5
#define COMBS_T 5
#define COMBS_S 18
#define CRYPTONITE_DECAF_WINDOW_BITS 5
#define CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS 5
#define CRYPTONITE_DECAF_WNAF_VAR_TABLE_BITS 3
#define EDDSA_USE_SIGMA_ISOGENY 0
static const int EDWARDS_D = -39081;
static const scalar_t point_scalarmul_adjustment = {{{
SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
}}}, precomputed_scalarmul_adjustment = {{{
SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad), SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
}}};
const uint8_t cryptonite_decaf_x448_base_point[CRYPTONITE_DECAF_X448_PUBLIC_BYTES] = { 0x05 };
#if COFACTOR==8 || EDDSA_USE_SIGMA_ISOGENY
static const gf SQRT_ONE_MINUS_D = {FIELD_LITERAL(
/* NONE */
)};
#endif
/* End of template stuff */
/* Sanity */
#if (COFACTOR == 8) && !IMAGINE_TWIST && !UNSAFE_CURVE_HAS_POINTS_AT_INFINITY
/* FUTURE MAGIC: Curve41417 doesn't have these properties. */
#error "Currently require IMAGINE_TWIST (and thus p=5 mod 8) for cofactor 8"
/* OK, but why?
* Two reasons: #1: There are bugs when COFACTOR == && IMAGINE_TWIST
# #2:
*/
#endif
#if IMAGINE_TWIST && (P_MOD_8 != 5)
#error "Cannot use IMAGINE_TWIST except for p == 5 mod 8"
#endif
#if (COFACTOR != 8) && (COFACTOR != 4)
#error "COFACTOR must be 4 or 8"
#endif
#if IMAGINE_TWIST
extern const gf SQRT_MINUS_ONE;
#endif
#define WBITS CRYPTONITE_DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
extern const point_t API_NS(point_base);
/* Projective Niels coordinates */
typedef struct { gf a, b, c; } niels_s, niels_t[1];
typedef struct { niels_t n; gf z; } VECTOR_ALIGNED pniels_s, pniels_t[1];
/* Precomputed base */
struct precomputed_s { niels_t table [COMBS_N<<(COMBS_T-1)]; };
extern const gf API_NS(precomputed_base_as_fe)[];
const precomputed_s *API_NS(precomputed_base) =
(const precomputed_s *) &API_NS(precomputed_base_as_fe);
const size_t API_NS(sizeof_precomputed_s) = sizeof(precomputed_s);
const size_t API_NS(alignof_precomputed_s) = sizeof(big_register_t);
/** Inverse. */
static void
cryptonite_gf_invert(gf y, const gf x, int assert_nonzero) {
gf t1, t2;
cryptonite_gf_sqr(t1, x); // o^2
mask_t ret = cryptonite_gf_isr(t2, t1); // +-1/sqrt(o^2) = +-1/o
(void)ret;
if (assert_nonzero) assert(ret);
cryptonite_gf_sqr(t1, t2);
cryptonite_gf_mul(t2, t1, x); // not direct to y in case of alias.
cryptonite_gf_copy(y, t2);
}
/** Return high bit of x = low bit of 2x mod p */
static mask_t cryptonite_gf_lobit(const gf x) {
gf y;
cryptonite_gf_copy(y,x);
cryptonite_gf_strong_reduce(y);
return -(y->limb[0]&1);
}
/** identity = (0,1) */
const point_t API_NS(point_identity) = {{{{{0}}},{{{1}}},{{{1}}},{{{0}}}}};
void API_NS(deisogenize) (
cryptonite_gf_s *__restrict__ s,
cryptonite_gf_s *__restrict__ minus_t_over_s,
const point_t p,
mask_t toggle_hibit_s,
mask_t toggle_hibit_t_over_s,
mask_t toggle_rotation
);
void API_NS(deisogenize) (
cryptonite_gf_s *__restrict__ s,
cryptonite_gf_s *__restrict__ minus_t_over_s,
const point_t p,
mask_t toggle_hibit_s,
mask_t toggle_hibit_t_over_s,
mask_t toggle_rotation
) {
#if COFACTOR == 4 && !IMAGINE_TWIST
(void) toggle_rotation;
gf b, d;
cryptonite_gf_s *c = s, *a = minus_t_over_s;
cryptonite_gf_mulw(a, p->y, 1-EDWARDS_D);
cryptonite_gf_mul(c, a, p->t); /* -dYT, with EDWARDS_D = d-1 */
cryptonite_gf_mul(a, p->x, p->z);
cryptonite_gf_sub(d, c, a); /* aXZ-dYT with a=-1 */
cryptonite_gf_add(a, p->z, p->y);
cryptonite_gf_sub(b, p->z, p->y);
cryptonite_gf_mul(c, b, a);
cryptonite_gf_mulw(b, c, -EDWARDS_D); /* (a-d)(Z+Y)(Z-Y) */
mask_t ok = cryptonite_gf_isr (a,b); /* r in the paper */
(void)ok; assert(ok | cryptonite_gf_eq(b,ZERO));
cryptonite_gf_mulw (b, a, -EDWARDS_D); /* u in the paper */
cryptonite_gf_mul(c,a,d); /* r(aZX-dYT) */
cryptonite_gf_mul(a,b,p->z); /* uZ */
cryptonite_gf_add(a,a,a); /* 2uZ */
mask_t tg = toggle_hibit_t_over_s ^ ~cryptonite_gf_hibit(minus_t_over_s);
cryptonite_gf_cond_neg(minus_t_over_s, tg); /* t/s <-? -t/s */
cryptonite_gf_cond_neg(c, tg); /* u <- -u if negative. */
cryptonite_gf_add(d,c,p->y);
cryptonite_gf_mul(s,b,d);
cryptonite_gf_cond_neg(s, toggle_hibit_s ^ cryptonite_gf_hibit(s));
#else
/* More complicated because of rotation */
/* MAGIC This code is wrong for certain non-Curve25519 curves;
* check if it's because of Cofactor==8 or IMAGINE_TWIST */
gf c, d;
cryptonite_gf_s *b = s, *a = minus_t_over_s;
#if IMAGINE_TWIST
gf x, t;
cryptonite_gf_div_qnr(x,p->x);
cryptonite_gf_div_qnr(t,p->t);
cryptonite_gf_add ( a, p->z, x );
cryptonite_gf_sub ( b, p->z, x );
cryptonite_gf_mul ( c, a, b ); /* "zx" = Z^2 - aX^2 = Z^2 - X^2 */
#else
const cryptonite_gf_s *x = p->x, *t = p->t;
cryptonite_gf_sqr ( a, p->z );
cryptonite_gf_sqr ( b, p->x );
cryptonite_gf_add ( c, a, b ); /* "zx" = Z^2 - aX^2 = Z^2 + X^2 */
#endif
/* Here: c = "zx" in the SAGE code = Z^2 - aX^2 */
cryptonite_gf_mul ( a, p->z, t ); /* "tz" = T*Z */
cryptonite_gf_sqr ( b, a );
cryptonite_gf_mul ( d, b, c ); /* (TZ)^2 * (Z^2-aX^2) */
mask_t ok = cryptonite_gf_isr(b, d);
(void)ok; assert(ok | cryptonite_gf_eq(d,ZERO));
cryptonite_gf_mul ( d, b, a ); /* "osx" = 1 / sqrt(z^2-ax^2) */
cryptonite_gf_mul ( a, b, c );
cryptonite_gf_mul ( b, a, d ); /* 1/tz */
mask_t rotate;
#if (COFACTOR == 8)
gf e;
cryptonite_gf_sqr(e, p->z);
cryptonite_gf_mul(a, e, b); /* z^2 / tz = z/t = 1/xy */
rotate = cryptonite_gf_hibit(a) ^ toggle_rotation;
/* Curve25519: cond select between zx * 1/tz or sqrt(1-d); y=-x */
cryptonite_gf_mul ( a, b, c );
cryptonite_gf_cond_sel ( a, a, SQRT_ONE_MINUS_D, rotate );
cryptonite_gf_cond_sel ( e, p->y, x, rotate );
#else
const cryptonite_gf_s *e = x;
(void)toggle_rotation;
rotate = 0;
#endif
cryptonite_gf_mul ( c, a, d ); // new "osx"
cryptonite_gf_mul ( a, c, p->z );
cryptonite_gf_add ( minus_t_over_s, a, a ); // 2 * "osx" * Z
cryptonite_gf_mul ( d, b, p->z );
mask_t tg = toggle_hibit_t_over_s ^~ cryptonite_gf_hibit(minus_t_over_s);
cryptonite_gf_cond_neg ( minus_t_over_s, tg );
cryptonite_gf_cond_neg ( c, rotate ^ tg );
cryptonite_gf_add ( d, d, c );
cryptonite_gf_mul ( s, d, e ); /* here "x" = y unless rotate */
cryptonite_gf_cond_neg ( s, toggle_hibit_s ^ cryptonite_gf_hibit(s) );
#endif
}
void API_NS(point_encode)( unsigned char ser[SER_BYTES], const point_t p ) {
gf s, mtos;
API_NS(deisogenize)(s,mtos,p,0,0,0);
cryptonite_gf_serialize(ser,s,0);
}
cryptonite_decaf_error_t API_NS(point_decode) (
point_t p,
const unsigned char ser[SER_BYTES],
cryptonite_decaf_bool_t allow_identity
) {
gf s, a, b, c, d, e, f;
mask_t succ = cryptonite_gf_deserialize(s, ser, 0);
mask_t zero = cryptonite_gf_eq(s, ZERO);
succ &= bool_to_mask(allow_identity) | ~zero;
cryptonite_gf_sqr ( a, s ); /* s^2 */
#if IMAGINE_TWIST
cryptonite_gf_sub ( f, ONE, a ); /* f = 1-as^2 = 1-s^2*/
#else
cryptonite_gf_add ( f, ONE, a ); /* f = 1-as^2 = 1+s^2 */
#endif
succ &= ~ cryptonite_gf_eq( f, ZERO );
cryptonite_gf_sqr ( b, f ); /* (1-as^2)^2 = 1 - 2as^2 + a^2 s^4 */
cryptonite_gf_mulw ( c, a, 4*IMAGINE_TWIST-4*EDWARDS_D );
cryptonite_gf_add ( c, c, b ); /* t^2 = 1 + (2a-4d) s^2 + s^4 */
cryptonite_gf_mul ( d, f, s ); /* s * (1-as^2) for denoms */
cryptonite_gf_sqr ( e, d ); /* s^2 * (1-as^2)^2 */
cryptonite_gf_mul ( b, c, e ); /* t^2 * s^2 * (1-as^2)^2 */
succ &= cryptonite_gf_isr(e,b) | cryptonite_gf_eq(b,ZERO); /* e = 1/(t s (1-as^2)) */
cryptonite_gf_mul ( b, e, d ); /* 1 / t */
cryptonite_gf_mul ( d, e, c ); /* t / (s(1-as^2)) */
cryptonite_gf_mul ( e, d, f ); /* t / s */
mask_t negtos = cryptonite_gf_hibit(e);
cryptonite_gf_cond_neg(b, negtos);
cryptonite_gf_cond_neg(d, negtos);
#if IMAGINE_TWIST
cryptonite_gf_add ( p->z, ONE, a); /* Z = 1+as^2 = 1-s^2 */
#else
cryptonite_gf_sub ( p->z, ONE, a); /* Z = 1+as^2 = 1-s^2 */
#endif
#if COFACTOR == 8
cryptonite_gf_mul ( a, p->z, d); /* t(1+s^2) / s(1-s^2) = 2/xy */
succ &= ~cryptonite_gf_lobit(a); /* = ~cryptonite_gf_hibit(a/2), since cryptonite_gf_hibit(x) = cryptonite_gf_lobit(2x) */
#endif
cryptonite_gf_mul ( a, f, b ); /* y = (1-s^2) / t */
cryptonite_gf_mul ( p->y, p->z, a ); /* Y = yZ */
#if IMAGINE_TWIST
cryptonite_gf_add ( b, s, s );
cryptonite_gf_mul(p->x, b, SQRT_MINUS_ONE); /* Curve25519 */
#else
cryptonite_gf_add ( p->x, s, s );
#endif
cryptonite_gf_mul ( p->t, p->x, a ); /* T = 2s (1-as^2)/t */
#if UNSAFE_CURVE_HAS_POINTS_AT_INFINITY
/* This can't happen for any of the supported configurations.
*
* If it can happen (because s=1), it's because the curve has points
* at infinity, which means that there may be critical security bugs
* elsewhere in the library. In that case, it's better that you hit
* the assertion in point_valid, which will happen in the test suite
* since it tests s=1.
*
* This debugging option is to allow testing of IMAGINE_TWIST = 0 on
* Ed25519, without hitting that assertion. Don't use it in
* production.
*/
succ &= ~cryptonite_gf_eq(p->z,ZERO);
#endif
p->y->limb[0] -= zero;
assert(API_NS(point_valid)(p) | ~succ);
return cryptonite_decaf_succeed_if(mask_to_bool(succ));
}
#if IMAGINE_TWIST
#define TWISTED_D (-(EDWARDS_D))
#else
#define TWISTED_D ((EDWARDS_D)-1)
#endif
#if TWISTED_D < 0
#define EFF_D (-(TWISTED_D))
#define NEG_D 1
#else
#define EFF_D TWISTED_D
#define NEG_D 0
#endif
void API_NS(point_sub) (
point_t p,
const point_t q,
const point_t r
) {
gf a, b, c, d;
cryptonite_gf_sub_nr ( b, q->y, q->x ); /* 3+e */
cryptonite_gf_sub_nr ( d, r->y, r->x ); /* 3+e */
cryptonite_gf_add_nr ( c, r->y, r->x ); /* 2+e */
cryptonite_gf_mul ( a, c, b );
cryptonite_gf_add_nr ( b, q->y, q->x ); /* 2+e */
cryptonite_gf_mul ( p->y, d, b );
cryptonite_gf_mul ( b, r->t, q->t );
cryptonite_gf_mulw ( p->x, b, 2*EFF_D );
cryptonite_gf_add_nr ( b, a, p->y ); /* 2+e */
cryptonite_gf_sub_nr ( c, p->y, a ); /* 3+e */
cryptonite_gf_mul ( a, q->z, r->z );
cryptonite_gf_add_nr ( a, a, a ); /* 2+e */
if (GF_HEADROOM <= 3) cryptonite_gf_weak_reduce(a); /* or 1+e */
#if NEG_D
cryptonite_gf_sub_nr ( p->y, a, p->x ); /* 4+e or 3+e */
cryptonite_gf_add_nr ( a, a, p->x ); /* 3+e or 2+e */
#else
cryptonite_gf_add_nr ( p->y, a, p->x ); /* 3+e or 2+e */
cryptonite_gf_sub_nr ( a, a, p->x ); /* 4+e or 3+e */
#endif
cryptonite_gf_mul ( p->z, a, p->y );
cryptonite_gf_mul ( p->x, p->y, c );
cryptonite_gf_mul ( p->y, a, b );
cryptonite_gf_mul ( p->t, b, c );
}
void API_NS(point_add) (
point_t p,
const point_t q,
const point_t r
) {
gf a, b, c, d;
cryptonite_gf_sub_nr ( b, q->y, q->x ); /* 3+e */
cryptonite_gf_sub_nr ( c, r->y, r->x ); /* 3+e */
cryptonite_gf_add_nr ( d, r->y, r->x ); /* 2+e */
cryptonite_gf_mul ( a, c, b );
cryptonite_gf_add_nr ( b, q->y, q->x ); /* 2+e */
cryptonite_gf_mul ( p->y, d, b );
cryptonite_gf_mul ( b, r->t, q->t );
cryptonite_gf_mulw ( p->x, b, 2*EFF_D );
cryptonite_gf_add_nr ( b, a, p->y ); /* 2+e */
cryptonite_gf_sub_nr ( c, p->y, a ); /* 3+e */
cryptonite_gf_mul ( a, q->z, r->z );
cryptonite_gf_add_nr ( a, a, a ); /* 2+e */
if (GF_HEADROOM <= 3) cryptonite_gf_weak_reduce(a); /* or 1+e */
#if NEG_D
cryptonite_gf_add_nr ( p->y, a, p->x ); /* 3+e or 2+e */
cryptonite_gf_sub_nr ( a, a, p->x ); /* 4+e or 3+e */
#else
cryptonite_gf_sub_nr ( p->y, a, p->x ); /* 4+e or 3+e */
cryptonite_gf_add_nr ( a, a, p->x ); /* 3+e or 2+e */
#endif
cryptonite_gf_mul ( p->z, a, p->y );
cryptonite_gf_mul ( p->x, p->y, c );
cryptonite_gf_mul ( p->y, a, b );
cryptonite_gf_mul ( p->t, b, c );
}
static CRYPTONITE_DECAF_NOINLINE void
point_double_internal (
point_t p,
const point_t q,
int before_double
) {
gf a, b, c, d;
cryptonite_gf_sqr ( c, q->x );
cryptonite_gf_sqr ( a, q->y );
cryptonite_gf_add_nr ( d, c, a ); /* 2+e */
cryptonite_gf_add_nr ( p->t, q->y, q->x ); /* 2+e */
cryptonite_gf_sqr ( b, p->t );
cryptonite_gf_subx_nr ( b, b, d, 3 ); /* 4+e */
cryptonite_gf_sub_nr ( p->t, a, c ); /* 3+e */
cryptonite_gf_sqr ( p->x, q->z );
cryptonite_gf_add_nr ( p->z, p->x, p->x ); /* 2+e */
cryptonite_gf_subx_nr ( a, p->z, p->t, 4 ); /* 6+e */
if (GF_HEADROOM == 5) cryptonite_gf_weak_reduce(a); /* or 1+e */
cryptonite_gf_mul ( p->x, a, b );
cryptonite_gf_mul ( p->z, p->t, a );
cryptonite_gf_mul ( p->y, p->t, d );
if (!before_double) cryptonite_gf_mul ( p->t, b, d );
}
void API_NS(point_double)(point_t p, const point_t q) {
point_double_internal(p,q,0);
}
void API_NS(point_negate) (
point_t nega,
const point_t a
) {
cryptonite_gf_sub(nega->x, ZERO, a->x);
cryptonite_gf_copy(nega->y, a->y);
cryptonite_gf_copy(nega->z, a->z);
cryptonite_gf_sub(nega->t, ZERO, a->t);
}
/* Operations on [p]niels */
static CRYPTONITE_DECAF_INLINE void
cond_neg_niels (
niels_t n,
mask_t neg
) {
cryptonite_gf_cond_swap(n->a, n->b, neg);
cryptonite_gf_cond_neg(n->c, neg);
}
static CRYPTONITE_DECAF_NOINLINE void pt_to_pniels (
pniels_t b,
const point_t a
) {
cryptonite_gf_sub ( b->n->a, a->y, a->x );
cryptonite_gf_add ( b->n->b, a->x, a->y );
cryptonite_gf_mulw ( b->n->c, a->t, 2*TWISTED_D );
cryptonite_gf_add ( b->z, a->z, a->z );
}
static CRYPTONITE_DECAF_NOINLINE void pniels_to_pt (
point_t e,
const pniels_t d
) {
gf eu;
cryptonite_gf_add ( eu, d->n->b, d->n->a );
cryptonite_gf_sub ( e->y, d->n->b, d->n->a );
cryptonite_gf_mul ( e->t, e->y, eu);
cryptonite_gf_mul ( e->x, d->z, e->y );
cryptonite_gf_mul ( e->y, d->z, eu );
cryptonite_gf_sqr ( e->z, d->z );
}
static CRYPTONITE_DECAF_NOINLINE void
niels_to_pt (
point_t e,
const niels_t n
) {
cryptonite_gf_add ( e->y, n->b, n->a );
cryptonite_gf_sub ( e->x, n->b, n->a );
cryptonite_gf_mul ( e->t, e->y, e->x );
cryptonite_gf_copy ( e->z, ONE );
}
static CRYPTONITE_DECAF_NOINLINE void
add_niels_to_pt (
point_t d,
const niels_t e,
int before_double
) {
gf a, b, c;
cryptonite_gf_sub_nr ( b, d->y, d->x ); /* 3+e */
cryptonite_gf_mul ( a, e->a, b );
cryptonite_gf_add_nr ( b, d->x, d->y ); /* 2+e */
cryptonite_gf_mul ( d->y, e->b, b );
cryptonite_gf_mul ( d->x, e->c, d->t );
cryptonite_gf_add_nr ( c, a, d->y ); /* 2+e */
cryptonite_gf_sub_nr ( b, d->y, a ); /* 3+e */
cryptonite_gf_sub_nr ( d->y, d->z, d->x ); /* 3+e */
cryptonite_gf_add_nr ( a, d->x, d->z ); /* 2+e */
cryptonite_gf_mul ( d->z, a, d->y );
cryptonite_gf_mul ( d->x, d->y, b );
cryptonite_gf_mul ( d->y, a, c );
if (!before_double) cryptonite_gf_mul ( d->t, b, c );
}
static CRYPTONITE_DECAF_NOINLINE void
sub_niels_from_pt (
point_t d,
const niels_t e,
int before_double
) {
gf a, b, c;
cryptonite_gf_sub_nr ( b, d->y, d->x ); /* 3+e */
cryptonite_gf_mul ( a, e->b, b );
cryptonite_gf_add_nr ( b, d->x, d->y ); /* 2+e */
cryptonite_gf_mul ( d->y, e->a, b );
cryptonite_gf_mul ( d->x, e->c, d->t );
cryptonite_gf_add_nr ( c, a, d->y ); /* 2+e */
cryptonite_gf_sub_nr ( b, d->y, a ); /* 3+e */
cryptonite_gf_add_nr ( d->y, d->z, d->x ); /* 2+e */
cryptonite_gf_sub_nr ( a, d->z, d->x ); /* 3+e */
cryptonite_gf_mul ( d->z, a, d->y );
cryptonite_gf_mul ( d->x, d->y, b );
cryptonite_gf_mul ( d->y, a, c );
if (!before_double) cryptonite_gf_mul ( d->t, b, c );
}
static void
add_pniels_to_pt (
point_t p,
const pniels_t pn,
int before_double
) {
gf L0;
cryptonite_gf_mul ( L0, p->z, pn->z );
cryptonite_gf_copy ( p->z, L0 );
add_niels_to_pt( p, pn->n, before_double );
}
static void
sub_pniels_from_pt (
point_t p,
const pniels_t pn,
int before_double
) {
gf L0;
cryptonite_gf_mul ( L0, p->z, pn->z );
cryptonite_gf_copy ( p->z, L0 );
sub_niels_from_pt( p, pn->n, before_double );
}
static CRYPTONITE_DECAF_NOINLINE void
prepare_fixed_window(
pniels_t *multiples,
const point_t b,
int ntable
) {
point_t tmp;
pniels_t pn;
int i;
point_double_internal(tmp, b, 0);
pt_to_pniels(pn, tmp);
pt_to_pniels(multiples[0], b);
API_NS(point_copy)(tmp, b);
for (i=1; i<ntable; i++) {
add_pniels_to_pt(tmp, pn, 0);
pt_to_pniels(multiples[i], tmp);
}
cryptonite_decaf_bzero(pn,sizeof(pn));
cryptonite_decaf_bzero(tmp,sizeof(tmp));
}
void API_NS(point_scalarmul) (
point_t a,
const point_t b,
const scalar_t scalar
) {
const int WINDOW = CRYPTONITE_DECAF_WINDOW_BITS,
WINDOW_MASK = (1<<WINDOW)-1,
WINDOW_T_MASK = WINDOW_MASK >> 1,
NTABLE = 1<<(WINDOW-1);
scalar_t scalar1x;
API_NS(scalar_add)(scalar1x, scalar, point_scalarmul_adjustment);
API_NS(scalar_halve)(scalar1x,scalar1x);
/* Set up a precomputed table with odd multiples of b. */
pniels_t pn, multiples[NTABLE];
point_t tmp;
prepare_fixed_window(multiples, b, NTABLE);
/* Initialize. */
int i,j,first=1;
i = SCALAR_BITS - ((SCALAR_BITS-1) % WINDOW) - 1;
for (; i>=0; i-=WINDOW) {
/* Fetch another block of bits */
word_t bits = scalar1x->limb[i/WBITS] >> (i%WBITS);
if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
bits ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
}
bits &= WINDOW_MASK;
mask_t inv = (bits>>(WINDOW-1))-1;
bits ^= inv;
/* Add in from table. Compute t only on last iteration. */
constant_time_lookup(pn, multiples, sizeof(pn), NTABLE, bits & WINDOW_T_MASK);
cond_neg_niels(pn->n, inv);
if (first) {
pniels_to_pt(tmp, pn);
first = 0;
} else {
/* Using Hisil et al's lookahead method instead of extensible here
* for no particular reason. Double WINDOW times, but only compute t on
* the last one.
*/
for (j=0; j<WINDOW-1; j++)
point_double_internal(tmp, tmp, -1);
point_double_internal(tmp, tmp, 0);
add_pniels_to_pt(tmp, pn, i ? -1 : 0);
}
}
/* Write out the answer */
API_NS(point_copy)(a,tmp);
cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
cryptonite_decaf_bzero(pn,sizeof(pn));
cryptonite_decaf_bzero(multiples,sizeof(multiples));
cryptonite_decaf_bzero(tmp,sizeof(tmp));
}
void API_NS(point_double_scalarmul) (
point_t a,
const point_t b,
const scalar_t scalarb,
const point_t c,
const scalar_t scalarc
) {
const int WINDOW = CRYPTONITE_DECAF_WINDOW_BITS,
WINDOW_MASK = (1<<WINDOW)-1,
WINDOW_T_MASK = WINDOW_MASK >> 1,
NTABLE = 1<<(WINDOW-1);
scalar_t scalar1x, scalar2x;
API_NS(scalar_add)(scalar1x, scalarb, point_scalarmul_adjustment);
API_NS(scalar_halve)(scalar1x,scalar1x);
API_NS(scalar_add)(scalar2x, scalarc, point_scalarmul_adjustment);
API_NS(scalar_halve)(scalar2x,scalar2x);
/* Set up a precomputed table with odd multiples of b. */
pniels_t pn, multiples1[NTABLE], multiples2[NTABLE];
point_t tmp;
prepare_fixed_window(multiples1, b, NTABLE);
prepare_fixed_window(multiples2, c, NTABLE);
/* Initialize. */
int i,j,first=1;
i = SCALAR_BITS - ((SCALAR_BITS-1) % WINDOW) - 1;
for (; i>=0; i-=WINDOW) {
/* Fetch another block of bits */
word_t bits1 = scalar1x->limb[i/WBITS] >> (i%WBITS),
bits2 = scalar2x->limb[i/WBITS] >> (i%WBITS);
if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
bits1 ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
bits2 ^= scalar2x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
}
bits1 &= WINDOW_MASK;
bits2 &= WINDOW_MASK;
mask_t inv1 = (bits1>>(WINDOW-1))-1;
mask_t inv2 = (bits2>>(WINDOW-1))-1;
bits1 ^= inv1;
bits2 ^= inv2;
/* Add in from table. Compute t only on last iteration. */
constant_time_lookup(pn, multiples1, sizeof(pn), NTABLE, bits1 & WINDOW_T_MASK);
cond_neg_niels(pn->n, inv1);
if (first) {
pniels_to_pt(tmp, pn);
first = 0;
} else {
/* Using Hisil et al's lookahead method instead of extensible here
* for no particular reason. Double WINDOW times, but only compute t on
* the last one.
*/
for (j=0; j<WINDOW-1; j++)
point_double_internal(tmp, tmp, -1);
point_double_internal(tmp, tmp, 0);
add_pniels_to_pt(tmp, pn, 0);
}
constant_time_lookup(pn, multiples2, sizeof(pn), NTABLE, bits2 & WINDOW_T_MASK);
cond_neg_niels(pn->n, inv2);
add_pniels_to_pt(tmp, pn, i?-1:0);
}
/* Write out the answer */
API_NS(point_copy)(a,tmp);
cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
cryptonite_decaf_bzero(scalar2x,sizeof(scalar2x));
cryptonite_decaf_bzero(pn,sizeof(pn));
cryptonite_decaf_bzero(multiples1,sizeof(multiples1));
cryptonite_decaf_bzero(multiples2,sizeof(multiples2));
cryptonite_decaf_bzero(tmp,sizeof(tmp));
}
void API_NS(point_dual_scalarmul) (
point_t a1,
point_t a2,
const point_t b,
const scalar_t scalar1,
const scalar_t scalar2
) {
const int WINDOW = CRYPTONITE_DECAF_WINDOW_BITS,
WINDOW_MASK = (1<<WINDOW)-1,
WINDOW_T_MASK = WINDOW_MASK >> 1,
NTABLE = 1<<(WINDOW-1);
scalar_t scalar1x, scalar2x;
API_NS(scalar_add)(scalar1x, scalar1, point_scalarmul_adjustment);
API_NS(scalar_halve)(scalar1x,scalar1x);
API_NS(scalar_add)(scalar2x, scalar2, point_scalarmul_adjustment);
API_NS(scalar_halve)(scalar2x,scalar2x);
/* Set up a precomputed table with odd multiples of b. */
point_t multiples1[NTABLE], multiples2[NTABLE], working, tmp;
pniels_t pn;
API_NS(point_copy)(working, b);
/* Initialize. */
int i,j;
for (i=0; i<NTABLE; i++) {
API_NS(point_copy)(multiples1[i], API_NS(point_identity));
API_NS(point_copy)(multiples2[i], API_NS(point_identity));
}
for (i=0; i<SCALAR_BITS; i+=WINDOW) {
if (i) {
for (j=0; j<WINDOW-1; j++)
point_double_internal(working, working, -1);
point_double_internal(working, working, 0);
}
/* Fetch another block of bits */
word_t bits1 = scalar1x->limb[i/WBITS] >> (i%WBITS),
bits2 = scalar2x->limb[i/WBITS] >> (i%WBITS);
if (i%WBITS >= WBITS-WINDOW && i/WBITS<SCALAR_LIMBS-1) {
bits1 ^= scalar1x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
bits2 ^= scalar2x->limb[i/WBITS+1] << (WBITS - (i%WBITS));
}
bits1 &= WINDOW_MASK;
bits2 &= WINDOW_MASK;
mask_t inv1 = (bits1>>(WINDOW-1))-1;
mask_t inv2 = (bits2>>(WINDOW-1))-1;
bits1 ^= inv1;
bits2 ^= inv2;
pt_to_pniels(pn, working);
constant_time_lookup(tmp, multiples1, sizeof(tmp), NTABLE, bits1 & WINDOW_T_MASK);
cond_neg_niels(pn->n, inv1);
/* add_pniels_to_pt(multiples1[bits1 & WINDOW_T_MASK], pn, 0); */
add_pniels_to_pt(tmp, pn, 0);
constant_time_insert(multiples1, tmp, sizeof(tmp), NTABLE, bits1 & WINDOW_T_MASK);
constant_time_lookup(tmp, multiples2, sizeof(tmp), NTABLE, bits2 & WINDOW_T_MASK);
cond_neg_niels(pn->n, inv1^inv2);
/* add_pniels_to_pt(multiples2[bits2 & WINDOW_T_MASK], pn, 0); */
add_pniels_to_pt(tmp, pn, 0);
constant_time_insert(multiples2, tmp, sizeof(tmp), NTABLE, bits2 & WINDOW_T_MASK);
}
if (NTABLE > 1) {
API_NS(point_copy)(working, multiples1[NTABLE-1]);
API_NS(point_copy)(tmp , multiples2[NTABLE-1]);
for (i=NTABLE-1; i>1; i--) {
API_NS(point_add)(multiples1[i-1], multiples1[i-1], multiples1[i]);
API_NS(point_add)(multiples2[i-1], multiples2[i-1], multiples2[i]);
API_NS(point_add)(working, working, multiples1[i-1]);
API_NS(point_add)(tmp, tmp, multiples2[i-1]);
}
API_NS(point_add)(multiples1[0], multiples1[0], multiples1[1]);
API_NS(point_add)(multiples2[0], multiples2[0], multiples2[1]);
point_double_internal(working, working, 0);
point_double_internal(tmp, tmp, 0);
API_NS(point_add)(a1, working, multiples1[0]);
API_NS(point_add)(a2, tmp, multiples2[0]);
} else {
API_NS(point_copy)(a1, multiples1[0]);
API_NS(point_copy)(a2, multiples2[0]);
}
cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
cryptonite_decaf_bzero(scalar2x,sizeof(scalar2x));
cryptonite_decaf_bzero(pn,sizeof(pn));
cryptonite_decaf_bzero(multiples1,sizeof(multiples1));
cryptonite_decaf_bzero(multiples2,sizeof(multiples2));
cryptonite_decaf_bzero(tmp,sizeof(tmp));
cryptonite_decaf_bzero(working,sizeof(working));
}
cryptonite_decaf_bool_t API_NS(point_eq) ( const point_t p, const point_t q ) {
/* equality mod 2-torsion compares x/y */
gf a, b;
cryptonite_gf_mul ( a, p->y, q->x );
cryptonite_gf_mul ( b, q->y, p->x );
mask_t succ = cryptonite_gf_eq(a,b);
#if (COFACTOR == 8) && IMAGINE_TWIST
cryptonite_gf_mul ( a, p->y, q->y );
cryptonite_gf_mul ( b, q->x, p->x );
#if !(IMAGINE_TWIST)
cryptonite_gf_sub ( a, ZERO, a );
#else
/* Interesting note: the 4tor would normally be rotation.
* But because of the *i twist, it's actually
* (x,y) <-> (iy,ix)
*/
/* No code, just a comment. */
#endif
succ |= cryptonite_gf_eq(a,b);
#endif
return mask_to_bool(succ);
}
cryptonite_decaf_bool_t API_NS(point_valid) (
const point_t p
) {
gf a,b,c;
cryptonite_gf_mul(a,p->x,p->y);
cryptonite_gf_mul(b,p->z,p->t);
mask_t out = cryptonite_gf_eq(a,b);
cryptonite_gf_sqr(a,p->x);
cryptonite_gf_sqr(b,p->y);
cryptonite_gf_sub(a,b,a);
cryptonite_gf_sqr(b,p->t);
cryptonite_gf_mulw(c,b,TWISTED_D);
cryptonite_gf_sqr(b,p->z);
cryptonite_gf_add(b,b,c);
out &= cryptonite_gf_eq(a,b);
out &= ~cryptonite_gf_eq(p->z,ZERO);
return mask_to_bool(out);
}
void API_NS(point_debugging_torque) (
point_t q,
const point_t p
) {
#if COFACTOR == 8 && IMAGINE_TWIST
gf tmp;
cryptonite_gf_mul(tmp,p->x,SQRT_MINUS_ONE);
cryptonite_gf_mul(q->x,p->y,SQRT_MINUS_ONE);
cryptonite_gf_copy(q->y,tmp);
cryptonite_gf_copy(q->z,p->z);
cryptonite_gf_sub(q->t,ZERO,p->t);
#else
cryptonite_gf_sub(q->x,ZERO,p->x);
cryptonite_gf_sub(q->y,ZERO,p->y);
cryptonite_gf_copy(q->z,p->z);
cryptonite_gf_copy(q->t,p->t);
#endif
}
void API_NS(point_debugging_pscale) (
point_t q,
const point_t p,
const uint8_t factor[SER_BYTES]
) {
gf gfac,tmp;
/* NB this means you'll never pscale by negative numbers for p521 */
ignore_result(cryptonite_gf_deserialize(gfac,factor,0));
cryptonite_gf_cond_sel(gfac,gfac,ONE,cryptonite_gf_eq(gfac,ZERO));
cryptonite_gf_mul(tmp,p->x,gfac);
cryptonite_gf_copy(q->x,tmp);
cryptonite_gf_mul(tmp,p->y,gfac);
cryptonite_gf_copy(q->y,tmp);
cryptonite_gf_mul(tmp,p->z,gfac);
cryptonite_gf_copy(q->z,tmp);
cryptonite_gf_mul(tmp,p->t,gfac);
cryptonite_gf_copy(q->t,tmp);
}
static void cryptonite_gf_batch_invert (
gf *__restrict__ out,
const gf *in,
unsigned int n
) {
gf t1;
assert(n>1);
cryptonite_gf_copy(out[1], in[0]);
int i;
for (i=1; i<(int) (n-1); i++) {
cryptonite_gf_mul(out[i+1], out[i], in[i]);
}
cryptonite_gf_mul(out[0], out[n-1], in[n-1]);
cryptonite_gf_invert(out[0], out[0], 1);
for (i=n-1; i>0; i--) {
cryptonite_gf_mul(t1, out[i], out[0]);
cryptonite_gf_copy(out[i], t1);
cryptonite_gf_mul(t1, out[0], in[i]);
cryptonite_gf_copy(out[0], t1);
}
}
static void batch_normalize_niels (
niels_t *table,
const gf *zs,
gf *__restrict__ zis,
int n
) {
int i;
gf product;
cryptonite_gf_batch_invert(zis, zs, n);
for (i=0; i<n; i++) {
cryptonite_gf_mul(product, table[i]->a, zis[i]);
cryptonite_gf_strong_reduce(product);
cryptonite_gf_copy(table[i]->a, product);
cryptonite_gf_mul(product, table[i]->b, zis[i]);
cryptonite_gf_strong_reduce(product);
cryptonite_gf_copy(table[i]->b, product);
cryptonite_gf_mul(product, table[i]->c, zis[i]);
cryptonite_gf_strong_reduce(product);
cryptonite_gf_copy(table[i]->c, product);
}
cryptonite_decaf_bzero(product,sizeof(product));
}
void API_NS(precompute) (
precomputed_s *table,
const point_t base
) {
const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
assert(n*t*s >= SCALAR_BITS);
point_t working, start, doubles[t-1];
API_NS(point_copy)(working, base);
pniels_t pn_tmp;
gf zs[n<<(t-1)], zis[n<<(t-1)];
unsigned int i,j,k;
/* Compute n tables */
for (i=0; i<n; i++) {
/* Doubling phase */
for (j=0; j<t; j++) {
if (j) API_NS(point_add)(start, start, working);
else API_NS(point_copy)(start, working);
if (j==t-1 && i==n-1) break;
point_double_internal(working, working,0);
if (j<t-1) API_NS(point_copy)(doubles[j], working);
for (k=0; k<s-1; k++)
point_double_internal(working, working, k<s-2);
}
/* Gray-code phase */
for (j=0;; j++) {
int gray = j ^ (j>>1);
int idx = (((i+1)<<(t-1))-1) ^ gray;
pt_to_pniels(pn_tmp, start);
memcpy(table->table[idx], pn_tmp->n, sizeof(pn_tmp->n));
cryptonite_gf_copy(zs[idx], pn_tmp->z);
if (j >= (1u<<(t-1)) - 1) break;
int delta = (j+1) ^ ((j+1)>>1) ^ gray;
for (k=0; delta>1; k++)
delta >>=1;
if (gray & (1<<k)) {
API_NS(point_add)(start, start, doubles[k]);
} else {
API_NS(point_sub)(start, start, doubles[k]);
}
}
}
batch_normalize_niels(table->table,(const gf *)zs,zis,n<<(t-1));
cryptonite_decaf_bzero(zs,sizeof(zs));
cryptonite_decaf_bzero(zis,sizeof(zis));
cryptonite_decaf_bzero(pn_tmp,sizeof(pn_tmp));
cryptonite_decaf_bzero(working,sizeof(working));
cryptonite_decaf_bzero(start,sizeof(start));
cryptonite_decaf_bzero(doubles,sizeof(doubles));
}
static CRYPTONITE_DECAF_INLINE void
constant_time_lookup_niels (
niels_s *__restrict__ ni,
const niels_t *table,
int nelts,
int idx
) {
constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
}
void API_NS(precomputed_scalarmul) (
point_t out,
const precomputed_s *table,
const scalar_t scalar
) {
int i;
unsigned j,k;
const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
scalar_t scalar1x;
API_NS(scalar_add)(scalar1x, scalar, precomputed_scalarmul_adjustment);
API_NS(scalar_halve)(scalar1x,scalar1x);
niels_t ni;
for (i=s-1; i>=0; i--) {
if (i != (int)s-1) point_double_internal(out,out,0);
for (j=0; j<n; j++) {
int tab = 0;
for (k=0; k<t; k++) {
unsigned int bit = i + s*(k + j*t);
if (bit < SCALAR_BITS) {
tab |= (scalar1x->limb[bit/WBITS] >> (bit%WBITS) & 1) << k;
}
}
mask_t invert = (tab>>(t-1))-1;
tab ^= invert;
tab &= (1<<(t-1)) - 1;
constant_time_lookup_niels(ni, &table->table[j<<(t-1)], 1<<(t-1), tab);
cond_neg_niels(ni, invert);
if ((i!=(int)s-1)||j) {
add_niels_to_pt(out, ni, j==n-1 && i);
} else {
niels_to_pt(out, ni);
}
}
}
cryptonite_decaf_bzero(ni,sizeof(ni));
cryptonite_decaf_bzero(scalar1x,sizeof(scalar1x));
}
void API_NS(point_cond_sel) (
point_t out,
const point_t a,
const point_t b,
cryptonite_decaf_bool_t pick_b
) {
constant_time_select(out,a,b,sizeof(point_t),bool_to_mask(pick_b),0);
}
/* FUTURE: restore Curve25519 Montgomery ladder? */
cryptonite_decaf_error_t API_NS(direct_scalarmul) (
uint8_t scaled[SER_BYTES],
const uint8_t base[SER_BYTES],
const scalar_t scalar,
cryptonite_decaf_bool_t allow_identity,
cryptonite_decaf_bool_t short_circuit
) {
point_t basep;
cryptonite_decaf_error_t succ = API_NS(point_decode)(basep, base, allow_identity);
if (short_circuit && succ != CRYPTONITE_DECAF_SUCCESS) return succ;
API_NS(point_cond_sel)(basep, API_NS(point_base), basep, succ);
API_NS(point_scalarmul)(basep, basep, scalar);
API_NS(point_encode)(scaled, basep);
API_NS(point_destroy)(basep);
return succ;
}
void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
uint8_t enc[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES],
const point_t p
) {
/* The point is now on the twisted curve. Move it to untwisted. */
gf x, y, z, t;
point_t q;
#if COFACTOR == 8
API_NS(point_double)(q,p);
#else
API_NS(point_copy)(q,p);
#endif
#if EDDSA_USE_SIGMA_ISOGENY
{
/* Use 4-isogeny like ed25519:
* 2*x*y*sqrt(d/a-1)/(ax^2 + y^2 - 2)
* (y^2 - ax^2)/(y^2 + ax^2)
* with a = -1, d = -EDWARDS_D:
* -2xysqrt(EDWARDS_D-1)/(2z^2-y^2+x^2)
* (y^2+x^2)/(y^2-x^2)
*/
gf u;
cryptonite_gf_sqr ( x, q->x ); // x^2
cryptonite_gf_sqr ( t, q->y ); // y^2
cryptonite_gf_add( u, x, t ); // x^2 + y^2
cryptonite_gf_add( z, q->y, q->x );
cryptonite_gf_sqr ( y, z);
cryptonite_gf_sub ( y, u, y ); // -2xy
cryptonite_gf_sub ( z, t, x ); // y^2 - x^2
cryptonite_gf_sqr ( x, q->z );
cryptonite_gf_add ( t, x, x);
cryptonite_gf_sub ( t, t, z); // 2z^2 - y^2 + x^2
cryptonite_gf_mul ( x, y, z ); // 2xy(y^2-x^2)
cryptonite_gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
cryptonite_gf_mul ( u, z, t );
cryptonite_gf_copy( z, u );
cryptonite_gf_mul ( u, x, SQRT_ONE_MINUS_D );
cryptonite_gf_copy( x, u );
cryptonite_decaf_bzero(u,sizeof(u));
}
#elif IMAGINE_TWIST
{
API_NS(point_double)(q,q);
API_NS(point_double)(q,q);
cryptonite_gf_mul_qnr(x, q->x);
cryptonite_gf_copy(y, q->y);
cryptonite_gf_copy(z, q->z);
}
#else
{
/* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
gf u;
cryptonite_gf_sqr ( x, q->x );
cryptonite_gf_sqr ( t, q->y );
cryptonite_gf_add( u, x, t );
cryptonite_gf_add( z, q->y, q->x );
cryptonite_gf_sqr ( y, z);
cryptonite_gf_sub ( y, u, y );
cryptonite_gf_sub ( z, t, x );
cryptonite_gf_sqr ( x, q->z );
cryptonite_gf_add ( t, x, x);
cryptonite_gf_sub ( t, t, z);
cryptonite_gf_mul ( x, t, y );
cryptonite_gf_mul ( y, z, u );
cryptonite_gf_mul ( z, u, t );
cryptonite_decaf_bzero(u,sizeof(u));
}
#endif
/* Affinize */
cryptonite_gf_invert(z,z,1);
cryptonite_gf_mul(t,x,z);
cryptonite_gf_mul(x,y,z);
/* Encode */
enc[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] = 0;
cryptonite_gf_serialize(enc, x, 1);
enc[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] |= 0x80 & cryptonite_gf_lobit(t);
cryptonite_decaf_bzero(x,sizeof(x));
cryptonite_decaf_bzero(y,sizeof(y));
cryptonite_decaf_bzero(z,sizeof(z));
cryptonite_decaf_bzero(t,sizeof(t));
API_NS(point_destroy)(q);
}
cryptonite_decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
point_t p,
const uint8_t enc[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES]
) {
uint8_t enc2[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES];
memcpy(enc2,enc,sizeof(enc2));
mask_t low = ~word_is_zero(enc2[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] & 0x80);
enc2[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1] &= ~0x80;
mask_t succ = cryptonite_gf_deserialize(p->y, enc2, 1);
#if 0 == 0
succ &= word_is_zero(enc2[CRYPTONITE_DECAF_EDDSA_448_PRIVATE_BYTES-1]);
#endif
cryptonite_gf_sqr(p->x,p->y);
cryptonite_gf_sub(p->z,ONE,p->x); /* num = 1-y^2 */
#if EDDSA_USE_SIGMA_ISOGENY
cryptonite_gf_mulw(p->t,p->z,EDWARDS_D); /* d-dy^2 */
cryptonite_gf_mulw(p->x,p->z,EDWARDS_D-1); /* num = (1-y^2)(d-1) */
cryptonite_gf_copy(p->z,p->x);
#else
cryptonite_gf_mulw(p->t,p->x,EDWARDS_D); /* dy^2 */
#endif
cryptonite_gf_sub(p->t,ONE,p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
cryptonite_gf_mul(p->x,p->z,p->t);
succ &= cryptonite_gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
cryptonite_gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
cryptonite_gf_cond_neg(p->x,~cryptonite_gf_lobit(p->x)^low);
cryptonite_gf_copy(p->z,ONE);
#if EDDSA_USE_SIGMA_ISOGENY
{
/* Use 4-isogeny like ed25519:
* 2*x*y/sqrt(1-d/a)/(ax^2 + y^2 - 2)
* (y^2 - ax^2)/(y^2 + ax^2)
* (MAGIC: above formula may be off by a factor of -a
* or something somewhere; check it for other a)
*
* with a = -1, d = -EDWARDS_D:
* -2xy/sqrt(1-EDWARDS_D)/(2z^2-y^2+x^2)
* (y^2+x^2)/(y^2-x^2)
*/
gf a, b, c, d;
cryptonite_gf_sqr ( c, p->x );
cryptonite_gf_sqr ( a, p->y );
cryptonite_gf_add ( d, c, a ); // x^2 + y^2
cryptonite_gf_add ( p->t, p->y, p->x );
cryptonite_gf_sqr ( b, p->t );
cryptonite_gf_sub ( b, b, d ); // 2xy
cryptonite_gf_sub ( p->t, a, c ); // y^2 - x^2
cryptonite_gf_sqr ( p->x, p->z );
cryptonite_gf_add ( p->z, p->x, p->x );
cryptonite_gf_sub ( a, p->z, p->t ); // 2z^2 - y^2 + x^2
cryptonite_gf_mul ( c, a, SQRT_ONE_MINUS_D );
cryptonite_gf_mul ( p->x, b, p->t); // (2xy)(y^2-x^2)
cryptonite_gf_mul ( p->z, p->t, c ); // (y^2-x^2)sd(2z^2 - y^2 + x^2)
cryptonite_gf_mul ( p->y, d, c ); // (y^2+x^2)sd(2z^2 - y^2 + x^2)
cryptonite_gf_mul ( p->t, d, b );
cryptonite_decaf_bzero(a,sizeof(a));
cryptonite_decaf_bzero(b,sizeof(b));
cryptonite_decaf_bzero(c,sizeof(c));
cryptonite_decaf_bzero(d,sizeof(d));
}
#elif IMAGINE_TWIST
{
cryptonite_gf_mul(p->t,p->x,SQRT_MINUS_ONE);
cryptonite_gf_copy(p->x,p->t);
cryptonite_gf_mul(p->t,p->x,p->y);
}
#else
{
/* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
gf a, b, c, d;
cryptonite_gf_sqr ( c, p->x );
cryptonite_gf_sqr ( a, p->y );
cryptonite_gf_add ( d, c, a );
cryptonite_gf_add ( p->t, p->y, p->x );
cryptonite_gf_sqr ( b, p->t );
cryptonite_gf_sub ( b, b, d );
cryptonite_gf_sub ( p->t, a, c );
cryptonite_gf_sqr ( p->x, p->z );
cryptonite_gf_add ( p->z, p->x, p->x );
cryptonite_gf_sub ( a, p->z, d );
cryptonite_gf_mul ( p->x, a, b );
cryptonite_gf_mul ( p->z, p->t, a );
cryptonite_gf_mul ( p->y, p->t, d );
cryptonite_gf_mul ( p->t, b, d );
cryptonite_decaf_bzero(a,sizeof(a));
cryptonite_decaf_bzero(b,sizeof(b));
cryptonite_decaf_bzero(c,sizeof(c));
cryptonite_decaf_bzero(d,sizeof(d));
}
#endif
cryptonite_decaf_bzero(enc2,sizeof(enc2));
assert(API_NS(point_valid)(p) || ~succ);
return cryptonite_decaf_succeed_if(mask_to_bool(succ));
}
cryptonite_decaf_error_t cryptonite_decaf_x448 (
uint8_t out[X_PUBLIC_BYTES],
const uint8_t base[X_PUBLIC_BYTES],
const uint8_t scalar[X_PRIVATE_BYTES]
) {
gf x1, x2, z2, x3, z3, t1, t2;
ignore_result(cryptonite_gf_deserialize(x1,base,1));
cryptonite_gf_copy(x2,ONE);
cryptonite_gf_copy(z2,ZERO);
cryptonite_gf_copy(x3,x1);
cryptonite_gf_copy(z3,ONE);
int t;
mask_t swap = 0;
for (t = X_PRIVATE_BITS-1; t>=0; t--) {
uint8_t sb = scalar[t/8];
/* Scalar conditioning */
if (t/8==0) sb &= -(uint8_t)COFACTOR;
else if (t == X_PRIVATE_BITS-1) sb = -1;
mask_t k_t = (sb>>(t%8)) & 1;
k_t = -k_t; /* set to all 0s or all 1s */
swap ^= k_t;
cryptonite_gf_cond_swap(x2,x3,swap);
cryptonite_gf_cond_swap(z2,z3,swap);
swap = k_t;
cryptonite_gf_add_nr(t1,x2,z2); /* A = x2 + z2 */ /* 2+e */
cryptonite_gf_sub_nr(t2,x2,z2); /* B = x2 - z2 */ /* 3+e */
cryptonite_gf_sub_nr(z2,x3,z3); /* D = x3 - z3 */ /* 3+e */
cryptonite_gf_mul(x2,t1,z2); /* DA */
cryptonite_gf_add_nr(z2,z3,x3); /* C = x3 + z3 */ /* 2+e */
cryptonite_gf_mul(x3,t2,z2); /* CB */
cryptonite_gf_sub_nr(z3,x2,x3); /* DA-CB */ /* 3+e */
cryptonite_gf_sqr(z2,z3); /* (DA-CB)^2 */
cryptonite_gf_mul(z3,x1,z2); /* z3 = x1(DA-CB)^2 */
cryptonite_gf_add_nr(z2,x2,x3); /* (DA+CB) */ /* 2+e */
cryptonite_gf_sqr(x3,z2); /* x3 = (DA+CB)^2 */
cryptonite_gf_sqr(z2,t1); /* AA = A^2 */
cryptonite_gf_sqr(t1,t2); /* BB = B^2 */
cryptonite_gf_mul(x2,z2,t1); /* x2 = AA*BB */
cryptonite_gf_sub_nr(t2,z2,t1); /* E = AA-BB */ /* 3+e */
cryptonite_gf_mulw(t1,t2,-EDWARDS_D); /* E*-d = a24*E */
cryptonite_gf_add_nr(t1,t1,z2); /* AA + a24*E */ /* 2+e */
cryptonite_gf_mul(z2,t2,t1); /* z2 = E(AA+a24*E) */
}
/* Finish */
cryptonite_gf_cond_swap(x2,x3,swap);
cryptonite_gf_cond_swap(z2,z3,swap);
cryptonite_gf_invert(z2,z2,0);
cryptonite_gf_mul(x1,x2,z2);
cryptonite_gf_serialize(out,x1,1);
mask_t nz = ~cryptonite_gf_eq(x1,ZERO);
cryptonite_decaf_bzero(x1,sizeof(x1));
cryptonite_decaf_bzero(x2,sizeof(x2));
cryptonite_decaf_bzero(z2,sizeof(z2));
cryptonite_decaf_bzero(x3,sizeof(x3));
cryptonite_decaf_bzero(z3,sizeof(z3));
cryptonite_decaf_bzero(t1,sizeof(t1));
cryptonite_decaf_bzero(t2,sizeof(t2));
return cryptonite_decaf_succeed_if(mask_to_bool(nz));
}
/* Thanks Johan Pascal */
void cryptonite_decaf_ed448_convert_public_key_to_x448 (
uint8_t x[CRYPTONITE_DECAF_X448_PUBLIC_BYTES],
const uint8_t ed[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES]
) {
gf y;
{
uint8_t enc2[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES];
memcpy(enc2,ed,sizeof(enc2));
/* retrieve y from the ed compressed point */
enc2[CRYPTONITE_DECAF_EDDSA_448_PUBLIC_BYTES-1] &= ~0x80;
ignore_result(cryptonite_gf_deserialize(y, enc2, 0));
cryptonite_decaf_bzero(enc2,sizeof(enc2));
}
{
gf n,d;
#if EDDSA_USE_SIGMA_ISOGENY
/* u = (1+y)/(1-y)*/
cryptonite_gf_add(n, y, ONE); /* n = y+1 */
cryptonite_gf_sub(d, ONE, y); /* d = 1-y */
cryptonite_gf_invert(d, d, 0); /* d = 1/(1-y) */
cryptonite_gf_mul(y, n, d); /* u = (y+1)/(1-y) */
cryptonite_gf_serialize(x,y,1);
#else /* EDDSA_USE_SIGMA_ISOGENY */
/* u = y^2 * (1-dy^2) / (1-y^2) */
cryptonite_gf_sqr(n,y); /* y^2*/
cryptonite_gf_sub(d,ONE,n); /* 1-y^2*/
cryptonite_gf_invert(d,d,0); /* 1/(1-y^2)*/
cryptonite_gf_mul(y,n,d); /* y^2 / (1-y^2) */
cryptonite_gf_mulw(d,n,EDWARDS_D); /* dy^2*/
cryptonite_gf_sub(d, ONE, d); /* 1-dy^2*/
cryptonite_gf_mul(n, y, d); /* y^2 * (1-dy^2) / (1-y^2) */
cryptonite_gf_serialize(x,n,1);
#endif /* EDDSA_USE_SIGMA_ISOGENY */
cryptonite_decaf_bzero(y,sizeof(y));
cryptonite_decaf_bzero(n,sizeof(n));
cryptonite_decaf_bzero(d,sizeof(d));
}
}
void cryptonite_decaf_x448_generate_key (
uint8_t out[X_PUBLIC_BYTES],
const uint8_t scalar[X_PRIVATE_BYTES]
) {
cryptonite_decaf_x448_derive_public_key(out,scalar);
}
void cryptonite_decaf_x448_derive_public_key (
uint8_t out[X_PUBLIC_BYTES],
const uint8_t scalar[X_PRIVATE_BYTES]
) {
/* Scalar conditioning */
uint8_t scalar2[X_PRIVATE_BYTES];
memcpy(scalar2,scalar,sizeof(scalar2));
scalar2[0] &= -(uint8_t)COFACTOR;
scalar2[X_PRIVATE_BYTES-1] &= ~(-1u<<((X_PRIVATE_BITS+7)%8));
scalar2[X_PRIVATE_BYTES-1] |= 1<<((X_PRIVATE_BITS+7)%8);
scalar_t the_scalar;
API_NS(scalar_decode_long)(the_scalar,scalar2,sizeof(scalar2));
/* We're gonna isogenize by 2, so divide by 2.
*
* Why by 2, even though it's a 4-isogeny?
*
* The isogeny map looks like
* Montgomery <-2-> Jacobi <-2-> Edwards
*
* Since the Jacobi base point is the PREimage of the iso to
* the Montgomery curve, and we're going
* Jacobi -> Edwards -> Jacobi -> Montgomery,
* we pick up only a factor of 2 over Jacobi -> Montgomery.
*/
API_NS(scalar_halve)(the_scalar,the_scalar);
point_t p;
API_NS(precomputed_scalarmul)(p,API_NS(precomputed_base),the_scalar);
/* Isogenize to Montgomery curve.
*
* Why isn't this just a separate function, eg cryptonite_decaf_encode_like_x448?
* Basically because in general it does the wrong thing if there is a cofactor
* component in the input. In this function though, there isn't a cofactor
* component in the input.
*/
cryptonite_gf_invert(p->t,p->x,0); /* 1/x */
cryptonite_gf_mul(p->z,p->t,p->y); /* y/x */
cryptonite_gf_sqr(p->y,p->z); /* (y/x)^2 */
#if IMAGINE_TWIST
cryptonite_gf_sub(p->y,ZERO,p->y);
#endif
cryptonite_gf_serialize(out,p->y,1);
cryptonite_decaf_bzero(scalar2,sizeof(scalar2));
API_NS(scalar_destroy)(the_scalar);
API_NS(point_destroy)(p);
}
/**
* @cond internal
* Control for variable-time scalar multiply algorithms.
*/
struct smvt_control {
int power, addend;
};
static int recode_wnaf (
struct smvt_control *control, /* [nbits/(table_bits+1) + 3] */
const scalar_t scalar,
unsigned int table_bits
) {
unsigned int table_size = SCALAR_BITS/(table_bits+1) + 3;
int position = table_size - 1; /* at the end */
/* place the end marker */
control[position].power = -1;
control[position].addend = 0;
position--;
/* PERF: Could negate scalar if it's large. But then would need more cases
* in the actual code that uses it, all for an expected reduction of like 1/5 op.
* Probably not worth it.
*/
uint64_t current = scalar->limb[0] & 0xFFFF;
uint32_t mask = (1<<(table_bits+1))-1;
unsigned int w;
const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
for (w = 1; w<(SCALAR_BITS-1)/16+3; w++) {
if (w < (SCALAR_BITS-1)/16+1) {
/* Refill the 16 high bits of current */
current += (uint32_t)((scalar->limb[w/B_OVER_16]>>(16*(w%B_OVER_16)))<<16);
}
while (current & 0xFFFF) {
assert(position >= 0);
uint32_t pos = __builtin_ctz((uint32_t)current), odd = (uint32_t)current >> pos;
int32_t delta = odd & mask;
if (odd & 1<<(table_bits+1)) delta -= (1<<(table_bits+1));
current -= delta << pos;
control[position].power = pos + 16*(w-1);
control[position].addend = delta;
position--;
}
current >>= 16;
}
assert(current==0);
position++;
unsigned int n = table_size - position;
unsigned int i;
for (i=0; i<n; i++) {
control[i] = control[i+position];
}
return n-1;
}
static void
prepare_wnaf_table(
pniels_t *output,
const point_t working,
unsigned int tbits
) {
point_t tmp;
int i;
pt_to_pniels(output[0], working);
if (tbits == 0) return;
API_NS(point_double)(tmp,working);
pniels_t twop;
pt_to_pniels(twop, tmp);
add_pniels_to_pt(tmp, output[0],0);
pt_to_pniels(output[1], tmp);
for (i=2; i < 1<<tbits; i++) {
add_pniels_to_pt(tmp, twop,0);
pt_to_pniels(output[i], tmp);
}
API_NS(point_destroy)(tmp);
cryptonite_decaf_bzero(twop,sizeof(twop));
}
extern const gf API_NS(precomputed_wnaf_as_fe)[];
static const niels_t *API_NS(wnaf_base) = (const niels_t *)API_NS(precomputed_wnaf_as_fe);
const size_t API_NS(sizeof_precomputed_wnafs)
= sizeof(niels_t)<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS;
void API_NS(precompute_wnafs) (
niels_t out[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS],
const point_t base
);
void API_NS(precompute_wnafs) (
niels_t out[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS],
const point_t base
) {
pniels_t tmp[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS];
gf zs[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS], zis[1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS];
int i;
prepare_wnaf_table(tmp,base,CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS);
for (i=0; i<1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS; i++) {
memcpy(out[i], tmp[i]->n, sizeof(niels_t));
cryptonite_gf_copy(zs[i], tmp[i]->z);
}
batch_normalize_niels(out, (const gf *)zs, zis, 1<<CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS);
cryptonite_decaf_bzero(tmp,sizeof(tmp));
cryptonite_decaf_bzero(zs,sizeof(zs));
cryptonite_decaf_bzero(zis,sizeof(zis));
}
void API_NS(base_double_scalarmul_non_secret) (
point_t combo,
const scalar_t scalar1,
const point_t base2,
const scalar_t scalar2
) {
const int table_bits_var = CRYPTONITE_DECAF_WNAF_VAR_TABLE_BITS,
table_bits_pre = CRYPTONITE_DECAF_WNAF_FIXED_TABLE_BITS;
struct smvt_control control_var[SCALAR_BITS/(table_bits_var+1)+3];
struct smvt_control control_pre[SCALAR_BITS/(table_bits_pre+1)+3];
int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
pniels_t precmp_var[1<<table_bits_var];
prepare_wnaf_table(precmp_var, base2, table_bits_var);
int contp=0, contv=0, i = control_var[0].power;
if (i < 0) {
API_NS(point_copy)(combo, API_NS(point_identity));
return;
} else if (i > control_pre[0].power) {
pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
contv++;
} else if (i == control_pre[0].power && i >=0 ) {
pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
add_niels_to_pt(combo, API_NS(wnaf_base)[control_pre[0].addend >> 1], i);
contv++; contp++;
} else {
i = control_pre[0].power;
niels_to_pt(combo, API_NS(wnaf_base)[control_pre[0].addend >> 1]);
contp++;
}
for (i--; i >= 0; i--) {
int cv = (i==control_var[contv].power), cp = (i==control_pre[contp].power);
point_double_internal(combo,combo,i && !(cv||cp));
if (cv) {
assert(control_var[contv].addend);
if (control_var[contv].addend > 0) {
add_pniels_to_pt(combo, precmp_var[control_var[contv].addend >> 1], i&&!cp);
} else {
sub_pniels_from_pt(combo, precmp_var[(-control_var[contv].addend) >> 1], i&&!cp);
}
contv++;
}
if (cp) {
assert(control_pre[contp].addend);
if (control_pre[contp].addend > 0) {
add_niels_to_pt(combo, API_NS(wnaf_base)[control_pre[contp].addend >> 1], i);
} else {
sub_niels_from_pt(combo, API_NS(wnaf_base)[(-control_pre[contp].addend) >> 1], i);
}
contp++;
}
}
/* This function is non-secret, but whatever this is cheap. */
cryptonite_decaf_bzero(control_var,sizeof(control_var));
cryptonite_decaf_bzero(control_pre,sizeof(control_pre));
cryptonite_decaf_bzero(precmp_var,sizeof(precmp_var));
assert(contv == ncb_var); (void)ncb_var;
assert(contp == ncb_pre); (void)ncb_pre;
}
void API_NS(point_destroy) (
point_t point
) {
cryptonite_decaf_bzero(point, sizeof(point_t));
}
void API_NS(precomputed_destroy) (
precomputed_s *pre
) {
cryptonite_decaf_bzero(pre, API_NS(sizeof_precomputed_s));
}