/*
- * Copyright 2017 The OpenSSL Project Authors. All Rights Reserved.
+ * Copyright 2017-2018 The OpenSSL Project Authors. All Rights Reserved.
* Copyright 2015-2016 Cryptography Research, Inc.
*
* Licensed under the OpenSSL license (the "License"). You may not use
#define COFACTOR 4
-/* Comb config: number of combs, n, t, s. */
-#define COMBS_N 5
-#define COMBS_T 5
-#define COMBS_S 18
-#define DECAF_WINDOW_BITS 5
-#define DECAF_WNAF_FIXED_TABLE_BITS 5
-#define DECAF_WNAF_VAR_TABLE_BITS 3
+#define C448_WNAF_FIXED_TABLE_BITS 5
+#define C448_WNAF_VAR_TABLE_BITS 3
static const int EDWARDS_D = -39081;
-static const curve448_scalar_t precomputed_scalarmul_adjustment = { {{
- SC_LIMB
- (0xc873d6d54a7bb0cf),
- SC_LIMB
- (0xe933d8d723a70aad),
- SC_LIMB
- (0xbb124b65129c96fd),
- SC_LIMB
- (0x00000008335dc163)
- }}
+static const curve448_scalar_t precomputed_scalarmul_adjustment = {
+ {
+ {
+ SC_LIMB(0xc873d6d54a7bb0cf), SC_LIMB(0xe933d8d723a70aad),
+ SC_LIMB(0xbb124b65129c96fd), SC_LIMB(0x00000008335dc163)
+ }
+ }
};
-const uint8_t decaf_x448_base_point[DECAF_X448_PUBLIC_BYTES] = { 0x05 };
-
#define TWISTED_D ((EDWARDS_D)-1)
-#define EFF_D (-(TWISTED_D))
-#define NEG_D 1
-
-/* End of template stuff */
-
-#define WBITS DECAF_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
-
-/* 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 curve448_precomputed_s {
- niels_t table[COMBS_N << (COMBS_T - 1)];
-};
+#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
-extern const gf curve448_precomputed_base_as_fe[];
-const curve448_precomputed_s *curve448_precomputed_base =
- (const curve448_precomputed_s *)&curve448_precomputed_base_as_fe;
-
-/** Inverse. */
+/* Inverse. */
static void gf_invert(gf y, const gf x, int assert_nonzero)
{
mask_t ret;
-
gf t1, t2;
+
gf_sqr(t1, x); /* o^2 */
ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
(void)ret;
const curve448_point_t curve448_point_identity =
{ {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} };
-static void
-point_double_internal(curve448_point_t p,
- const curve448_point_t q, int before_double)
+static void point_double_internal(curve448_point_t p, const curve448_point_t q,
+ int before_double)
{
gf a, b, c, d;
+
gf_sqr(c, q->x);
gf_sqr(a, q->y);
gf_add_nr(d, c, a); /* 2+e */
static void pniels_to_pt(curve448_point_t e, const pniels_t d)
{
gf eu;
+
gf_add(eu, d->n->b, d->n->a);
gf_sub(e->y, d->n->b, d->n->a);
gf_mul(e->t, e->y, eu);
gf_copy(e->z, ONE);
}
-static void
-add_niels_to_pt(curve448_point_t d, const niels_t e, int before_double)
+static void add_niels_to_pt(curve448_point_t d, const niels_t e,
+ int before_double)
{
gf a, b, c;
+
gf_sub_nr(b, d->y, d->x); /* 3+e */
gf_mul(a, e->a, b);
gf_add_nr(b, d->x, d->y); /* 2+e */
gf_mul(d->t, b, c);
}
-static void
-sub_niels_from_pt(curve448_point_t d, const niels_t e, int before_double)
+static void sub_niels_from_pt(curve448_point_t d, const niels_t e,
+ int before_double)
{
gf a, b, c;
+
gf_sub_nr(b, d->y, d->x); /* 3+e */
gf_mul(a, e->b, b);
gf_add_nr(b, d->x, d->y); /* 2+e */
gf_mul(d->t, b, c);
}
-static void
-add_pniels_to_pt(curve448_point_t p, const pniels_t pn, int before_double)
+static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn,
+ int before_double)
{
gf L0;
+
gf_mul(L0, p->z, pn->z);
gf_copy(p->z, L0);
add_niels_to_pt(p, pn->n, before_double);
}
-static void
-sub_pniels_from_pt(curve448_point_t p, const pniels_t pn, int before_double)
+static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn,
+ int before_double)
{
gf L0;
+
gf_mul(L0, p->z, pn->z);
gf_copy(p->z, L0);
sub_niels_from_pt(p, pn->n, before_double);
}
-decaf_bool_t curve448_point_eq(const curve448_point_t p,
- const curve448_point_t q)
+c448_bool_t curve448_point_eq(const curve448_point_t p,
+ const curve448_point_t q)
{
mask_t succ;
+ gf a, b;
/* equality mod 2-torsion compares x/y */
- gf a, b;
gf_mul(a, p->y, q->x);
gf_mul(b, q->y, p->x);
succ = gf_eq(a, b);
return mask_to_bool(succ);
}
-decaf_bool_t curve448_point_valid(const curve448_point_t p)
+c448_bool_t curve448_point_valid(const curve448_point_t p)
{
mask_t out;
-
gf a, b, c;
+
gf_mul(a, p->x, p->y);
gf_mul(b, p->z, p->t);
out = gf_eq(a, b);
return mask_to_bool(out);
}
-static ossl_inline void
-constant_time_lookup_niels(niels_s * __restrict__ ni,
- const niels_t * table, int nelts, int idx)
+static ossl_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);
}
const curve448_precomputed_s * table,
const curve448_scalar_t scalar)
{
- int i;
- unsigned j, k;
+ unsigned int i, j, k;
const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
niels_t ni;
-
curve448_scalar_t scalar1x;
+
curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
curve448_scalar_halve(scalar1x, scalar1x);
- for (i = s - 1; i >= 0; i--) {
- if (i != (int)s - 1)
+ for (i = s; i > 0; i--) {
+ if (i != s)
point_double_internal(out, out, 0);
for (j = 0; j < n; j++) {
mask_t invert;
for (k = 0; k < t; k++) {
- unsigned int bit = i + s * (k + j * t);
- if (bit < DECAF_448_SCALAR_BITS) {
+ unsigned int bit = (i - 1) + s * (k + j * t);
+
+ if (bit < C448_SCALAR_BITS)
tab |=
(scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
- }
}
invert = (tab >> (t - 1)) - 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 {
+ if ((i != s) || j != 0)
+ add_niels_to_pt(out, ni, j == n - 1 && i != 1);
+ else
niels_to_pt(out, ni);
- }
}
}
OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
}
-void curve448_point_mul_by_ratio_and_encode_like_eddsa(uint8_t
- enc
- [DECAF_EDDSA_448_PUBLIC_BYTES],
- const curve448_point_t p)
+void curve448_point_mul_by_ratio_and_encode_like_eddsa(
+ uint8_t enc[EDDSA_448_PUBLIC_BYTES],
+ const curve448_point_t p)
{
-
- /* The point is now on the twisted curve. Move it to untwisted. */
gf x, y, z, t;
curve448_point_t q;
+
+ /* The point is now on the twisted curve. Move it to untwisted. */
curve448_point_copy(q, p);
{
/* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
gf u;
+
gf_sqr(x, q->x);
gf_sqr(t, q->y);
gf_add(u, x, t);
gf_mul(x, y, z);
/* Encode */
- enc[DECAF_EDDSA_448_PRIVATE_BYTES - 1] = 0;
+ enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;
gf_serialize(enc, x, 1);
- enc[DECAF_EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
+ enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
OPENSSL_cleanse(x, sizeof(x));
OPENSSL_cleanse(y, sizeof(y));
curve448_point_destroy(q);
}
-decaf_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio(curve448_point_t
- p,
- const uint8_t
- enc
- [DECAF_EDDSA_448_PUBLIC_BYTES]
- )
+c448_error_t curve448_point_decode_like_eddsa_and_mul_by_ratio(
+ curve448_point_t p,
+ const uint8_t enc[EDDSA_448_PUBLIC_BYTES])
{
- uint8_t enc2[DECAF_EDDSA_448_PUBLIC_BYTES];
+ uint8_t enc2[EDDSA_448_PUBLIC_BYTES];
mask_t low;
mask_t succ;
memcpy(enc2, enc, sizeof(enc2));
- low = ~word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
- enc2[DECAF_EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
+ low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
+ enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
succ = gf_deserialize(p->y, enc2, 1, 0);
-#if 0 == 0
- succ &= word_is_zero(enc2[DECAF_EDDSA_448_PRIVATE_BYTES - 1]);
-#endif
+ succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);
gf_sqr(p->x, p->y);
gf_sub(p->z, ONE, p->x); /* num = 1-y^2 */
gf_copy(p->z, ONE);
{
- /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
gf a, b, c, d;
+
+ /* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
gf_sqr(c, p->x);
gf_sqr(a, p->y);
gf_add(d, c, a);
OPENSSL_cleanse(enc2, sizeof(enc2));
assert(curve448_point_valid(p) || ~succ);
- return decaf_succeed_if(mask_to_bool(succ));
+ return c448_succeed_if(mask_to_bool(succ));
}
-decaf_error_t decaf_x448(uint8_t out[X_PUBLIC_BYTES],
- const uint8_t base[X_PUBLIC_BYTES],
- const uint8_t scalar[X_PRIVATE_BYTES]
- )
+c448_error_t x448_int(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;
int t;
sb = -1;
k_t = (sb >> (t % 8)) & 1;
- k_t = -k_t; /* set to all 0s or all 1s */
+ k_t = 0 - k_t; /* set to all 0s or all 1s */
swap ^= k_t;
gf_cond_swap(x2, x3, swap);
OPENSSL_cleanse(t1, sizeof(t1));
OPENSSL_cleanse(t2, sizeof(t2));
- return decaf_succeed_if(mask_to_bool(nz));
-}
-
-/* Thanks Johan Pascal */
-void decaf_ed448_convert_public_key_to_x448(uint8_t x[DECAF_X448_PUBLIC_BYTES],
- const uint8_t
- ed[DECAF_EDDSA_448_PUBLIC_BYTES]
- )
-{
- gf y;
- const uint8_t mask = (uint8_t)(0xFE << (7));
- ignore_result(gf_deserialize(y, ed, 1, mask));
-
- {
- gf n, d;
-
- /* u = y^2 * (1-dy^2) / (1-y^2) */
- gf_sqr(n, y); /* y^2 */
- gf_sub(d, ONE, n); /* 1-y^2 */
- gf_invert(d, d, 0); /* 1/(1-y^2) */
- gf_mul(y, n, d); /* y^2 / (1-y^2) */
- gf_mulw(d, n, EDWARDS_D); /* dy^2 */
- gf_sub(d, ONE, d); /* 1-dy^2 */
- gf_mul(n, y, d); /* y^2 * (1-dy^2) / (1-y^2) */
- gf_serialize(x, n, 1);
-
- OPENSSL_cleanse(y, sizeof(y));
- OPENSSL_cleanse(n, sizeof(n));
- OPENSSL_cleanse(d, sizeof(d));
- }
+ return c448_succeed_if(mask_to_bool(nz));
}
void curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t
const curve448_point_t p)
{
curve448_point_t q;
+
curve448_point_copy(q, p);
gf_invert(q->t, q->x, 0); /* 1/x */
gf_mul(q->z, q->t, q->y); /* y/x */
curve448_point_destroy(q);
}
-void decaf_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],
- const uint8_t scalar[X_PRIVATE_BYTES]
- )
+void 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] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8));
scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);
curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
/* Compensate for the encoding ratio */
- for (i = 1; i < DECAF_X448_ENCODE_RATIO; i <<= 1) {
+ for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)
curve448_scalar_halve(the_scalar, the_scalar);
- }
+
curve448_precomputed_scalarmul(p, curve448_precomputed_base, the_scalar);
curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
curve448_point_destroy(p);
}
-/**
- * @cond internal
- * Control for variable-time scalar multiply algorithms.
- */
+/* 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 curve448_scalar_t scalar, unsigned int table_bits)
+#if defined(__GNUC__) || defined(__clang__)
+# define NUMTRAILINGZEROS __builtin_ctz
+#else
+# define NUMTRAILINGZEROS numtrailingzeros
+static uint32_t numtrailingzeros(uint32_t i)
+{
+ uint32_t tmp;
+ uint32_t num = 31;
+
+ if (i == 0)
+ return 32;
+
+ tmp = i << 16;
+ if (tmp != 0) {
+ i = tmp;
+ num -= 16;
+ }
+ tmp = i << 8;
+ if (tmp != 0) {
+ i = tmp;
+ num -= 8;
+ }
+ tmp = i << 4;
+ if (tmp != 0) {
+ i = tmp;
+ num -= 4;
+ }
+ tmp = i << 2;
+ if (tmp != 0) {
+ i = tmp;
+ num -= 2;
+ }
+ tmp = i << 1;
+ if (tmp != 0)
+ num--;
+
+ return num;
+}
+#endif
+
+static int recode_wnaf(struct smvt_control *control,
+ /* [nbits/(table_bits + 1) + 3] */
+ const curve448_scalar_t scalar,
+ unsigned int table_bits)
{
- unsigned int table_size = DECAF_448_SCALAR_BITS / (table_bits + 1) + 3;
+ unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3;
int position = table_size - 1; /* at the end */
uint64_t current = scalar->limb[0] & 0xFFFF;
uint32_t mask = (1 << (table_bits + 1)) - 1;
* 1/5 op. Probably not worth it.
*/
- for (w = 1; w < (DECAF_448_SCALAR_BITS - 1) / 16 + 3; w++) {
- if (w < (DECAF_448_SCALAR_BITS - 1) / 16 + 1) {
+ for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) {
+ if (w < (C448_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);
+ current += (uint32_t)((scalar->limb[w / B_OVER_16]
+ >> (16 * (w % B_OVER_16))) << 16);
}
while (current & 0xFFFF) {
- uint32_t pos = __builtin_ctz((uint32_t)current), odd =
- (uint32_t)current >> pos;
+ uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);
+ uint32_t odd = (uint32_t)current >> pos;
int32_t delta = odd & mask;
assert(position >= 0);
- if (odd & 1 << (table_bits + 1))
+ if (odd & (1 << (table_bits + 1)))
delta -= (1 << (table_bits + 1));
current -= delta << pos;
control[position].power = pos + 16 * (w - 1);
position++;
n = table_size - position;
- for (i = 0; i < n; i++) {
+ for (i = 0; i < n; i++)
control[i] = control[i + position];
- }
+
return n - 1;
}
-static void
-prepare_wnaf_table(pniels_t * output,
- const curve448_point_t working, unsigned int tbits)
+static void prepare_wnaf_table(pniels_t * output,
+ const curve448_point_t working,
+ unsigned int tbits)
{
curve448_point_t tmp;
int i;
OPENSSL_cleanse(twop, sizeof(twop));
}
-extern const gf curve448_precomputed_wnaf_as_fe[];
-static const niels_t *curve448_wnaf_base =
- (const niels_t *)curve448_precomputed_wnaf_as_fe;
-
void curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
const curve448_scalar_t scalar1,
const curve448_point_t base2,
const curve448_scalar_t scalar2)
{
- const int table_bits_var = DECAF_WNAF_VAR_TABLE_BITS,
- table_bits_pre = DECAF_WNAF_FIXED_TABLE_BITS;
- struct smvt_control control_var[DECAF_448_SCALAR_BITS /
- (DECAF_WNAF_VAR_TABLE_BITS + 1) + 3];
- struct smvt_control control_pre[DECAF_448_SCALAR_BITS /
- (DECAF_WNAF_FIXED_TABLE_BITS + 1) + 3];
+ const int table_bits_var = C448_WNAF_VAR_TABLE_BITS;
+ const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS;
+ struct smvt_control control_var[C448_SCALAR_BITS /
+ (C448_WNAF_VAR_TABLE_BITS + 1) + 3];
+ struct smvt_control control_pre[C448_SCALAR_BITS /
+ (C448_WNAF_FIXED_TABLE_BITS + 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 << DECAF_WNAF_VAR_TABLE_BITS];
+ pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS];
int contp = 0, contv = 0, i;
prepare_wnaf_table(precmp_var, base2, table_bits_var);
if (i < 0) {
curve448_point_copy(combo, curve448_point_identity);
return;
- } else if (i > control_pre[0].power) {
+ }
+ 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) {
}
for (i--; i >= 0; i--) {
- int cv = (i == control_var[contv].power), cp =
- (i == control_pre[contp].power);
+ int cv = (i == control_var[contv].power);
+ int 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) {
+ if (control_var[contv].addend > 0)
add_pniels_to_pt(combo,
- precmp_var[control_var[contv].addend >> 1], i
- && !cp);
- } else {
+ precmp_var[control_var[contv].addend >> 1],
+ i && !cp);
+ else
sub_pniels_from_pt(combo,
- precmp_var[(-control_var[contv].addend) >>
- 1], i && !cp);
- }
+ precmp_var[(-control_var[contv].addend)
+ >> 1], i && !cp);
contv++;
}
if (cp) {
assert(control_pre[contp].addend);
- if (control_pre[contp].addend > 0) {
+ if (control_pre[contp].addend > 0)
add_niels_to_pt(combo,
- curve448_wnaf_base[control_pre[contp].addend >>
- 1], i);
- } else {
+ curve448_wnaf_base[control_pre[contp].addend
+ >> 1], i);
+ else
sub_niels_from_pt(combo,
curve448_wnaf_base[(-control_pre
[contp].addend) >> 1], i);
- }
contp++;
}
}
int X448(uint8_t out_shared_key[56], const uint8_t private_key[56],
const uint8_t peer_public_value[56])
{
- return decaf_x448(out_shared_key, peer_public_value, private_key)
- == DECAF_SUCCESS;
+ return x448_int(out_shared_key, peer_public_value, private_key)
+ == C448_SUCCESS;
}
void X448_public_from_private(uint8_t out_public_value[56],
const uint8_t private_key[56])
{
- decaf_x448_derive_public_key(out_public_value, private_key);
+ x448_derive_public_key(out_public_value, private_key);
}
projects / openssl.git / blobdiff