/*
* Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
* BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
* ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include "inner.h"
/*
* Parameters for supported curves:
* - field modulus p
* - R^2 mod p (R = 2^(15k) for the smallest k such that R >= p)
* - b*R mod p (b is the second curve equation parameter)
*/
static const uint16_t P256_P[] = {
0x0111,
0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x003F, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x1000, 0x0000, 0x4000, 0x7FFF,
0x7FFF, 0x0001
};
static const uint16_t P256_R2[] = {
0x0111,
0x0000, 0x6000, 0x0000, 0x0000, 0x0000, 0x0000, 0x7FFC, 0x7FFF,
0x7FBF, 0x7FFF, 0x7FBF, 0x7FFF, 0x7FFF, 0x7FFF, 0x77FF, 0x7FFF,
0x4FFF, 0x0000
};
static const uint16_t P256_B[] = {
0x0111,
0x770C, 0x5EEF, 0x29C4, 0x3EC4, 0x6273, 0x0486, 0x4543, 0x3993,
0x3C01, 0x6B56, 0x212E, 0x57EE, 0x4882, 0x204B, 0x7483, 0x3C16,
0x0187, 0x0000
};
static const uint16_t P384_P[] = {
0x0199,
0x7FFF, 0x7FFF, 0x0003, 0x0000, 0x0000, 0x0000, 0x7FC0, 0x7FFF,
0x7EFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
0x7FFF, 0x01FF
};
static const uint16_t P384_R2[] = {
0x0199,
0x1000, 0x0000, 0x0000, 0x7FFF, 0x7FFF, 0x0001, 0x0000, 0x0010,
0x0000, 0x0000, 0x0000, 0x7F00, 0x7FFF, 0x01FF, 0x0000, 0x1000,
0x0000, 0x2000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000
};
static const uint16_t P384_B[] = {
0x0199,
0x7333, 0x2096, 0x70D1, 0x2310, 0x3020, 0x6197, 0x1464, 0x35BB,
0x70CA, 0x0117, 0x1920, 0x4136, 0x5FC8, 0x5713, 0x4938, 0x7DD2,
0x4DD2, 0x4A71, 0x0220, 0x683E, 0x2C87, 0x4DB1, 0x7BFF, 0x6C09,
0x0452, 0x0084
};
static const uint16_t P521_P[] = {
0x022B,
0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
0x7FFF, 0x7FFF, 0x07FF
};
static const uint16_t P521_R2[] = {
0x022B,
0x0100, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
0x0000, 0x0000, 0x0000
};
static const uint16_t P521_B[] = {
0x022B,
0x7002, 0x6A07, 0x751A, 0x228F, 0x71EF, 0x5869, 0x20F4, 0x1EFC,
0x7357, 0x37E0, 0x4EEC, 0x605E, 0x1652, 0x26F6, 0x31FA, 0x4A8F,
0x6193, 0x3C2A, 0x3C42, 0x48C7, 0x3489, 0x6771, 0x4C57, 0x5CCD,
0x2725, 0x545B, 0x503B, 0x5B42, 0x21A0, 0x2534, 0x687E, 0x70E4,
0x1618, 0x27D7, 0x0465
};
typedef struct {
const uint16_t *p;
const uint16_t *b;
const uint16_t *R2;
uint16_t p0i;
size_t point_len;
} curve_params;
static inline const curve_params *
id_to_curve(int curve)
{
static const curve_params pp[] = {
{ P256_P, P256_B, P256_R2, 0x0001, 65 },
{ P384_P, P384_B, P384_R2, 0x0001, 97 },
{ P521_P, P521_B, P521_R2, 0x0001, 133 }
};
return &pp[curve - BR_EC_secp256r1];
}
#define I15_LEN ((BR_MAX_EC_SIZE + 29) / 15)
/*
* Type for a point in Jacobian coordinates:
* -- three values, x, y and z, in Montgomery representation
* -- affine coordinates are X = x / z^2 and Y = y / z^3
* -- for the point at infinity, z = 0
*/
typedef struct {
uint16_t c[3][I15_LEN];
} jacobian;
/*
* We use a custom interpreter that uses a dozen registers, and
* only six operations:
* MSET(d, a) copy a into d
* MADD(d, a) d = d+a (modular)
* MSUB(d, a) d = d-a (modular)
* MMUL(d, a, b) d = a*b (Montgomery multiplication)
* MINV(d, a, b) invert d modulo p; a and b are used as scratch registers
* MTZ(d) clear return value if d = 0
* Destination of MMUL (d) must be distinct from operands (a and b).
* There is no such constraint for MSUB and MADD.
*
* Registers include the operand coordinates, and temporaries.
*/
#define MSET(d, a) (0x0000 + ((d) << 8) + ((a) << 4))
#define MADD(d, a) (0x1000 + ((d) << 8) + ((a) << 4))
#define MSUB(d, a) (0x2000 + ((d) << 8) + ((a) << 4))
#define MMUL(d, a, b) (0x3000 + ((d) << 8) + ((a) << 4) + (b))
#define MINV(d, a, b) (0x4000 + ((d) << 8) + ((a) << 4) + (b))
#define MTZ(d) (0x5000 + ((d) << 8))
#define ENDCODE 0
/*
* Registers for the input operands.
*/
#define P1x 0
#define P1y 1
#define P1z 2
#define P2x 3
#define P2y 4
#define P2z 5
/*
* Alternate names for the first input operand.
*/
#define Px 0
#define Py 1
#define Pz 2
/*
* Temporaries.
*/
#define t1 6
#define t2 7
#define t3 8
#define t4 9
#define t5 10
#define t6 11
#define t7 12
/*
* Extra scratch registers available when there is no second operand (e.g.
* for "double" and "affine").
*/
#define t8 3
#define t9 4
#define t10 5
/*
* Doubling formulas are:
*
* s = 4*x*y^2
* m = 3*(x + z^2)*(x - z^2)
* x' = m^2 - 2*s
* y' = m*(s - x') - 8*y^4
* z' = 2*y*z
*
* If y = 0 (P has order 2) then this yields infinity (z' = 0), as it
* should. This case should not happen anyway, because our curves have
* prime order, and thus do not contain any point of order 2.
*
* If P is infinity (z = 0), then again the formulas yield infinity,
* which is correct. Thus, this code works for all points.
*
* Cost: 8 multiplications
*/
static const uint16_t code_double[] = {
/*
* Compute z^2 (in t1).
*/
MMUL(t1, Pz, Pz),
/*
* Compute x-z^2 (in t2) and then x+z^2 (in t1).
*/
MSET(t2, Px),
MSUB(t2, t1),
MADD(t1, Px),
/*
* Compute m = 3*(x+z^2)*(x-z^2) (in t1).
*/
MMUL(t3, t1, t2),
MSET(t1, t3),
MADD(t1, t3),
MADD(t1, t3),
/*
* Compute s = 4*x*y^2 (in t2) and 2*y^2 (in t3).
*/
MMUL(t3, Py, Py),
MADD(t3, t3),
MMUL(t2, Px, t3),
MADD(t2, t2),
/*
* Compute x' = m^2 - 2*s.
*/
MMUL(Px, t1, t1),
MSUB(Px, t2),
MSUB(Px, t2),
/*
* Compute z' = 2*y*z.
*/
MMUL(t4, Py, Pz),
MSET(Pz, t4),
MADD(Pz, t4),
/*
* Compute y' = m*(s - x') - 8*y^4. Note that we already have
* 2*y^2 in t3.
*/
MSUB(t2, Px),
MMUL(Py, t1, t2),
MMUL(t4, t3, t3),
MSUB(Py, t4),
MSUB(Py, t4),
ENDCODE
};
/*
* Addtions formulas are:
*
* u1 = x1 * z2^2
* u2 = x2 * z1^2
* s1 = y1 * z2^3
* s2 = y2 * z1^3
* h = u2 - u1
* r = s2 - s1
* x3 = r^2 - h^3 - 2 * u1 * h^2
* y3 = r * (u1 * h^2 - x3) - s1 * h^3
* z3 = h * z1 * z2
*
* If both P1 and P2 are infinity, then z1 == 0 and z2 == 0, implying that
* z3 == 0, so the result is correct.
* If either of P1 or P2 is infinity, but not both, then z3 == 0, which is
* not correct.
* h == 0 only if u1 == u2; this happens in two cases:
* -- if s1 == s2 then P1 and/or P2 is infinity, or P1 == P2
* -- if s1 != s2 then P1 + P2 == infinity (but neither P1 or P2 is infinity)
*
* Thus, the following situations are not handled correctly:
* -- P1 = 0 and P2 != 0
* -- P1 != 0 and P2 = 0
* -- P1 = P2
* All other cases are properly computed. However, even in "incorrect"
* situations, the three coordinates still are properly formed field
* elements.
*
* The returned flag is cleared if r == 0. This happens in the following
* cases:
* -- Both points are on the same horizontal line (same Y coordinate).
* -- Both points are infinity.
* -- One point is infinity and the other is on line Y = 0.
* The third case cannot happen with our curves (there is no valid point
* on line Y = 0 since that would be a point of order 2). If the two
* source points are non-infinity, then remains only the case where the
* two points are on the same horizontal line.
*
* This allows us to detect the "P1 == P2" case, assuming that P1 != 0 and
* P2 != 0:
* -- If the returned value is not the point at infinity, then it was properly
* computed.
* -- Otherwise, if the returned flag is 1, then P1+P2 = 0, and the result
* is indeed the point at infinity.
* -- Otherwise (result is infinity, flag is 0), then P1 = P2 and we should
* use the 'double' code.
*
* Cost: 16 multiplications
*/
static const uint16_t code_add[] = {
/*
* Compute u1 = x1*z2^2 (in t1) and s1 = y1*z2^3 (in t3).
*/
MMUL(t3, P2z, P2z),
MMUL(t1, P1x, t3),
MMUL(t4, P2z, t3),
MMUL(t3, P1y, t4),
/*
* Compute u2 = x2*z1^2 (in t2) and s2 = y2*z1^3 (in t4).
*/
MMUL(t4, P1z, P1z),
MMUL(t2, P2x, t4),
MMUL(t5, P1z, t4),
MMUL(t4, P2y, t5),
/*
* Compute h = u2 - u1 (in t2) and r = s2 - s1 (in t4).
*/
MSUB(t2, t1),
MSUB(t4, t3),
/*
* Report cases where r = 0 through the returned flag.
*/
MTZ(t4),
/*
* Compute u1*h^2 (in t6) and h^3 (in t5).
*/
MMUL(t7, t2, t2),
MMUL(t6, t1, t7),
MMUL(t5, t7, t2),
/*
* Compute x3 = r^2 - h^3 - 2*u1*h^2.
* t1 and t7 can be used as scratch registers.
*/
MMUL(P1x, t4, t4),
MSUB(P1x, t5),
MSUB(P1x, t6),
MSUB(P1x, t6),
/*
* Compute y3 = r*(u1*h^2 - x3) - s1*h^3.
*/
MSUB(t6, P1x),
MMUL(P1y, t4, t6),
MMUL(t1, t5, t3),
MSUB(P1y, t1),
/*
* Compute z3 = h*z1*z2.
*/
MMUL(t1, P1z, P2z),
MMUL(P1z, t1, t2),
ENDCODE
};
/*
* Check that the point is on the curve. This code snippet assumes the
* following conventions:
* -- Coordinates x and y have been freshly decoded in P1 (but not
* converted to Montgomery coordinates yet).
* -- P2x, P2y and P2z are set to, respectively, R^2, b*R and 1.
*/
static const uint16_t code_check[] = {
/* Convert x and y to Montgomery representation. */
MMUL(t1, P1x, P2x),
MMUL(t2, P1y, P2x),
MSET(P1x, t1),
MSET(P1y, t2),
/* Compute x^3 in t1. */
MMUL(t2, P1x, P1x),
MMUL(t1, P1x, t2),
/* Subtract 3*x from t1. */
MSUB(t1, P1x),
MSUB(t1, P1x),
MSUB(t1, P1x),
/* Add b. */
MADD(t1, P2y),
/* Compute y^2 in t2. */
MMUL(t2, P1y, P1y),
/* Compare y^2 with x^3 - 3*x + b; they must match. */
MSUB(t1, t2),
MTZ(t1),
/* Set z to 1 (in Montgomery representation). */
MMUL(P1z, P2x, P2z),
ENDCODE
};
/*
* Conversion back to affine coordinates. This code snippet assumes that
* the z coordinate of P2 is set to 1 (not in Montgomery representation).
*/
static const uint16_t code_affine[] = {
/* Save z*R in t1. */
MSET(t1, P1z),
/* Compute z^3 in t2. */
MMUL(t2, P1z, P1z),
MMUL(t3, P1z, t2),
MMUL(t2, t3, P2z),
/* Invert to (1/z^3) in t2. */
MINV(t2, t3, t4),
/* Compute y. */
MSET(t3, P1y),
MMUL(P1y, t2, t3),
/* Compute (1/z^2) in t3. */
MMUL(t3, t2, t1),
/* Compute x. */
MSET(t2, P1x),
MMUL(P1x, t2, t3),
ENDCODE
};
static uint32_t
run_code(jacobian *P1, const jacobian *P2,
const curve_params *cc, const uint16_t *code)
{
uint32_t r;
uint16_t t[13][I15_LEN];
size_t u;
r = 1;
/*
* Copy the two operands in the dedicated registers.
*/
memcpy(t[P1x], P1->c, 3 * I15_LEN * sizeof(uint16_t));
memcpy(t[P2x], P2->c, 3 * I15_LEN * sizeof(uint16_t));
/*
* Run formulas.
*/
for (u = 0;; u ++) {
unsigned op, d, a, b;
op = code[u];
if (op == 0) {
break;
}
d = (op >> 8) & 0x0F;
a = (op >> 4) & 0x0F;
b = op & 0x0F;
op >>= 12;
switch (op) {
uint32_t ctl;
size_t plen;
unsigned char tp[(BR_MAX_EC_SIZE + 7) >> 3];
case 0:
memcpy(t[d], t[a], I15_LEN * sizeof(uint16_t));
break;
case 1:
ctl = br_i15_add(t[d], t[a], 1);
ctl |= NOT(br_i15_sub(t[d], cc->p, 0));
br_i15_sub(t[d], cc->p, ctl);
break;
case 2:
br_i15_add(t[d], cc->p, br_i15_sub(t[d], t[a], 1));
break;
case 3:
br_i15_montymul(t[d], t[a], t[b], cc->p, cc->p0i);
break;
case 4:
plen = (cc->p[0] - (cc->p[0] >> 4) + 7) >> 3;
br_i15_encode(tp, plen, cc->p);
tp[plen - 1] -= 2;
br_i15_modpow(t[d], tp, plen,
cc->p, cc->p0i, t[a], t[b]);
break;
default:
r &= ~br_i15_iszero(t[d]);
break;
}
}
/*
* Copy back result.
*/
memcpy(P1->c, t[P1x], 3 * I15_LEN * sizeof(uint16_t));
return r;
}
static void
set_one(uint16_t *x, const uint16_t *p)
{
size_t plen;
plen = (p[0] + 31) >> 4;
memset(x, 0, plen * sizeof *x);
x[0] = p[0];
x[1] = 0x0001;
}
static void
point_zero(jacobian *P, const curve_params *cc)
{
memset(P, 0, sizeof *P);
P->c[0][0] = P->c[1][0] = P->c[2][0] = cc->p[0];
}
static inline void
point_double(jacobian *P, const curve_params *cc)
{
run_code(P, P, cc, code_double);
}
static inline uint32_t
point_add(jacobian *P1, const jacobian *P2, const curve_params *cc)
{
return run_code(P1, P2, cc, code_add);
}
static void
point_mul(jacobian *P, const unsigned char *x, size_t xlen,
const curve_params *cc)
{
/*
* We do a simple double-and-add ladder with a 2-bit window
* to make only one add every two doublings. We thus first
* precompute 2P and 3P in some local buffers.
*
* We always perform two doublings and one addition; the
* addition is with P, 2P and 3P and is done in a temporary
* array.
*
* The addition code cannot handle cases where one of the
* operands is infinity, which is the case at the start of the
* ladder. We therefore need to maintain a flag that controls
* this situation.
*/
uint32_t qz;
jacobian P2, P3, Q, T, U;
memcpy(&P2, P, sizeof P2);
point_double(&P2, cc);
memcpy(&P3, P, sizeof P3);
point_add(&P3, &P2, cc);
point_zero(&Q, cc);
qz = 1;
while (xlen -- > 0) {
int k;
for (k = 6; k >= 0; k -= 2) {
uint32_t bits;
uint32_t bnz;
point_double(&Q, cc);
point_double(&Q, cc);
memcpy(&T, P, sizeof T);
memcpy(&U, &Q, sizeof U);
bits = (*x >> k) & (uint32_t)3;
bnz = NEQ(bits, 0);
CCOPY(EQ(bits, 2), &T, &P2, sizeof T);
CCOPY(EQ(bits, 3), &T, &P3, sizeof T);
point_add(&U, &T, cc);
CCOPY(bnz & qz, &Q, &T, sizeof Q);
CCOPY(bnz & ~qz, &Q, &U, sizeof Q);
qz &= ~bnz;
}
x ++;
}
memcpy(P, &Q, sizeof Q);
}
/*
* Decode point into Jacobian coordinates. This function does not support
* the point at infinity. If the point is invalid then this returns 0, but
* the coordinates are still set to properly formed field elements.
*/
static uint32_t
point_decode(jacobian *P, const void *src, size_t len, const curve_params *cc)
{
/*
* Points must use uncompressed format:
* -- first byte is 0x04;
* -- coordinates X and Y use unsigned big-endian, with the same
* length as the field modulus.
*
* We don't support hybrid format (uncompressed, but first byte
* has value 0x06 or 0x07, depending on the least significant bit
* of Y) because it is rather useless, and explicitly forbidden
* by PKIX (RFC 5480, section 2.2).
*
* We don't support compressed format either, because it is not
* much used in practice (there are or were patent-related
* concerns about point compression, which explains the lack of
* generalised support). Also, point compression support would
* need a bit more code.
*/
const unsigned char *buf;
size_t plen, zlen;
uint32_t r;
jacobian Q;
buf = src;
point_zero(P, cc);
plen = (cc->p[0] - (cc->p[0] >> 4) + 7) >> 3;
if (len != 1 + (plen << 1)) {
return 0;
}
r = br_i15_decode_mod(P->c[0], buf + 1, plen, cc->p);
r &= br_i15_decode_mod(P->c[1], buf + 1 + plen, plen, cc->p);
/*
* Check first byte.
*/
r &= EQ(buf[0], 0x04);
/* obsolete
r &= EQ(buf[0], 0x04) | (EQ(buf[0] & 0xFE, 0x06)
& ~(uint32_t)(buf[0] ^ buf[plen << 1]));
*/
/*
* Convert coordinates and check that the point is valid.
*/
zlen = ((cc->p[0] + 31) >> 4) * sizeof(uint16_t);
memcpy(Q.c[0], cc->R2, zlen);
memcpy(Q.c[1], cc->b, zlen);
set_one(Q.c[2], cc->p);
r &= ~run_code(P, &Q, cc, code_check);
return r;
}
/*
* Encode a point. This method assumes that the point is correct and is
* not the point at infinity. Encoded size is always 1+2*plen, where
* plen is the field modulus length, in bytes.
*/
static void
point_encode(void *dst, const jacobian *P, const curve_params *cc)
{
unsigned char *buf;
size_t plen;
jacobian Q, T;
buf = dst;
plen = (cc->p[0] - (cc->p[0] >> 4) + 7) >> 3;
buf[0] = 0x04;
memcpy(&Q, P, sizeof *P);
set_one(T.c[2], cc->p);
run_code(&Q, &T, cc, code_affine);
br_i15_encode(buf + 1, plen, Q.c[0]);
br_i15_encode(buf + 1 + plen, plen, Q.c[1]);
}
static const br_ec_curve_def *
id_to_curve_def(int curve)
{
switch (curve) {
case BR_EC_secp256r1:
return &br_secp256r1;
case BR_EC_secp384r1:
return &br_secp384r1;
case BR_EC_secp521r1:
return &br_secp521r1;
}
return NULL;
}
static const unsigned char *
api_generator(int curve, size_t *len)
{
const br_ec_curve_def *cd;
cd = id_to_curve_def(curve);
*len = cd->generator_len;
return cd->generator;
}
static const unsigned char *
api_order(int curve, size_t *len)
{
const br_ec_curve_def *cd;
cd = id_to_curve_def(curve);
*len = cd->order_len;
return cd->order;
}
static size_t
api_xoff(int curve, size_t *len)
{
api_generator(curve, len);
*len >>= 1;
return 1;
}
static uint32_t
api_mul(unsigned char *G, size_t Glen,
const unsigned char *x, size_t xlen, int curve)
{
uint32_t r;
const curve_params *cc;
jacobian P;
cc = id_to_curve(curve);
r = point_decode(&P, G, Glen, cc);
point_mul(&P, x, xlen, cc);
if (Glen == cc->point_len) {
point_encode(G, &P, cc);
}
return r;
}
static size_t
api_mulgen(unsigned char *R,
const unsigned char *x, size_t xlen, int curve)
{
const unsigned char *G;
size_t Glen;
G = api_generator(curve, &Glen);
memcpy(R, G, Glen);
api_mul(R, Glen, x, xlen, curve);
return Glen;
}
static uint32_t
api_muladd(unsigned char *A, const unsigned char *B, size_t len,
const unsigned char *x, size_t xlen,
const unsigned char *y, size_t ylen, int curve)
{
uint32_t r, t, z;
const curve_params *cc;
jacobian P, Q;
/*
* TODO: see about merging the two ladders. Right now, we do
* two independent point multiplications, which is a bit
* wasteful of CPU resources (but yields short code).
*/
cc = id_to_curve(curve);
r = point_decode(&P, A, len, cc);
if (B == NULL) {
size_t Glen;
B = api_generator(curve, &Glen);
}
r &= point_decode(&Q, B, len, cc);
point_mul(&P, x, xlen, cc);
point_mul(&Q, y, ylen, cc);
/*
* We want to compute P+Q. Since the base points A and B are distinct
* from infinity, and the multipliers are non-zero and lower than the
* curve order, then we know that P and Q are non-infinity. This
* leaves two special situations to test for:
* -- If P = Q then we must use point_double().
* -- If P+Q = 0 then we must report an error.
*/
t = point_add(&P, &Q, cc);
point_double(&Q, cc);
z = br_i15_iszero(P.c[2]);
/*
* If z is 1 then either P+Q = 0 (t = 1) or P = Q (t = 0). So we
* have the following:
*
* z = 0, t = 0 return P (normal addition)
* z = 0, t = 1 return P (normal addition)
* z = 1, t = 0 return Q (a 'double' case)
* z = 1, t = 1 report an error (P+Q = 0)
*/
CCOPY(z & ~t, &P, &Q, sizeof Q);
point_encode(A, &P, cc);
r &= ~(z & t);
return r;
}
/* see bearssl_ec.h */
const br_ec_impl br_ec_prime_i15 = {
(uint32_t)0x03800000,
&api_generator,
&api_order,
&api_xoff,
&api_mul,
&api_mulgen,
&api_muladd
};