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Convert the scalar constant initialization to static consts
This commit is contained in:
Pieter Wuille
parent
50cc6ab062
commit
f1ebfe399f
6 changed files with 77 additions and 130 deletions
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@ -21,9 +21,6 @@
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#error "Please select scalar implementation"
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#endif
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static void secp256k1_scalar_start(void);
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static void secp256k1_scalar_stop(void);
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/** Clear a scalar to prevent the leak of sensitive data. */
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static void secp256k1_scalar_clear(secp256k1_scalar_t *r);
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@ -14,4 +14,6 @@ typedef struct {
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uint64_t d[4];
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} secp256k1_scalar_t;
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#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
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#endif
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@ -14,4 +14,6 @@ typedef struct {
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uint32_t d[8];
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} secp256k1_scalar_t;
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#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
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#endif
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@ -24,121 +24,6 @@
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#error "Please select scalar implementation"
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#endif
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typedef struct {
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#ifndef USE_NUM_NONE
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secp256k1_num_t order;
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#endif
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#ifdef USE_ENDOMORPHISM
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secp256k1_scalar_t minus_lambda, minus_b1, minus_b2, g1, g2;
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#endif
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} secp256k1_scalar_consts_t;
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static const secp256k1_scalar_consts_t *secp256k1_scalar_consts = NULL;
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static void secp256k1_scalar_start(void) {
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if (secp256k1_scalar_consts != NULL)
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return;
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/* Allocate. */
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secp256k1_scalar_consts_t *ret = (secp256k1_scalar_consts_t*)checked_malloc(sizeof(secp256k1_scalar_consts_t));
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#ifndef USE_NUM_NONE
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static const unsigned char secp256k1_scalar_consts_order[] = {
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
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0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
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0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
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};
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secp256k1_num_set_bin(&ret->order, secp256k1_scalar_consts_order, sizeof(secp256k1_scalar_consts_order));
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#endif
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#ifdef USE_ENDOMORPHISM
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/**
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* Lambda is a scalar which has the property for secp256k1 that point multiplication by
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* it is efficiently computable (see secp256k1_gej_mul_lambda). */
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static const unsigned char secp256k1_scalar_consts_lambda[32] = {
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0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,
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0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
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0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,
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0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72
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};
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/**
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* "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
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* (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
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* and k2 have a small size.
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* It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
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*
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* - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
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* - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
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* - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
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* - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
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*
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* The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
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* k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
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* compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
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*
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* g1, g2 are precomputed constants used to replace division with a rounded multiplication
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* when decomposing the scalar for an endomorphism-based point multiplication.
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*
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* The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
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* Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
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*
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* The derivation is described in the paper "Efficient Software Implementation of Public-Key
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* Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
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* Section 4.3 (here we use a somewhat higher-precision estimate):
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* d = a1*b2 - b1*a2
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* g1 = round((2^272)*b2/d)
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* g2 = round((2^272)*b1/d)
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*
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* (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
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* as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
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*/
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static const unsigned char secp256k1_scalar_consts_minus_b1[32] = {
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0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,
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0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3
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};
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static const unsigned char secp256k1_scalar_consts_b2[32] = {
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0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
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0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15
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};
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static const unsigned char secp256k1_scalar_consts_g1[32] = {
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0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0x00,0x00,0x00,0x00,0x00,0x00,0x30,0x86,
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0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,
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0x90,0xe4,0x92,0x84,0xeb,0x15,0x3d,0xab
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};
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static const unsigned char secp256k1_scalar_consts_g2[32] = {
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0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
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0x00,0x00,0x00,0x00,0x00,0x00,0xe4,0x43,
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0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,
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0x7f,0xa9,0x0a,0xbf,0xe4,0xc4,0x22,0x12
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};
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secp256k1_scalar_set_b32(&ret->minus_lambda, secp256k1_scalar_consts_lambda, NULL);
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secp256k1_scalar_negate(&ret->minus_lambda, &ret->minus_lambda);
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secp256k1_scalar_set_b32(&ret->minus_b1, secp256k1_scalar_consts_minus_b1, NULL);
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secp256k1_scalar_set_b32(&ret->minus_b2, secp256k1_scalar_consts_b2, NULL);
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secp256k1_scalar_negate(&ret->minus_b2, &ret->minus_b2);
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secp256k1_scalar_set_b32(&ret->g1, secp256k1_scalar_consts_g1, NULL);
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secp256k1_scalar_set_b32(&ret->g2, secp256k1_scalar_consts_g2, NULL);
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#endif
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/* Set the global pointer. */
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secp256k1_scalar_consts = ret;
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}
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static void secp256k1_scalar_stop(void) {
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if (secp256k1_scalar_consts == NULL)
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return;
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secp256k1_scalar_consts_t *c = (secp256k1_scalar_consts_t*)secp256k1_scalar_consts;
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secp256k1_scalar_consts = NULL;
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free(c);
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}
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#ifndef USE_NUM_NONE
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static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a) {
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unsigned char c[32];
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@ -147,7 +32,13 @@ static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_
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}
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static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
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*r = secp256k1_scalar_consts->order;
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static const unsigned char order[32] = {
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
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0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
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0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
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0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
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};
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secp256k1_num_set_bin(r, order, 32);
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}
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#endif
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@ -308,9 +199,10 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
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#elif defined(USE_SCALAR_INV_NUM)
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unsigned char b[32];
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secp256k1_scalar_get_b32(b, x);
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secp256k1_num_t n;
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secp256k1_num_t n, m;
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secp256k1_num_set_bin(&n, b, 32);
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secp256k1_num_mod_inverse(&n, &n, &secp256k1_scalar_consts->order);
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secp256k1_scalar_order_get_num(&m);
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secp256k1_num_mod_inverse(&n, &n, &m);
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secp256k1_num_get_bin(b, 32, &n);
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secp256k1_scalar_set_b32(r, b, NULL);
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#else
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@ -319,16 +211,74 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
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}
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#ifdef USE_ENDOMORPHISM
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/**
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* The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
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* lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
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* 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
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*
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* "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
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* (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
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* and k2 have a small size.
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* It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
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*
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* - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
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* - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
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* - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
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* - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
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*
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* The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
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* k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
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* compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
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*
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* g1, g2 are precomputed constants used to replace division with a rounded multiplication
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* when decomposing the scalar for an endomorphism-based point multiplication.
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*
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* The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
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* Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
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*
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* The derivation is described in the paper "Efficient Software Implementation of Public-Key
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* Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
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* Section 4.3 (here we use a somewhat higher-precision estimate):
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* d = a1*b2 - b1*a2
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* g1 = round((2^272)*b2/d)
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* g2 = round((2^272)*b1/d)
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*
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* (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
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* as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
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*
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* The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
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*/
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static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
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static const secp256k1_scalar_t minus_lambda = SECP256K1_SCALAR_CONST(
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0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
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0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
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);
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static const secp256k1_scalar_t minus_b1 = SECP256K1_SCALAR_CONST(
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0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
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0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
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);
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static const secp256k1_scalar_t minus_b2 = SECP256K1_SCALAR_CONST(
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0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
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0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
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);
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static const secp256k1_scalar_t g1 = SECP256K1_SCALAR_CONST(
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0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
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0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
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);
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static const secp256k1_scalar_t g2 = SECP256K1_SCALAR_CONST(
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0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
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0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
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);
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VERIFY_CHECK(r1 != a);
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VERIFY_CHECK(r2 != a);
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secp256k1_scalar_t c1, c2;
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secp256k1_scalar_mul_shift_var(&c1, a, &secp256k1_scalar_consts->g1, 272);
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secp256k1_scalar_mul_shift_var(&c2, a, &secp256k1_scalar_consts->g2, 272);
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secp256k1_scalar_mul(&c1, &c1, &secp256k1_scalar_consts->minus_b1);
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secp256k1_scalar_mul(&c2, &c2, &secp256k1_scalar_consts->minus_b2);
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secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
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secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
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secp256k1_scalar_mul(&c1, &c1, &minus_b1);
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secp256k1_scalar_mul(&c2, &c2, &minus_b2);
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secp256k1_scalar_add(r2, &c1, &c2);
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secp256k1_scalar_mul(r1, r2, &secp256k1_scalar_consts->minus_lambda);
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secp256k1_scalar_mul(r1, r2, &minus_lambda);
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secp256k1_scalar_add(r1, r1, a);
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}
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#endif
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@ -22,7 +22,6 @@
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void secp256k1_start(unsigned int flags) {
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secp256k1_fe_start();
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secp256k1_ge_start();
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secp256k1_scalar_start();
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secp256k1_ecdsa_start();
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if (flags & SECP256K1_START_SIGN) {
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secp256k1_ecmult_gen_start();
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@ -36,7 +35,6 @@ void secp256k1_stop(void) {
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secp256k1_ecmult_stop();
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secp256k1_ecmult_gen_stop();
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secp256k1_ecdsa_stop();
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secp256k1_scalar_stop();
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secp256k1_ge_stop();
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secp256k1_fe_stop();
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}
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@ -1660,7 +1660,6 @@ int main(int argc, char **argv) {
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/* Likewise, re-running the internal init functions should be harmless. */
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secp256k1_fe_start();
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secp256k1_ge_start();
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secp256k1_scalar_start();
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secp256k1_ecdsa_start();
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run_sha256_tests();
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@ -1711,7 +1710,6 @@ int main(int argc, char **argv) {
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/* Same for the internal shutdown functions. */
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secp256k1_fe_stop();
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secp256k1_ge_stop();
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secp256k1_scalar_stop();
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secp256k1_ecdsa_stop();
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return 0;
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}
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