| /* LibTomCrypt, modular cryptographic library -- Tom St Denis |
| * |
| * LibTomCrypt is a library that provides various cryptographic |
| * algorithms in a highly modular and flexible manner. |
| * |
| * The library is free for all purposes without any express |
| * guarantee it works. |
| * |
| * Tom St Denis, tomstdenis@iahu.ca, http://libtomcrypt.org |
| */ |
| |
| /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b |
| * |
| * All curves taken from NIST recommendation paper of July 1999 |
| * Available at http://csrc.nist.gov/cryptval/dss.htm |
| */ |
| |
| #include "mycrypt.h" |
| |
| #ifdef MECC |
| |
| /* size of our temp buffers for exported keys */ |
| #define ECC_BUF_SIZE 160 |
| |
| /* max private key size */ |
| #define ECC_MAXSIZE 66 |
| |
| /* This holds the key settings. ***MUST*** be organized by size from smallest to largest. */ |
| static const struct { |
| int size; |
| char *name, *prime, *B, *order, *Gx, *Gy; |
| } sets[] = { |
| #ifdef ECC160 |
| { |
| 20, |
| "ECC-160", |
| /* prime */ |
| "G00000000000000000000000007", |
| /* B */ |
| "1oUV2vOaSlWbxr6", |
| /* order */ |
| "G0000000000004sCQUtDxaqDUN5", |
| /* Gx */ |
| "jpqOf1BHus6Yd/pyhyVpP", |
| /* Gy */ |
| "D/wykuuIFfr+vPyx7kQEPu8MixO", |
| }, |
| #endif |
| #ifdef ECC192 |
| { |
| 24, |
| "ECC-192", |
| /* prime */ |
| "/////////////////////l//////////", |
| |
| /* B */ |
| "P2456UMSWESFf+chSYGmIVwutkp1Hhcn", |
| |
| /* order */ |
| "////////////////cTxuDXHhoR6qqYWn", |
| |
| /* Gx */ |
| "68se3h0maFPylo3hGw680FJ/2ls2/n0I", |
| |
| /* Gy */ |
| "1nahbV/8sdXZ417jQoJDrNFvTw4UUKWH" |
| }, |
| #endif |
| #ifdef ECC224 |
| { |
| 28, |
| "ECC-224", |
| |
| /* prime */ |
| "400000000000000000000000000000000000BV", |
| |
| /* B */ |
| "21HkWGL2CxJIp", |
| |
| /* order */ |
| "4000000000000000000Kxnixk9t8MLzMiV264/", |
| |
| /* Gx */ |
| "jpqOf1BHus6Yd/pyhyVpP", |
| |
| /* Gy */ |
| "3FCtyo2yHA5SFjkCGbYxbOvNeChwS+j6wSIwck", |
| }, |
| #endif |
| #ifdef ECC256 |
| { |
| 32, |
| "ECC-256", |
| /* Prime */ |
| "F////y000010000000000000000////////////////", |
| |
| /* B */ |
| "5h6DTYgEfFdi+kzLNQOXhnb7GQmp5EmzZlEF3udqc1B", |
| |
| /* Order */ |
| "F////y00000//////////+yvlgjfnUUXFEvoiByOoLH", |
| |
| /* Gx */ |
| "6iNqVBXB497+BpcvMEaGF9t0ts1BUipeFIXEKNOcCAM", |
| |
| /* Gy */ |
| "4/ZGkB+6d+RZkVhIdmFdXOhpZDNQp5UpiksG6Wtlr7r" |
| }, |
| #endif |
| #ifdef ECC384 |
| { |
| 48, |
| "ECC-384", |
| /* prime */ |
| "//////////////////////////////////////////x/////00000000003/" |
| "////", |
| |
| /* B */ |
| "ip4lf+8+v+IOZWLhu/Wj6HWTd6x+WK4I0nG8Zr0JXrh6LZcDYYxHdIg5oEtJ" |
| "x2hl", |
| |
| /* Order */ |
| "////////////////////////////////nsDDWVGtBTzO6WsoIB2dUkpi6MhC" |
| "nIbp", |
| |
| /* Gx and Gy */ |
| "geVA8hwB1JUEiSSUyo2jT6uTEsABfvkOMVT1u89KAZXL0l9TlrKfR3fKNZXo" |
| "TWgt", |
| |
| "DXVUIfOcB6zTdfY/afBSAVZq7RqecXHywTen4xNmkC0AOB7E7Nw1dNf37NoG" |
| "wWvV" |
| }, |
| #endif |
| #ifdef ECC521 |
| { |
| 65, |
| "ECC-521", |
| /* prime */ |
| "V///////////////////////////////////////////////////////////" |
| "///////////////////////////", |
| |
| /* B */ |
| "56LFhbXZXoQ7vAQ8Q2sXK3kejfoMvcp5VEuj8cHZl49uLOPEL7iVfDx5bB0l" |
| "JknlmSrSz+8FImqyUz57zHhK3y0", |
| |
| /* Order */ |
| "V//////////////////////////////////////////+b66XuE/BvPhVym1I" |
| "FS9fT0xjScuYPn7hhjljnwHE6G9", |
| |
| /* Gx and Gy */ |
| "CQ5ZWQt10JfpPu+osOZbRH2d6I1EGK/jI7uAAzWQqqzkg5BNdVlvrae/Xt19" |
| "wB/gDupIBF1XMf2c/b+VZ72vRrc", |
| |
| "HWvAMfucZl015oANxGiVHlPcFL4ILURH6WNhxqN9pvcB9VkSfbUz2P0nL2v0" |
| "J+j1s4rF726edB2G8Y+b7QVqMPG", |
| }, |
| #endif |
| { |
| 0, |
| NULL, NULL, NULL, NULL, NULL, NULL |
| } |
| }; |
| |
| #if 0 |
| |
| /* you plug in a prime and B value and it finds a pseudo-random base point */ |
| void ecc_find_base(void) |
| { |
| static char *prime = "26959946667150639794667015087019630673637144422540572481103610249951"; |
| static char *order = "26959946667150639794667015087019637467111563745054605861463538557247"; |
| static char *b = "9538957348957353489587"; |
| mp_int pp, p, r, B, tmp1, tmp2, tx, ty, x, y; |
| char buf[4096]; |
| int i; |
| |
| mp_init_multi(&tx, &ty, &x, &y, &p, &pp, &r, &B, &tmp1, &tmp2, NULL); |
| mp_read_radix(&p, prime, 10); |
| mp_read_radix(&r, order, 10); |
| mp_read_radix(&B, b, 10); |
| |
| /* get (p+1)/4 */ |
| mp_add_d(&p, 1, &pp); |
| mp_div_2(&pp, &pp); |
| mp_div_2(&pp, &pp); |
| |
| buf[0] = 0; |
| do { |
| printf("."); fflush(stdout); |
| /* make a random value of x */ |
| for (i = 0; i < 16; i++) buf[i+1] = rand() & 255; |
| mp_read_raw(&x, buf, 17); |
| mp_copy(&x, &tx); |
| |
| /* now compute x^3 - 3x + b */ |
| mp_expt_d(&x, 3, &tmp1); |
| mp_mul_d(&x, 3, &tmp2); |
| mp_sub(&tmp1, &tmp2, &tmp1); |
| mp_add(&tmp1, &B, &tmp1); |
| mp_mod(&tmp1, &p, &tmp1); |
| |
| /* now compute sqrt via x^((p+1)/4) */ |
| mp_exptmod(&tmp1, &pp, &p, &tmp2); |
| mp_copy(&tmp2, &ty); |
| |
| /* now square it */ |
| mp_sqrmod(&tmp2, &p, &tmp2); |
| |
| /* tmp2 should equal tmp1 */ |
| } while (mp_cmp(&tmp1, &tmp2)); |
| |
| /* now output values in way that libtomcrypt wants */ |
| mp_todecimal(&p, buf); |
| printf("\n\np==%s\n", buf); |
| mp_tohex(&B, buf); |
| printf("b==%s\n", buf); |
| mp_todecimal(&r, buf); |
| printf("r==%s\n", buf); |
| mp_tohex(&tx, buf); |
| printf("Gx==%s\n", buf); |
| mp_tohex(&ty, buf); |
| printf("Gy==%s\n", buf); |
| |
| mp_clear_multi(&tx, &ty, &x, &y, &p, &pp, &r, &B, &tmp1, &tmp2, NULL); |
| } |
| |
| #endif |
| |
| static int is_valid_idx(int n) |
| { |
| int x; |
| |
| for (x = 0; sets[x].size != 0; x++); |
| if ((n < 0) || (n >= x)) { |
| return 0; |
| } |
| return 1; |
| } |
| |
| static ecc_point *new_point(void) |
| { |
| ecc_point *p; |
| p = XMALLOC(sizeof(ecc_point)); |
| if (p == NULL) { |
| return NULL; |
| } |
| if (mp_init_multi(&p->x, &p->y, NULL) != MP_OKAY) { |
| XFREE(p); |
| return NULL; |
| } |
| return p; |
| } |
| |
| static void del_point(ecc_point *p) |
| { |
| /* prevents free'ing null arguments */ |
| if (p != NULL) { |
| mp_clear_multi(&p->x, &p->y, NULL); |
| XFREE(p); |
| } |
| } |
| |
| /* double a point R = 2P, R can be P*/ |
| static int dbl_point(ecc_point *P, ecc_point *R, mp_int *modulus, mp_int *mu) |
| { |
| mp_int s, tmp, tmpx; |
| int err; |
| |
| if ((err = mp_init_multi(&s, &tmp, &tmpx, NULL)) != MP_OKAY) { |
| return mpi_to_ltc_error(err); |
| } |
| |
| /* s = (3Xp^2 + a) / (2Yp) */ |
| if ((err = mp_mul_2(&P->y, &tmp)) != MP_OKAY) { goto error; } /* tmp = 2*y */ |
| if ((err = mp_invmod(&tmp, modulus, &tmp)) != MP_OKAY) { goto error; } /* tmp = 1/tmp mod modulus */ |
| if ((err = mp_sqr(&P->x, &s)) != MP_OKAY) { goto error; } /* s = x^2 */ |
| if ((err = mp_reduce(&s, modulus, mu)) != MP_OKAY) { goto error; } |
| if ((err = mp_mul_d(&s,(mp_digit)3, &s)) != MP_OKAY) { goto error; } /* s = 3*(x^2) */ |
| if ((err = mp_sub_d(&s,(mp_digit)3, &s)) != MP_OKAY) { goto error; } /* s = 3*(x^2) - 3 */ |
| if (mp_cmp_d(&s, 0) == MP_LT) { /* if s < 0 add modulus */ |
| if ((err = mp_add(&s, modulus, &s)) != MP_OKAY) { goto error; } |
| } |
| if ((err = mp_mul(&s, &tmp, &s)) != MP_OKAY) { goto error; } /* s = tmp * s mod modulus */ |
| if ((err = mp_reduce(&s, modulus, mu)) != MP_OKAY) { goto error; } |
| |
| /* Xr = s^2 - 2Xp */ |
| if ((err = mp_sqr(&s, &tmpx)) != MP_OKAY) { goto error; } /* tmpx = s^2 */ |
| if ((err = mp_reduce(&tmpx, modulus, mu)) != MP_OKAY) { goto error; } /* tmpx = tmpx mod modulus */ |
| if ((err = mp_sub(&tmpx, &P->x, &tmpx)) != MP_OKAY) { goto error; } /* tmpx = tmpx - x */ |
| if ((err = mp_submod(&tmpx, &P->x, modulus, &tmpx)) != MP_OKAY) { goto error; } /* tmpx = tmpx - x mod modulus */ |
| |
| /* Yr = -Yp + s(Xp - Xr) */ |
| if ((err = mp_sub(&P->x, &tmpx, &tmp)) != MP_OKAY) { goto error; } /* tmp = x - tmpx */ |
| if ((err = mp_mul(&tmp, &s, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp * s */ |
| if ((err = mp_submod(&tmp, &P->y, modulus, &R->y)) != MP_OKAY) { goto error; } /* y = tmp - y mod modulus */ |
| if ((err = mp_copy(&tmpx, &R->x)) != MP_OKAY) { goto error; } /* x = tmpx */ |
| |
| err = CRYPT_OK; |
| goto done; |
| error: |
| err = mpi_to_ltc_error(err); |
| done: |
| mp_clear_multi(&tmpx, &tmp, &s, NULL); |
| return err; |
| } |
| |
| /* add two different points over Z/pZ, R = P + Q, note R can equal either P or Q */ |
| static int add_point(ecc_point *P, ecc_point *Q, ecc_point *R, mp_int *modulus, mp_int *mu) |
| { |
| mp_int s, tmp, tmpx; |
| int err; |
| |
| if ((err = mp_init(&tmp)) != MP_OKAY) { |
| return mpi_to_ltc_error(err); |
| } |
| |
| /* is P==Q or P==-Q? */ |
| if (((err = mp_neg(&Q->y, &tmp)) != MP_OKAY) || ((err = mp_mod(&tmp, modulus, &tmp)) != MP_OKAY)) { |
| mp_clear(&tmp); |
| return mpi_to_ltc_error(err); |
| } |
| |
| if (mp_cmp(&P->x, &Q->x) == MP_EQ) |
| if (mp_cmp(&P->y, &Q->y) == MP_EQ || mp_cmp(&P->y, &tmp) == MP_EQ) { |
| mp_clear(&tmp); |
| return dbl_point(P, R, modulus, mu); |
| } |
| |
| if ((err = mp_init_multi(&tmpx, &s, NULL)) != MP_OKAY) { |
| mp_clear(&tmp); |
| return mpi_to_ltc_error(err); |
| } |
| |
| /* get s = (Yp - Yq)/(Xp-Xq) mod p */ |
| if ((err = mp_sub(&P->x, &Q->x, &tmp)) != MP_OKAY) { goto error; } /* tmp = Px - Qx mod modulus */ |
| if (mp_cmp_d(&tmp, 0) == MP_LT) { /* if tmp<0 add modulus */ |
| if ((err = mp_add(&tmp, modulus, &tmp)) != MP_OKAY) { goto error; } |
| } |
| if ((err = mp_invmod(&tmp, modulus, &tmp)) != MP_OKAY) { goto error; } /* tmp = 1/tmp mod modulus */ |
| if ((err = mp_sub(&P->y, &Q->y, &s)) != MP_OKAY) { goto error; } /* s = Py - Qy mod modulus */ |
| if (mp_cmp_d(&s, 0) == MP_LT) { /* if s<0 add modulus */ |
| if ((err = mp_add(&s, modulus, &s)) != MP_OKAY) { goto error; } |
| } |
| if ((err = mp_mul(&s, &tmp, &s)) != MP_OKAY) { goto error; } /* s = s * tmp mod modulus */ |
| if ((err = mp_reduce(&s, modulus, mu)) != MP_OKAY) { goto error; } |
| |
| /* Xr = s^2 - Xp - Xq */ |
| if ((err = mp_sqr(&s, &tmp)) != MP_OKAY) { goto error; } /* tmp = s^2 mod modulus */ |
| if ((err = mp_reduce(&tmp, modulus, mu)) != MP_OKAY) { goto error; } |
| if ((err = mp_sub(&tmp, &P->x, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp - Px */ |
| if ((err = mp_sub(&tmp, &Q->x, &tmpx)) != MP_OKAY) { goto error; } /* tmpx = tmp - Qx */ |
| |
| /* Yr = -Yp + s(Xp - Xr) */ |
| if ((err = mp_sub(&P->x, &tmpx, &tmp)) != MP_OKAY) { goto error; } /* tmp = Px - tmpx */ |
| if ((err = mp_mul(&tmp, &s, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp * s */ |
| if ((err = mp_submod(&tmp, &P->y, modulus, &R->y)) != MP_OKAY) { goto error; } /* Ry = tmp - Py mod modulus */ |
| if ((err = mp_mod(&tmpx, modulus, &R->x)) != MP_OKAY) { goto error; } /* Rx = tmpx mod modulus */ |
| |
| err = CRYPT_OK; |
| goto done; |
| error: |
| err = mpi_to_ltc_error(err); |
| done: |
| mp_clear_multi(&s, &tmpx, &tmp, NULL); |
| return err; |
| } |
| |
| /* size of sliding window, don't change this! */ |
| #define WINSIZE 4 |
| |
| /* perform R = kG where k == integer and G == ecc_point */ |
| static int ecc_mulmod(mp_int *k, ecc_point *G, ecc_point *R, mp_int *modulus) |
| { |
| ecc_point *tG, *M[8]; |
| int i, j, err; |
| mp_int mu; |
| mp_digit buf; |
| int first, bitbuf, bitcpy, bitcnt, mode, digidx; |
| |
| /* init barrett reduction */ |
| if ((err = mp_init(&mu)) != MP_OKAY) { |
| return mpi_to_ltc_error(err); |
| } |
| if ((err = mp_reduce_setup(&mu, modulus)) != MP_OKAY) { |
| mp_clear(&mu); |
| return mpi_to_ltc_error(err); |
| } |
| |
| /* alloc ram for window temps */ |
| for (i = 0; i < 8; i++) { |
| M[i] = new_point(); |
| if (M[i] == NULL) { |
| for (j = 0; j < i; j++) { |
| del_point(M[j]); |
| } |
| mp_clear(&mu); |
| return CRYPT_MEM; |
| } |
| } |
| |
| /* make a copy of G incase R==G */ |
| tG = new_point(); |
| if (tG == NULL) { err = CRYPT_MEM; goto done; } |
| |
| /* tG = G */ |
| if ((err = mp_copy(&G->x, &tG->x)) != MP_OKAY) { goto error; } |
| if ((err = mp_copy(&G->y, &tG->y)) != MP_OKAY) { goto error; } |
| |
| /* calc the M tab, which holds kG for k==8..15 */ |
| /* M[0] == 8G */ |
| if ((err = dbl_point(G, M[0], modulus, &mu)) != CRYPT_OK) { goto done; } |
| if ((err = dbl_point(M[0], M[0], modulus, &mu)) != CRYPT_OK) { goto done; } |
| if ((err = dbl_point(M[0], M[0], modulus, &mu)) != CRYPT_OK) { goto done; } |
| |
| /* now find (8+k)G for k=1..7 */ |
| for (j = 9; j < 16; j++) { |
| if ((err = add_point(M[j-9], G, M[j-8], modulus, &mu)) != CRYPT_OK) { goto done; } |
| } |
| |
| /* setup sliding window */ |
| mode = 0; |
| bitcnt = 1; |
| buf = 0; |
| digidx = k->used - 1; |
| bitcpy = bitbuf = 0; |
| first = 1; |
| |
| /* perform ops */ |
| for (;;) { |
| /* grab next digit as required */ |
| if (--bitcnt == 0) { |
| if (digidx == -1) { |
| break; |
| } |
| buf = k->dp[digidx--]; |
| bitcnt = (int) DIGIT_BIT; |
| } |
| |
| /* grab the next msb from the multiplicand */ |
| i = (buf >> (DIGIT_BIT - 1)) & 1; |
| buf <<= 1; |
| |
| /* skip leading zero bits */ |
| if (mode == 0 && i == 0) { |
| continue; |
| } |
| |
| /* if the bit is zero and mode == 1 then we double */ |
| if (mode == 1 && i == 0) { |
| if ((err = dbl_point(R, R, modulus, &mu)) != CRYPT_OK) { goto done; } |
| continue; |
| } |
| |
| /* else we add it to the window */ |
| bitbuf |= (i << (WINSIZE - ++bitcpy)); |
| mode = 2; |
| |
| if (bitcpy == WINSIZE) { |
| /* if this is the first window we do a simple copy */ |
| if (first == 1) { |
| /* R = kG [k = first window] */ |
| if ((err = mp_copy(&M[bitbuf-8]->x, &R->x)) != MP_OKAY) { goto error; } |
| if ((err = mp_copy(&M[bitbuf-8]->y, &R->y)) != MP_OKAY) { goto error; } |
| first = 0; |
| } else { |
| /* normal window */ |
| /* ok window is filled so double as required and add */ |
| /* double first */ |
| for (j = 0; j < WINSIZE; j++) { |
| if ((err = dbl_point(R, R, modulus, &mu)) != CRYPT_OK) { goto done; } |
| } |
| |
| /* then add, bitbuf will be 8..15 [8..2^WINSIZE] guaranteed */ |
| if ((err = add_point(R, M[bitbuf-8], R, modulus, &mu)) != CRYPT_OK) { goto done; } |
| } |
| /* empty window and reset */ |
| bitcpy = bitbuf = 0; |
| mode = 1; |
| } |
| } |
| |
| /* if bits remain then double/add */ |
| if (mode == 2 && bitcpy > 0) { |
| /* double then add */ |
| for (j = 0; j < bitcpy; j++) { |
| /* only double if we have had at least one add first */ |
| if (first == 0) { |
| if ((err = dbl_point(R, R, modulus, &mu)) != CRYPT_OK) { goto done; } |
| } |
| |
| bitbuf <<= 1; |
| if ((bitbuf & (1 << WINSIZE)) != 0) { |
| if (first == 1){ |
| /* first add, so copy */ |
| if ((err = mp_copy(&tG->x, &R->x)) != MP_OKAY) { goto error; } |
| if ((err = mp_copy(&tG->y, &R->y)) != MP_OKAY) { goto error; } |
| first = 0; |
| } else { |
| /* then add */ |
| if ((err = add_point(R, tG, R, modulus, &mu)) != CRYPT_OK) { goto done; } |
| } |
| } |
| } |
| } |
| err = CRYPT_OK; |
| goto done; |
| error: |
| err = mpi_to_ltc_error(err); |
| done: |
| del_point(tG); |
| for (i = 0; i < 8; i++) { |
| del_point(M[i]); |
| } |
| mp_clear(&mu); |
| return err; |
| } |
| |
| #undef WINSIZE |
| |
| int ecc_test(void) |
| { |
| mp_int modulus, order; |
| ecc_point *G, *GG; |
| int i, err, primality; |
| |
| if ((err = mp_init_multi(&modulus, &order, NULL)) != MP_OKAY) { |
| return mpi_to_ltc_error(err); |
| } |
| |
| G = new_point(); |
| GG = new_point(); |
| if (G == NULL || GG == NULL) { |
| mp_clear_multi(&modulus, &order, NULL); |
| del_point(G); |
| del_point(GG); |
| return CRYPT_MEM; |
| } |
| |
| for (i = 0; sets[i].size; i++) { |
| #if 0 |
| printf("Testing %d\n", sets[i].size); |
| #endif |
| if ((err = mp_read_radix(&modulus, (char *)sets[i].prime, 64)) != MP_OKAY) { goto error; } |
| if ((err = mp_read_radix(&order, (char *)sets[i].order, 64)) != MP_OKAY) { goto error; } |
| |
| /* is prime actually prime? */ |
| if ((err = is_prime(&modulus, &primality)) != CRYPT_OK) { goto done; } |
| if (primality == 0) { |
| err = CRYPT_FAIL_TESTVECTOR; |
| goto done; |
| } |
| |
| /* is order prime ? */ |
| if ((err = is_prime(&order, &primality)) != CRYPT_OK) { goto done; } |
| if (primality == 0) { |
| err = CRYPT_FAIL_TESTVECTOR; |
| goto done; |
| } |
| |
| if ((err = mp_read_radix(&G->x, (char *)sets[i].Gx, 64)) != MP_OKAY) { goto error; } |
| if ((err = mp_read_radix(&G->y, (char *)sets[i].Gy, 64)) != MP_OKAY) { goto error; } |
| |
| /* then we should have G == (order + 1)G */ |
| if ((err = mp_add_d(&order, 1, &order)) != MP_OKAY) { goto error; } |
| if ((err = ecc_mulmod(&order, G, GG, &modulus)) != CRYPT_OK) { goto done; } |
| if (mp_cmp(&G->x, &GG->x) != 0 || mp_cmp(&G->y, &GG->y) != 0) { |
| err = CRYPT_FAIL_TESTVECTOR; |
| goto done; |
| } |
| } |
| err = CRYPT_OK; |
| goto done; |
| error: |
| err = mpi_to_ltc_error(err); |
| done: |
| del_point(GG); |
| del_point(G); |
| mp_clear_multi(&order, &modulus, NULL); |
| return err; |
| } |
| |
| void ecc_sizes(int *low, int *high) |
| { |
| int i; |
| _ARGCHK(low != NULL); |
| _ARGCHK(high != NULL); |
| |
| *low = INT_MAX; |
| *high = 0; |
| for (i = 0; sets[i].size != 0; i++) { |
| if (sets[i].size < *low) { |
| *low = sets[i].size; |
| } |
| if (sets[i].size > *high) { |
| *high = sets[i].size; |
| } |
| } |
| } |
| |
| int ecc_make_key(prng_state *prng, int wprng, int keysize, ecc_key *key) |
| { |
| int x, err; |
| ecc_point *base; |
| mp_int prime; |
| unsigned char *buf; |
| |
| _ARGCHK(key != NULL); |
| |
| /* good prng? */ |
| if ((err = prng_is_valid(wprng)) != CRYPT_OK) { |
| return err; |
| } |
| |
| /* find key size */ |
| for (x = 0; (keysize > sets[x].size) && (sets[x].size != 0); x++); |
| keysize = sets[x].size; |
| _ARGCHK(keysize <= ECC_MAXSIZE); |
| |
| if (sets[x].size == 0) { |
| return CRYPT_INVALID_KEYSIZE; |
| } |
| key->idx = x; |
| |
| /* allocate ram */ |
| base = NULL; |
| buf = XMALLOC(ECC_MAXSIZE); |
| if (buf == NULL) { |
| return CRYPT_MEM; |
| } |
| |
| /* make up random string */ |
| if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) { |
| err = CRYPT_ERROR_READPRNG; |
| goto __ERR2; |
| } |
| |
| /* setup the key variables */ |
| if ((err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->k, &prime, NULL)) != MP_OKAY) { |
| err = mpi_to_ltc_error(err); |
| goto __ERR; |
| } |
| base = new_point(); |
| if (base == NULL) { |
| mp_clear_multi(&key->pubkey.x, &key->pubkey.y, &key->k, &prime, NULL); |
| err = CRYPT_MEM; |
| goto __ERR; |
| } |
| |
| /* read in the specs for this key */ |
| if ((err = mp_read_radix(&prime, (char *)sets[key->idx].prime, 64)) != MP_OKAY) { goto error; } |
| if ((err = mp_read_radix(&base->x, (char *)sets[key->idx].Gx, 64)) != MP_OKAY) { goto error; } |
| if ((err = mp_read_radix(&base->y, (char *)sets[key->idx].Gy, 64)) != MP_OKAY) { goto error; } |
| if ((err = mp_read_unsigned_bin(&key->k, (unsigned char *)buf, keysize)) != MP_OKAY) { goto error; } |
| |
| /* make the public key */ |
| if ((err = ecc_mulmod(&key->k, base, &key->pubkey, &prime)) != CRYPT_OK) { goto __ERR; } |
| key->type = PK_PRIVATE; |
| |
| /* shrink key */ |
| if ((err = mp_shrink(&key->k)) != MP_OKAY) { goto error; } |
| if ((err = mp_shrink(&key->pubkey.x)) != MP_OKAY) { goto error; } |
| if ((err = mp_shrink(&key->pubkey.y)) != MP_OKAY) { goto error; } |
| |
| /* free up ram */ |
| err = CRYPT_OK; |
| goto __ERR; |
| error: |
| err = mpi_to_ltc_error(err); |
| __ERR: |
| del_point(base); |
| mp_clear(&prime); |
| __ERR2: |
| #ifdef CLEAN_STACK |
| zeromem(buf, ECC_MAXSIZE); |
| #endif |
| |
| XFREE(buf); |
| |
| return err; |
| } |
| |
| void ecc_free(ecc_key *key) |
| { |
| _ARGCHK(key != NULL); |
| mp_clear_multi(&key->pubkey.x, &key->pubkey.y, &key->k, NULL); |
| } |
| |
| static int compress_y_point(ecc_point *pt, int idx, int *result) |
| { |
| mp_int tmp, tmp2, p; |
| int err; |
| |
| _ARGCHK(pt != NULL); |
| _ARGCHK(result != NULL); |
| |
| if ((err = mp_init_multi(&tmp, &tmp2, &p, NULL)) != MP_OKAY) { |
| return mpi_to_ltc_error(err); |
| } |
| |
| /* get x^3 - 3x + b */ |
| if ((err = mp_read_radix(&p, (char *)sets[idx].B, 64)) != MP_OKAY) { goto error; } /* p = B */ |
| if ((err = mp_expt_d(&pt->x, 3, &tmp)) != MP_OKAY) { goto error; } /* tmp = pX^3 */ |
| if ((err = mp_mul_d(&pt->x, 3, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = 3*pX^3 */ |
| if ((err = mp_sub(&tmp, &tmp2, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp - tmp2 */ |
| if ((err = mp_add(&tmp, &p, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp + p */ |
| if ((err = mp_read_radix(&p, (char *)sets[idx].prime, 64)) != MP_OKAY) { goto error; } /* p = prime */ |
| if ((err = mp_mod(&tmp, &p, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp mod p */ |
| |
| /* now find square root */ |
| if ((err = mp_add_d(&p, 1, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = p + 1 */ |
| if ((err = mp_div_2d(&tmp2, 2, &tmp2, NULL)) != MP_OKAY) { goto error; } /* tmp2 = (p+1)/4 */ |
| if ((err = mp_exptmod(&tmp, &tmp2, &p, &tmp)) != MP_OKAY) { goto error; } /* tmp = (x^3 - 3x + b)^((p+1)/4) mod p */ |
| |
| /* if tmp equals the y point give a 0, otherwise 1 */ |
| if (mp_cmp(&tmp, &pt->y) == 0) { |
| *result = 0; |
| } else { |
| *result = 1; |
| } |
| |
| err = CRYPT_OK; |
| goto done; |
| error: |
| err = mpi_to_ltc_error(err); |
| done: |
| mp_clear_multi(&p, &tmp, &tmp2, NULL); |
| return err; |
| } |
| |
| static int expand_y_point(ecc_point *pt, int idx, int result) |
| { |
| mp_int tmp, tmp2, p; |
| int err; |
| |
| _ARGCHK(pt != NULL); |
| |
| if ((err = mp_init_multi(&tmp, &tmp2, &p, NULL)) != MP_OKAY) { |
| return CRYPT_MEM; |
| } |
| |
| /* get x^3 - 3x + b */ |
| if ((err = mp_read_radix(&p, (char *)sets[idx].B, 64)) != MP_OKAY) { goto error; } /* p = B */ |
| if ((err = mp_expt_d(&pt->x, 3, &tmp)) != MP_OKAY) { goto error; } /* tmp = pX^3 */ |
| if ((err = mp_mul_d(&pt->x, 3, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = 3*pX^3 */ |
| if ((err = mp_sub(&tmp, &tmp2, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp - tmp2 */ |
| if ((err = mp_add(&tmp, &p, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp + p */ |
| if ((err = mp_read_radix(&p, (char *)sets[idx].prime, 64)) != MP_OKAY) { goto error; } /* p = prime */ |
| if ((err = mp_mod(&tmp, &p, &tmp)) != MP_OKAY) { goto error; } /* tmp = tmp mod p */ |
| |
| /* now find square root */ |
| if ((err = mp_add_d(&p, 1, &tmp2)) != MP_OKAY) { goto error; } /* tmp2 = p + 1 */ |
| if ((err = mp_div_2d(&tmp2, 2, &tmp2, NULL)) != MP_OKAY) { goto error; } /* tmp2 = (p+1)/4 */ |
| if ((err = mp_exptmod(&tmp, &tmp2, &p, &tmp)) != MP_OKAY) { goto error; } /* tmp = (x^3 - 3x + b)^((p+1)/4) mod p */ |
| |
| /* if result==0, then y==tmp, otherwise y==p-tmp */ |
| if (result == 0) { |
| if ((err = mp_copy(&tmp, &pt->y) != MP_OKAY)) { goto error; } |
| } else { |
| if ((err = mp_sub(&p, &tmp, &pt->y) != MP_OKAY)) { goto error; } |
| } |
| |
| err = CRYPT_OK; |
| goto done; |
| error: |
| err = mpi_to_ltc_error(err); |
| done: |
| mp_clear_multi(&p, &tmp, &tmp2, NULL); |
| return err; |
| } |
| |
| int ecc_export(unsigned char *out, unsigned long *outlen, int type, ecc_key *key) |
| { |
| unsigned long y, z; |
| int cp, err; |
| |
| _ARGCHK(out != NULL); |
| _ARGCHK(outlen != NULL); |
| _ARGCHK(key != NULL); |
| |
| /* can we store the static header? */ |
| if (*outlen < (PACKET_SIZE + 3)) { |
| return CRYPT_BUFFER_OVERFLOW; |
| } |
| |
| /* type valid? */ |
| if (key->type != PK_PRIVATE && type == PK_PRIVATE) { |
| return CRYPT_PK_TYPE_MISMATCH; |
| } |
| |
| /* output type and magic byte */ |
| y = PACKET_SIZE; |
| out[y++] = (unsigned char)type; |
| out[y++] = (unsigned char)sets[key->idx].size; |
| |
| /* output x coordinate */ |
| OUTPUT_BIGNUM(&(key->pubkey.x), out, y, z); |
| |
| /* compress y and output it */ |
| if ((err = compress_y_point(&key->pubkey, key->idx, &cp)) != CRYPT_OK) { |
| return err; |
| } |
| out[y++] = (unsigned char)cp; |
| |
| if (type == PK_PRIVATE) { |
| OUTPUT_BIGNUM(&key->k, out, y, z); |
| } |
| |
| /* store header */ |
| packet_store_header(out, PACKET_SECT_ECC, PACKET_SUB_KEY); |
| *outlen = y; |
| |
| return CRYPT_OK; |
| } |
| |
| int ecc_import(const unsigned char *in, unsigned long inlen, ecc_key *key) |
| { |
| unsigned long x, y, s; |
| int err; |
| |
| _ARGCHK(in != NULL); |
| _ARGCHK(key != NULL); |
| |
| /* check length */ |
| if ((3+PACKET_SIZE) > inlen) { |
| return CRYPT_INVALID_PACKET; |
| } |
| |
| /* check type */ |
| if ((err = packet_valid_header((unsigned char *)in, PACKET_SECT_ECC, PACKET_SUB_KEY)) != CRYPT_OK) { |
| return err; |
| } |
| |
| /* init key */ |
| if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->k, NULL) != MP_OKAY) { |
| return CRYPT_MEM; |
| } |
| |
| y = PACKET_SIZE; |
| key->type = (int)in[y++]; |
| s = (unsigned long)in[y++]; |
| |
| for (x = 0; (s > (unsigned long)sets[x].size) && (sets[x].size != 0); x++); |
| if (sets[x].size == 0) { |
| err = CRYPT_INVALID_KEYSIZE; |
| goto error; |
| } |
| key->idx = (int)x; |
| |
| /* type check both values */ |
| if ((key->type != PK_PUBLIC) && (key->type != PK_PRIVATE)) { |
| err = CRYPT_INVALID_PACKET; |
| goto error; |
| } |
| |
| /* is the key idx valid? */ |
| if (is_valid_idx(key->idx) != 1) { |
| err = CRYPT_INVALID_PACKET; |
| goto error; |
| } |
| |
| /* load x coordinate */ |
| INPUT_BIGNUM(&key->pubkey.x, in, x, y, inlen); |
| |
| /* load y */ |
| x = (unsigned long)in[y++]; |
| if ((err = expand_y_point(&key->pubkey, key->idx, (int)x)) != CRYPT_OK) { |
| goto error; |
| } |
| |
| if (key->type == PK_PRIVATE) { |
| /* load private key */ |
| INPUT_BIGNUM(&key->k, in, x, y, inlen); |
| } |
| |
| /* eliminate private key if public */ |
| if (key->type == PK_PUBLIC) { |
| mp_clear(&key->k); |
| } |
| |
| return CRYPT_OK; |
| error: |
| mp_clear_multi(&key->pubkey.x, &key->pubkey.y, &key->k, NULL); |
| return err; |
| } |
| |
| int ecc_shared_secret(ecc_key *private_key, ecc_key *public_key, |
| unsigned char *out, unsigned long *outlen) |
| { |
| unsigned long x, y; |
| ecc_point *result; |
| mp_int prime; |
| int err; |
| |
| _ARGCHK(private_key != NULL); |
| _ARGCHK(public_key != NULL); |
| _ARGCHK(out != NULL); |
| _ARGCHK(outlen != NULL); |
| |
| /* type valid? */ |
| if (private_key->type != PK_PRIVATE) { |
| return CRYPT_PK_NOT_PRIVATE; |
| } |
| |
| if (private_key->idx != public_key->idx) { |
| return CRYPT_PK_TYPE_MISMATCH; |
| } |
| |
| /* make new point */ |
| result = new_point(); |
| if (result == NULL) { |
| return CRYPT_MEM; |
| } |
| |
| if ((err = mp_init(&prime)) != MP_OKAY) { |
| del_point(result); |
| return mpi_to_ltc_error(err); |
| } |
| |
| if ((err = mp_read_radix(&prime, (char *)sets[private_key->idx].prime, 64)) != MP_OKAY) { goto error; } |
| if ((err = ecc_mulmod(&private_key->k, &public_key->pubkey, result, &prime)) != CRYPT_OK) { goto done1; } |
| |
| x = (unsigned long)mp_unsigned_bin_size(&result->x); |
| y = (unsigned long)mp_unsigned_bin_size(&result->y); |
| |
| if (*outlen < (x+y)) { |
| err = CRYPT_BUFFER_OVERFLOW; |
| goto done1; |
| } |
| *outlen = x+y; |
| if ((err = mp_to_unsigned_bin(&result->x, out)) != MP_OKAY) { goto error; } |
| if ((err = mp_to_unsigned_bin(&result->y, out+x)) != MP_OKAY) { goto error; } |
| |
| err = CRYPT_OK; |
| goto done1; |
| error: |
| err = mpi_to_ltc_error(err); |
| done1: |
| mp_clear(&prime); |
| del_point(result); |
| return err; |
| } |
| |
| int ecc_get_size(ecc_key *key) |
| { |
| _ARGCHK(key != NULL); |
| if (is_valid_idx(key->idx)) |
| return sets[key->idx].size; |
| else |
| return INT_MAX; /* large value known to cause it to fail when passed to ecc_make_key() */ |
| } |
| |
| #include "ecc_sys.c" |
| |
| #endif |
| |
| |
