// // Created by Andrew on 09/04/2023. // #include "header.h" const char pSv[] = "C9AE7AED19F6A7E100AADE98134111AD8118E59B8264734327940064BC675A0C682E19C89695FBFA3A4653E47D47FD7592258C7E3C3C61BBEA07FE5A7E842379"; const long aSv = 1; const long bSv = 0; // Base point G (Generator) const char genXSv[] = "85ACEC9F9F9B456A78E43C3637DC88D21F977A9EC15E5225BD5060CE5B892F24FEDEE574BF5801F06BC232EEF2161074496613698D88FAC4B397CE3B475406A7"; const char genYSv[] = "66B7D1983F5D4FE43E8B4F1E28685DE0E22BBE6576A1A6B86C67533BF72FD3D082DBA281A556A16E593DB522942C8DD7120BA50C9413DF944E7258BDDF30B3C4"; // Inverse of the public key const char pubXSv[] = "90BF6BD980C536A8DB93B52AA9AEBA640BABF1D31BEC7AA345BB7510194A9B07379F552DA7B4A3EF81A9B87E0B85B5118E1E20A098641EE4CCF2045558C98C0E"; const char pubYSv[] = "6B87D1E658D03868362945CDD582E2CF33EE4BA06369E0EFE9E4851F6DCBEC7F15081E250D171EA0CC4CB06435BCFCFEA8F438C9766743A06CBD06E7EFB4C3AE"; // Order of G <- from MSKey 4-in-1 const char genOrderSv[] = "4CC5C56529F0237D"; // Computed private key const char privateKeySv[] = "2606120F59C05118"; void unpackServer(ul32 *osFamily, ul32 *hash, ul32 *sig, ul32 *prefix, ul32 *raw) { osFamily[0] = raw[0] & 0x7ff; hash[0] = ((raw[0] >> 11) | (raw[1] << 21)) & 0x7fffffff; sig[0] = (raw[1] >> 10) | (raw[2] << 22); sig[1] = ((raw[2] >> 10) | (raw[3] << 22)) & 0x3fffffff; prefix[0] = (raw[3] >> 8) & 0x3ff; } void packServer(ul32 *raw, ul32 *osFamily, ul32 *hash, ul32 *sig, ul32 *prefix) { raw[0] = osFamily[0] | (hash[0] << 11); raw[1] = (hash[0] >> 21) | (sig[0] << 10); raw[2] = (sig[0] >> 22) | (sig[1] << 10); raw[3] = (sig[1] >> 22) | (prefix[0] << 8); } bool verifyServerKey(EC_GROUP *eCurve, EC_POINT *generator, EC_POINT *public_key, char *cdKey) { int i, j, k; BN_CTX *ctx = BN_CTX_new(); ul32 bkey[4] = {0}; ul32 osfamily[1], hash[1], sig[2], prefix[1]; unbase24(bkey, cdKey); printf("%.8x %.8x %.8x %.8x\n", bkey[3], bkey[2], bkey[1], bkey[0]); unpackServer(osfamily, hash, sig, prefix, bkey); printf("OS Family: %u\nHash: %.8x\nSig: %.8x %.8x\nPrefix: %.8x\n", osfamily[0], hash[0], sig[1], sig[0], prefix[0]); byte buf[FIELD_BYTES_2003], md[SHA_DIGEST_LENGTH]; ul32 h1[2]; SHA_CTX h_ctx; /* h1 = SHA-1(5D || OS Family || Hash || Prefix || 00 00) */ SHA1_Init(&h_ctx); buf[0] = 0x5d; buf[1] = osfamily[0] & 0xff; buf[2] = (osfamily[0] & 0xff00) >> 8; buf[3] = hash[0] & 0xff; buf[4] = (hash[0] & 0xff00) >> 8; buf[5] = (hash[0] & 0xff0000) >> 16; buf[6] = (hash[0] & 0xff000000) >> 24; buf[7] = prefix[0] & 0xff; buf[8] = (prefix[0] & 0xff00) >> 8; buf[9] = buf[10] = 0; SHA1_Update(&h_ctx, buf, 11); SHA1_Final(md, &h_ctx); h1[0] = md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24); h1[1] = (md[4] | (md[5] << 8) | (md[6] << 16) | (md[7] << 24)) >> 2; h1[1] &= 0x3FFFFFFF; printf("h1: %.8x %.8x\n", h1[1], h1[0]); BIGNUM *s, *h, *x, *y; x = BN_new(); y = BN_new(); endiannessConvert((byte *) sig, 8); endiannessConvert((byte *) h1, 8); s = BN_bin2bn((byte *)sig, 8, nullptr); h = BN_bin2bn((byte *)h1, 8, nullptr); EC_POINT *r = EC_POINT_new(eCurve); EC_POINT *t = EC_POINT_new(eCurve); /* r = sig*(sig*generator + h1*public_key) */ EC_POINT_mul(eCurve, t, nullptr, generator, s, ctx); EC_POINT_mul(eCurve, r, nullptr, public_key, h, ctx); EC_POINT_add(eCurve, r, r, t, ctx); EC_POINT_mul(eCurve, r, nullptr, r, s, ctx); EC_POINT_get_affine_coordinates_GFp(eCurve, r, x, y, ctx); ul32 h2[1]; /* h2 = SHA-1(79 || OS Family || r.x || r.y) */ SHA1_Init(&h_ctx); buf[0] = 0x79; buf[1] = osfamily[0] & 0xff; buf[2] = (osfamily[0] & 0xff00) >> 8; SHA1_Update(&h_ctx, buf, 3); memset(buf, 0, FIELD_BYTES_2003); BN_bn2bin(x, buf); endiannessConvert((byte *) buf, FIELD_BYTES_2003); SHA1_Update(&h_ctx, buf, FIELD_BYTES_2003); memset(buf, 0, FIELD_BYTES_2003); BN_bn2bin(y, buf); endiannessConvert((byte *) buf, FIELD_BYTES_2003); SHA1_Update(&h_ctx, buf, FIELD_BYTES_2003); SHA1_Final(md, &h_ctx); h2[0] = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff; printf("Calculated hash: %.8x\n", h2[0]); BN_free(s); BN_free(h); BN_free(x); BN_free(y); EC_POINT_free(r); EC_POINT_free(t); BN_CTX_free(ctx); if (h2[0] == hash[0]) return true; else return false; } void generateServerKey(char *pKey, EC_GROUP *eCurve, EC_POINT *generator, BIGNUM *order, BIGNUM *privateKey, ul32 *osFamily, ul32 *prefix) { BN_CTX *ctx = BN_CTX_new(); BIGNUM *c = BN_new(); BIGNUM *s = BN_new(); BIGNUM *x = BN_new(); BIGNUM *y = BN_new(); BIGNUM *b = BN_new(); EC_POINT *r = EC_POINT_new(eCurve); ul32 bKey[4]; ul32 h1[2]; do { ul32 hash = 0, sig[2]{}; memset(bKey, 0, 4); // Generate a random number c consisting of 512 bits without any constraints. BN_rand(c, FIELD_BITS_2003, BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY); // r = generator * c EC_POINT_mul(eCurve, r, nullptr, generator, c, ctx); // x = r.x; y = r.y; EC_POINT_get_affine_coordinates(eCurve, r, x, y, ctx); SHA_CTX hContext; byte md[SHA_DIGEST_LENGTH]{}, buf[FIELD_BYTES_2003]{}; // hash = SHA-1(79 || OS Family || r.x || r.y) SHA1_Init(&hContext); buf[0] = 0x79; buf[1] = (*osFamily & 0xff); buf[2] = (*osFamily & 0xff00) >> 8; SHA1_Update(&hContext, buf, 3); memset(buf, 0, FIELD_BYTES_2003); BN_bn2bin(x, buf); endiannessConvert((byte *) buf, FIELD_BYTES_2003); SHA1_Update(&hContext, buf, FIELD_BYTES_2003); memset(buf, 0, FIELD_BYTES_2003); BN_bn2bin(y, buf); endiannessConvert((byte *) buf, FIELD_BYTES_2003); SHA1_Update(&hContext, buf, FIELD_BYTES_2003); SHA1_Final(md, &hContext); hash = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff; /* h1 = SHA-1(5D || OS Family || Hash || Prefix || 00 00) */ SHA1_Init(&hContext); buf[0] = 0x5D; buf[1] = (*osFamily & 0xff); buf[2] = (*osFamily & 0xff00) >> 8; buf[3] = (hash & 0xff); buf[4] = (hash & 0xff00) >> 8; buf[5] = (hash & 0xff0000) >> 16; buf[6] = (hash & 0xff000000) >> 24; buf[7] = prefix[0] & 0xff; buf[8] = (prefix[0] & 0xff00) >> 8; buf[9] = 0x00; buf[10] = 0x00; SHA1_Update(&hContext, buf, 11); SHA1_Final(md, &hContext); h1[0] = md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24); h1[1] = (md[4] | (md[5] << 8) | (md[6] << 16) | (md[7] << 24)) >> 2; h1[1] &= 0x3FFFFFFF; printf("h1: %.8x %.8x\n", h1[1], h1[0]); /* s = ( -h1*privateKey + sqrt( (h1*privateKey)^2 + 4k ) ) / 2 */ endiannessConvert((byte *) h1, 8); BN_bin2bn((byte *)h1, 8, b); BN_mod_mul(b, b, privateKey, order, ctx); BN_copy(s, b); BN_mod_sqr(s, s, order, ctx); BN_lshift(c, c, 2); BN_add(s, s, c); BN_mod_sqrt(s, s, order, ctx); BN_mod_sub(s, s, b, order, ctx); if (BN_is_odd(s)) { BN_add(s, s, order); } BN_rshift1(s, s); sig[0] = sig[1] = 0; BN_bn2bin(s, (byte *)sig); endiannessConvert((byte *)sig, BN_num_bytes(s)); packServer(bKey, osFamily, &hash, sig, prefix); printf("OS family: %u\nHash: %.8x\nSig: %.8x %.8x\nPrefix: %.8x\n", *osFamily, hash, sig[1], sig[0], *prefix); printf("%.8x %.8x %.8x %.8x\n", bKey[3], bKey[2], bKey[1], bKey[0]); } while (bKey[3] >= 0x40000000); base24(pKey, bKey); BN_free(c); BN_free(s); BN_free(x); BN_free(y); BN_free(b); BN_CTX_free(ctx); EC_POINT_free(r); } bool keyServer(char *pKey) { // We cannot produce a valid key without knowing the private key k. The reason for this is that // we need the result of the function K(x; y) = kG(x; y). BIGNUM *privateKey = BN_new(); // We can, however, validate any given key using the available public key: {p, a, b, G, K}. // genOrder the order of the generator G, a value we have to reverse -> Schoof's Algorithm. BIGNUM *genOrder = BN_new(); /* Computed data */ BN_hex2bn(&genOrder, genOrderSv); BN_hex2bn(&privateKey, privateKeySv); EC_POINT *genPoint, *pubPoint; EC_GROUP *eCurve = initializeEllipticCurve( pSv, aSv, bSv, genXSv, genYSv, pubXSv, pubYSv, genOrder, privateKey, &genPoint, &pubPoint ); ul32 osFamily = 1280, prefix = 0; RAND_bytes((byte *)&prefix, 4); prefix &= 0x3ff; generateServerKey(pKey, eCurve, genPoint, genOrder, privateKey, &osFamily, &prefix); printProductKey(pKey); printf("\n\n"); return verifyServerKey(eCurve, genPoint, pubPoint, pKey); }