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#include <stdio.h> |
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#include <string.h> |
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#include <openssl/bn.h> |
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#include <openssl/ec.h> |
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#include <openssl/sha.h> |
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#include <assert.h> |
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#define FIELD_BITS 384 |
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#define FIELD_BYTES 48 |
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uint8_t cset[] = "BCDFGHJKMPQRTVWXY2346789"; |
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static void unpack(uint32_t *pid, uint32_t *hash, uint32_t *sig, uint32_t *raw) |
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{ |
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// pid = Bit 0..30 |
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pid[0] = raw[0] & 0x7fffffff; |
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// hash(s) = Bit 31..58 |
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hash[0] = ((raw[0] >> 31) | (raw[1] << 1)) & 0xfffffff; |
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// sig(e) = bit 58..113 |
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sig[0] = (raw[1] >> 27) | (raw[2] << 5); |
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sig[1] = (raw[2] >> 27) | (raw[3] << 5); |
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} |
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static void pack(uint32_t *raw, uint32_t *pid, uint32_t *hash, uint32_t *sig) |
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{ |
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raw[0] = pid[0] | ((hash[0] & 1) << 31); |
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raw[1] = (hash[0] >> 1) | ((sig[0] & 0x1f) << 27); |
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raw[2] = (sig[0] >> 5) | (sig[1] << 27); |
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raw[3] = sig[1] >> 5; |
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} |
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// Reverse data |
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static void endian(uint8_t *data, int len) |
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{ |
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int i; |
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for (i = 0; i < len/2; i++) { |
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uint8_t temp; |
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temp = data[i]; |
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data[i] = data[len-i-1]; |
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data[len-i-1] = temp; |
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} |
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} |
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void unbase24(uint32_t *x, uint8_t *c) |
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{ |
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memset(x, 0, 16); |
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int i, n; |
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BIGNUM *y = BN_new(); |
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BN_zero(y); |
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for (i = 0; i < 25; i++) |
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{ |
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BN_mul_word(y, 24); |
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BN_add_word(y, c[i]); |
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} |
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n = BN_num_bytes(y); |
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BN_bn2bin(y, (uint8_t *)x); |
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BN_free(y); |
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endian((uint8_t *)x, n); |
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} |
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void base24(uint8_t *c, uint32_t *x) |
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{ |
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uint8_t y[16]; |
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int i; |
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BIGNUM *z; |
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// Convert x to BigNum z |
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memcpy(y, x, sizeof(y)); // Copy X to Y; Y=X |
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for (i = 15; y[i] == 0; i--) {} i++; // skip following nulls |
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endian(y, i); // Reverse y |
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z = BN_bin2bn(y, i, NULL); // Convert y to BigNum z |
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// Divide z by 24 and convert remainder with cset to Base24-CDKEY Char |
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c[25] = 0; |
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for (i = 24; i >= 0; i--) { |
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uint8_t t = BN_div_word(z, 24); |
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c[i] = cset[t]; |
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} |
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BN_free(z); |
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} |
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void print_product_id(uint32_t *pid) |
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{ |
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char raw[12]; |
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char b[6], c[8]; |
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int i, digit = 0; |
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// Cut a away last bit of pid and convert it to an accii-number (=raw) |
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sprintf(raw, "%d", pid[0] >> 1); |
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// Make b-part {640-....} |
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strncpy(b, raw, 3); |
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b[3] = 0; |
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// Make c-part {...-123456X...} |
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strcpy(c, raw + 3); |
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// Make checksum digit-part {...56X-} |
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assert(strlen(c) == 6); |
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for (i = 0; i < 6; i++) |
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digit -= c[i] - '0'; // Sum digits |
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while (digit < 0) |
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digit += 7; |
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c[6] = digit + '0'; |
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c[7] = 0; |
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printf("Product ID: 55274-%s-%s-23xxx\n", b, c); |
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} |
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void print_product_key(uint8_t *pk) |
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{ |
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int i; |
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assert(strlen((const char *)pk) == 25); |
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for (i = 0; i < 25; i++) { |
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putchar(pk[i]); |
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if (i != 24 && i % 5 == 4) putchar('-'); |
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} |
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} |
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void verify(EC_GROUP *ec, EC_POINT *generator, EC_POINT *public_key, char *cdkey) |
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{ |
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uint8_t key[25]; |
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int i, j, k; |
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BN_CTX *ctx = BN_CTX_new(); |
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// remove Dashs from CDKEY |
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for (i = 0, k = 0; i < strlen(cdkey); i++) { |
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for (j = 0; j < 24; j++) { |
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if (cdkey[i] != '-' && cdkey[i] == cset[j]) { |
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key[k++] = j; |
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break; |
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} |
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assert(j < 24); |
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} |
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if (k >= 25) break; |
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} |
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// Base24_CDKEY -> Bin_CDKEY |
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uint32_t bkey[4] = {0}; |
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uint32_t pid[1], hash[1], sig[2]; |
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unbase24(bkey, key); |
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// Output Bin_CDKEY |
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printf("%.8x %.8x %.8x %.8x\n", bkey[3], bkey[2], bkey[1], bkey[0]); |
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// Divide/Extract pid_data, hash, sig from Bin_CDKEY |
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unpack(pid, hash, sig, bkey); |
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print_product_id(pid); |
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printf("PID: %.8x\nHash: %.8x\nSig: %.8x %.8x\n", pid[0], hash[0], sig[1], sig[0]); |
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BIGNUM *e, *s; |
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/* e = hash, s = sig */ |
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e = BN_new(); |
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BN_set_word(e, hash[0]); |
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endian((uint8_t *)sig, sizeof(sig)); |
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s = BN_bin2bn((uint8_t *)sig, sizeof(sig), NULL); |
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BIGNUM *x = BN_new(); |
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BIGNUM *y = BN_new(); |
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EC_POINT *u = EC_POINT_new(ec); |
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EC_POINT *v = EC_POINT_new(ec); |
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/* v = s*generator + e*(-public_key) */ |
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EC_POINT_mul(ec, u, NULL, generator, s, ctx); |
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EC_POINT_mul(ec, v, NULL, public_key, e, ctx); |
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EC_POINT_add(ec, v, u, v, ctx); |
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EC_POINT_get_affine_coordinates_GFp(ec, v, x, y, ctx); |
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uint8_t buf[FIELD_BYTES], md[20]; |
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uint32_t h; |
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uint8_t t[4]; |
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SHA_CTX h_ctx; |
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/* h = (fist 32 bits of SHA1(pid || v.x, v.y)) >> 4 */ |
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SHA1_Init(&h_ctx); |
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t[0] = pid[0] & 0xff; |
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t[1] = (pid[0] & 0xff00) >> 8; |
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t[2] = (pid[0] & 0xff0000) >> 16; |
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t[3] = (pid[0] & 0xff000000) >> 24; |
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SHA1_Update(&h_ctx, t, sizeof(t)); |
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memset(buf, 0, sizeof(buf)); |
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BN_bn2bin(x, buf); |
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endian((uint8_t *)buf, sizeof(buf)); |
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SHA1_Update(&h_ctx, buf, sizeof(buf)); |
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memset(buf, 0, sizeof(buf)); |
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BN_bn2bin(y, buf); |
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endian((uint8_t *)buf, sizeof(buf)); |
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SHA1_Update(&h_ctx, buf, sizeof(buf)); |
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SHA1_Final(md, &h_ctx); |
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h = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) >> 4; |
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h &= 0xfffffff; |
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printf("Calculated hash: %.8x\n", h); |
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if (h == hash[0]) printf("Key valid\n"); |
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else printf("Key invalid\n"); |
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putchar('\n'); |
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BN_free(e); |
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BN_free(s); |
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BN_free(x); |
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BN_free(y); |
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EC_POINT_free(u); |
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EC_POINT_free(v); |
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BN_CTX_free(ctx); |
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} |
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void generate(uint8_t *pkey, EC_GROUP *ec, EC_POINT *generator, BIGNUM *order, BIGNUM *priv, uint32_t *pid) |
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{ |
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BN_CTX *ctx = BN_CTX_new(); |
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BIGNUM *k = BN_new(); |
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BIGNUM *s = BN_new(); |
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BIGNUM *x = BN_new(); |
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BIGNUM *y = BN_new(); |
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EC_POINT *r = EC_POINT_new(ec); |
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uint32_t bkey[4]; |
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// Loop in case signaturepart will make cdkey(base-24 "digits") longer than 25 |
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do { |
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BN_pseudo_rand(k, FIELD_BITS, -1, 0); |
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EC_POINT_mul(ec, r, NULL, generator, k, ctx); |
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EC_POINT_get_affine_coordinates_GFp(ec, r, x, y, ctx); |
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SHA_CTX h_ctx; |
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uint8_t t[4], md[20], buf[FIELD_BYTES]; |
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uint32_t hash[1]; |
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/* h = (fist 32 bits of SHA1(pid || r.x, r.y)) >> 4 */ |
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SHA1_Init(&h_ctx); |
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t[0] = pid[0] & 0xff; |
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t[1] = (pid[0] & 0xff00) >> 8; |
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t[2] = (pid[0] & 0xff0000) >> 16; |
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t[3] = (pid[0] & 0xff000000) >> 24; |
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SHA1_Update(&h_ctx, t, sizeof(t)); |
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memset(buf, 0, sizeof(buf)); |
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BN_bn2bin(x, buf); |
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endian((uint8_t *)buf, sizeof(buf)); |
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SHA1_Update(&h_ctx, buf, sizeof(buf)); |
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memset(buf, 0, sizeof(buf)); |
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BN_bn2bin(y, buf); |
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endian((uint8_t *)buf, sizeof(buf)); |
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SHA1_Update(&h_ctx, buf, sizeof(buf)); |
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SHA1_Final(md, &h_ctx); |
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hash[0] = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) >> 4; |
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hash[0] &= 0xfffffff; |
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/* s = priv*h + k */ |
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BN_copy(s, priv); |
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BN_mul_word(s, hash[0]); |
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BN_mod_add(s, s, k, order, ctx); |
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uint32_t sig[2] = {0}; |
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BN_bn2bin(s, (uint8_t *)sig); |
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endian((uint8_t *)sig, BN_num_bytes(s)); |
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pack(bkey, pid, hash, sig); |
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printf("PID: %.8x\nHash: %.8x\nSig: %.8x %.8x\n", pid[0], hash[0], sig[1], sig[0]); |
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} while (bkey[3] >= 0x62a32); |
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base24(pkey, bkey); |
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BN_free(k); |
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BN_free(s); |
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BN_free(x); |
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BN_free(y); |
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EC_POINT_free(r); |
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BN_CTX_free(ctx); |
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} |
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int main() |
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{ |
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// Init |
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BIGNUM *a, *b, *p, *gx, *gy, *pubx, *puby, *n, *priv; |
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BN_CTX *ctx = BN_CTX_new(); |
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// make BigNumbers |
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a = BN_new(); |
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b = BN_new(); |
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p = BN_new(); |
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gx = BN_new(); |
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gy = BN_new(); |
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pubx = BN_new(); |
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puby = BN_new(); |
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n = BN_new(); |
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priv = BN_new(); |
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// Data from pidgen-Bink-resources |
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/* Elliptic curve parameters: y^2 = x^3 + ax + b mod p */ |
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BN_hex2bn(&p, "92ddcf14cb9e71f4489a2e9ba350ae29454d98cb93bdbcc07d62b502ea12238ee904a8b20d017197aae0c103b32713a9"); |
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BN_set_word(a, 1); |
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BN_set_word(b, 0); |
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/* base point (generator) G */ |
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BN_hex2bn(&gx, "46E3775ECE21B0898D39BEA57050D422A0AF989E497962BAEE2CB17E0A28D5360D5476B8DC966443E37A14F1AEF37742"); |
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BN_hex2bn(&gy, "7C8E741D2C34F4478E325469CD491603D807222C9C4AC09DDB2B31B3CE3F7CC191B3580079932BC6BEF70BE27604F65E"); |
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/* inverse of public key */ |
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BN_hex2bn(&pubx, "5D8DBE75198015EC41C45AAB6143542EB098F6A5CC9CE4178A1B8A1E7ABBB5BC64DF64FAF6177DC1B0988AB00BA94BF8"); |
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BN_hex2bn(&puby, "23A2909A0B4803C89F910C7191758B48746CEA4D5FF07667444ACDB9512080DBCA55E6EBF30433672B894F44ACE92BFA"); |
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// Computed data |
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/* order of G - computed in 18 hours using a P3-450 */ |
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BN_hex2bn(&n, "DB6B4C58EFBAFD"); |
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/* THE private key - computed in 10 hours using a P3-450 */ |
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BN_hex2bn(&priv, "565B0DFF8496C8"); |
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// Calculation |
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EC_GROUP *ec = EC_GROUP_new_curve_GFp(p, a, b, ctx); |
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EC_POINT *g = EC_POINT_new(ec); |
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EC_POINT_set_affine_coordinates_GFp(ec, g, gx, gy, ctx); |
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EC_POINT *pub = EC_POINT_new(ec); |
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EC_POINT_set_affine_coordinates_GFp(ec, pub, pubx, puby, ctx); |
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uint8_t pkey[26]; |
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uint32_t pid[1]; |
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pid[0] = 640000000 << 1; /* <- change */ |
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// generate a key |
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generate(pkey, ec, g, n, priv, pid); |
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print_product_key(pkey); printf("\n\n"); |
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// verify the key |
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verify(ec, g, pub, (char*)pkey); |
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// Cleanup |
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BN_CTX_free(ctx); |
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return 0; |
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} |