370 lines
9.7 KiB
C++
370 lines
9.7 KiB
C++
//
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// Created by Andrew on 09/04/2023.
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//
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#include "header.h"
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const char pSv[] = "C9AE7AED19F6A7E100AADE98134111AD8118E59B8264734327940064BC675A0C682E19C89695FBFA3A4653E47D47FD7592258C7E3C3C61BBEA07FE5A7E842379";
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const long aSv = 1;
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const long bSv = 0;
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// Base point G (Generator)
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const char genXSv[] = "85ACEC9F9F9B456A78E43C3637DC88D21F977A9EC15E5225BD5060CE5B892F24FEDEE574BF5801F06BC232EEF2161074496613698D88FAC4B397CE3B475406A7";
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const char genYSv[] = "66B7D1983F5D4FE43E8B4F1E28685DE0E22BBE6576A1A6B86C67533BF72FD3D082DBA281A556A16E593DB522942C8DD7120BA50C9413DF944E7258BDDF30B3C4";
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// Inverse of the public key
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const char pubXSv[] = "90BF6BD980C536A8DB93B52AA9AEBA640BABF1D31BEC7AA345BB7510194A9B07379F552DA7B4A3EF81A9B87E0B85B5118E1E20A098641EE4CCF2045558C98C0E";
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const char pubYSv[] = "6B87D1E658D03868362945CDD582E2CF33EE4BA06369E0EFE9E4851F6DCBEC7F15081E250D171EA0CC4CB06435BCFCFEA8F438C9766743A06CBD06E7EFB4C3AE";
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// Order of G <- from MSKey 4-in-1
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const char genOrderSv[] = "4CC5C56529F0237D";
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// Computed private key
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const char privateKeySv[] = "2606120F59C05118";
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void unpackServer(ul32 *osFamily, ul32 *hash, ul32 *sig, ul32 *prefix, ul32 *raw) {
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// We're assuming that the quantity of information within the product key is at most 114 bits.
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// log2(24^25) = 114.
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// OS Family = Bits [0..10] -> 11 bits
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osFamily[0] = raw[0] & 0x7ff;
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// Hash = Bits [11..41] -> 31 bits
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hash[0] = ((raw[0] >> 11) | (raw[1] << 21)) & 0x7fffffff;
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// Signature = Bits [42..103] -> 62 bits
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sig[0] = (raw[1] >> 10) | (raw[2] << 22);
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sig[1] = ((raw[2] >> 10) | (raw[3] << 22)) & 0x3fffffff;
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// Prefix = Bits [104..113] -> 10 bits
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prefix[0] = (raw[3] >> 8) & 0x3ff;
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}
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void packServer(ul32 *raw, ul32 *osFamily, ul32 *hash, ul32 *sig, ul32 *prefix) {
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raw[0] = osFamily[0] | (hash[0] << 11);
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raw[1] = (hash[0] >> 21) | (sig[0] << 10);
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raw[2] = (sig[0] >> 22) | (sig[1] << 10);
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raw[3] = (sig[1] >> 22) | (prefix[0] << 8);
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}
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bool verifyServerKey(EC_GROUP *eCurve, EC_POINT *generator, EC_POINT *publicKey, char *cdKey) {
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BN_CTX *context = BN_CTX_new();
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// Convert Base24 CD-key to bytecode.
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ul32 osFamily, hash, sig[2], prefix;
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ul32 bKey[4]{};
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unbase24(bKey, cdKey);
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// Extract segments from the bytecode and reverse the signature.
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unpackServer(&osFamily, &hash, sig, &prefix, bKey);
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endiannessConvert((byte *)sig, 8);
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byte t[FIELD_BYTES_2003]{}, md[SHA_DIGEST_LENGTH]{};
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ul32 checkHash, newHash[2]{};
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SHA_CTX hContext;
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// H = SHA-1(5D || OS Family || Hash || Prefix || 00 00)
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SHA1_Init(&hContext);
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t[0] = 0x5D;
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t[1] = (osFamily & 0xff);
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t[2] = (osFamily & 0xff00) >> 8;
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t[3] = (hash & 0xff);
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t[4] = (hash & 0xff00) >> 8;
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t[5] = (hash & 0xff0000) >> 16;
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t[6] = (hash & 0xff000000) >> 24;
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t[7] = (prefix & 0xff);
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t[8] = (prefix & 0xff00) >> 8;
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t[9] = 0x00;
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t[10] = 0x00;
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SHA1_Update(&hContext, t, 11);
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SHA1_Final(md, &hContext);
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// First word.
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newHash[0] = md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24);
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// Second word, right shift 2 bits.
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newHash[1] = (md[4] | (md[5] << 8) | (md[6] << 16) | (md[7] << 24)) >> 2;
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newHash[1] &= 0x3FFFFFFF;
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endiannessConvert((byte *)newHash, 8);
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BIGNUM *x = BN_new();
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BIGNUM *y = BN_new();
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BIGNUM *s = BN_bin2bn((byte *)sig, 8, nullptr);
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BIGNUM *e = BN_bin2bn((byte *)newHash, 8, nullptr);
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EC_POINT *u = EC_POINT_new(eCurve);
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EC_POINT *v = EC_POINT_new(eCurve);
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// EC_POINT_mul calculates r = generator * n + q * m.
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// v = s * (s * generator + e * publicKey)
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// u = generator * s
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EC_POINT_mul(eCurve, u, nullptr, generator, s, context);
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// v = publicKey * e
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EC_POINT_mul(eCurve, v, nullptr, publicKey, e, context);
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// v += u
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EC_POINT_add(eCurve, v, u, v, context);
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// v *= s
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EC_POINT_mul(eCurve, v, nullptr, v, s, context);
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// EC_POINT_get_affine_coordinates() sets x and y, either of which may be nullptr, to the corresponding coordinates of p.
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// x = v.x; y = v.y;
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EC_POINT_get_affine_coordinates_GFp(eCurve, v, x, y, context);
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// Hash = First31(SHA-1(79 || OS Family || v.x || v.y))
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SHA1_Init(&hContext);
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t[0] = 0x79;
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t[1] = (osFamily & 0xff);
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t[2] = (osFamily & 0xff00) >> 8;
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// Hash chunk of data.
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SHA1_Update(&hContext, t, 3);
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// Empty buffer, place v.y in little-endian.
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memset(t, 0, FIELD_BYTES_2003);
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BN_bn2bin(x, t);
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endiannessConvert(t, FIELD_BYTES_2003);
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// Hash chunk of data.
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SHA1_Update(&hContext, t, FIELD_BYTES_2003);
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// Empty buffer, place v.y in little-endian.
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memset(t, 0, FIELD_BYTES_2003);
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BN_bn2bin(y, t);
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endiannessConvert(t, FIELD_BYTES_2003);
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// Hash chunk of data.
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SHA1_Update(&hContext, t, FIELD_BYTES_2003);
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// Store the final message from hContext in md.
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SHA1_Final(md, &hContext);
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// Hash = First31(SHA-1(79 || OS Family || v.x || v.y))
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checkHash = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff;
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BN_free(s);
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BN_free(e);
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BN_free(x);
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BN_free(y);
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BN_CTX_free(context);
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EC_POINT_free(v);
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EC_POINT_free(u);
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// If we managed to generate a key with the same hash, the key is correct.
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return checkHash == hash;
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}
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void generateServerKey(char *pKey, EC_GROUP *eCurve, EC_POINT *generator, BIGNUM *order, BIGNUM *privateKey, ul32 *osFamily, ul32 *prefix) {
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EC_POINT *r = EC_POINT_new(eCurve);
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BN_CTX *ctx = BN_CTX_new();
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ul32 bKey[4]{},
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bSig[2]{};
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do {
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BIGNUM *c = 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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BIGNUM *b = BN_new();
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ul32 hash = 0, h[2]{};
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memset(bKey, 0, 4);
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memset(bSig, 0, 2);
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// Generate a random number c consisting of 512 bits without any constraints.
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BN_rand(c, FIELD_BITS_2003, BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY);
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// r = generator * c
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EC_POINT_mul(eCurve, r, nullptr, generator, c, ctx);
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// x = r.x; y = r.y;
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EC_POINT_get_affine_coordinates(eCurve, r, x, y, ctx);
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SHA_CTX hContext;
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byte md[SHA_DIGEST_LENGTH]{}, buf[FIELD_BYTES_2003]{};
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// Hash = SHA-1(79 || OS Family || r.x || r.y)
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SHA1_Init(&hContext);
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buf[0] = 0x79;
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buf[1] = (*osFamily & 0xff);
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buf[2] = (*osFamily & 0xff00) >> 8;
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SHA1_Update(&hContext, buf, 3);
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memset(buf, 0, FIELD_BYTES_2003);
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BN_bn2bin(x, buf);
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endiannessConvert((byte *) buf, FIELD_BYTES_2003);
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SHA1_Update(&hContext, buf, FIELD_BYTES_2003);
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memset(buf, 0, FIELD_BYTES_2003);
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BN_bn2bin(y, buf);
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endiannessConvert((byte *) buf, FIELD_BYTES_2003);
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SHA1_Update(&hContext, buf, FIELD_BYTES_2003);
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SHA1_Final(md, &hContext);
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hash = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff;
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// H = SHA-1(5D || OS Family || Hash || Prefix || 00 00)
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SHA1_Init(&hContext);
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buf[0] = 0x5D;
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buf[1] = (*osFamily & 0xff);
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buf[2] = (*osFamily & 0xff00) >> 8;
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buf[3] = (hash & 0xff);
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buf[4] = (hash & 0xff00) >> 8;
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buf[5] = (hash & 0xff0000) >> 16;
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buf[6] = (hash & 0xff000000) >> 24;
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buf[7] = prefix[0] & 0xff;
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buf[8] = (prefix[0] & 0xff00) >> 8;
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buf[9] = 0x00;
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buf[10] = 0x00;
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// Input length is 11 bytes.
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SHA1_Update(&hContext, buf, 11);
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SHA1_Final(md, &hContext);
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// First word.
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h[0] = md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24);
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// Second word, right shift 2 bits.
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h[1] = (md[4] | (md[5] << 8) | (md[6] << 16) | (md[7] << 24)) >> 2;
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h[1] &= 0x3FFFFFFF;
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endiannessConvert((byte *)h, 8);
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BN_bin2bn((byte *)h, 8, b);
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/*
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* Signature * (Signature * G + H * K) = rG (mod p)
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* ↓ K = kG ↓
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*
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* Signature * (Signature * G + H * k * G) = rG (mod p)
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* Signature^2 * G + Signature * HkG = rG (mod p)
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* G(Signature^2 + Signature * HkG) = G (mod p) * r
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* ↓ G^(-1)(G (mod p)) = (mod n), n = order of G ↓
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*
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* Signature^2 + Hk * Signature = r (mod n)
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* Signature = -(b +- sqrt(D)) / 2a → Signature = (-Hk +- sqrt((Hk)^2 + 4r)) / 2
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*
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* S = (-Hk +- sqrt((Hk)^2 + 4r)) (mod n) / 2
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*
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* S = s
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* H = b
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* k = privateKey
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* n = order
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* r = c
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*
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* s = ( ( -b * privateKey +- sqrt( (b * privateKey)^2 + 4c ) ) / 2 ) % order
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*/
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// b = (b * privateKey) % order
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BN_mod_mul(b, b, privateKey, order, ctx);
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// s = b
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BN_copy(s, b);
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// s = (s % order)^2
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BN_mod_sqr(s, s, order, ctx);
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// c <<= 2 (c = 4c)
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BN_lshift(c, c, 2);
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// s = s + c
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BN_add(s, s, c);
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// s^2 = s % order (order must be prime)
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BN_mod_sqrt(s, s, order, ctx);
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// s = s - b
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BN_mod_sub(s, s, b, order, ctx);
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// if s is odd, s = s + order
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if (BN_is_odd(s)) {
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BN_add(s, s, order);
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}
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// s >>= 1 (s = s / 2)
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BN_rshift1(s, s);
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// Convert s from BigNum back to bytecode and reverse the endianness.
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BN_bn2bin(s, (byte *)bSig);
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endiannessConvert((byte *)bSig, BN_num_bytes(s));
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// Pack product key.
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packServer(bKey, osFamily, &hash, bSig, prefix);
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BN_free(c);
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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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BN_free(b);
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} while (bSig[1] >= 0x40000000);
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base24(pKey, bKey);
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BN_CTX_free(ctx);
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EC_POINT_free(r);
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}
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bool keyServer(char *pKey) {
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// We cannot produce a valid key without knowing the private key k. The reason for this is that
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// we need the result of the function K(x; y) = kG(x; y).
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BIGNUM *privateKey = BN_new();
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// We can, however, validate any given key using the available public key: {p, a, b, G, K}.
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// genOrder the order of the generator G, a value we have to reverse -> Schoof's Algorithm.
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BIGNUM *genOrder = BN_new();
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/* Computed data */
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BN_hex2bn(&genOrder, genOrderSv);
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BN_hex2bn(&privateKey, privateKeySv);
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EC_POINT *genPoint, *pubPoint;
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EC_GROUP *eCurve = initializeEllipticCurve(
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pSv,
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aSv,
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bSv,
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genXSv,
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genYSv,
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pubXSv,
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pubYSv,
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genOrder,
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privateKey,
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&genPoint,
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&pubPoint
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);
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ul32 osFamily = 1280, prefix = 0;
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// Generate a 30-bit prefix.
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RAND_bytes((byte *)&prefix, 4);
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prefix &= 0x3FF;
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do {
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generateServerKey(pKey, eCurve, genPoint, genOrder, privateKey, &osFamily, &prefix);
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} while (!verifyServerKey(eCurve, genPoint, pubPoint, pKey));
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return true;
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} |