295 lines
8.6 KiB
C++
295 lines
8.6 KiB
C++
//
|
|
// Created by Andrew on 09/04/2023.
|
|
//
|
|
|
|
#include "header.h"
|
|
|
|
const char pXP[] = "92ddcf14cb9e71f4489a2e9ba350ae29454d98cb93bdbcc07d62b502ea12238ee904a8b20d017197aae0c103b32713a9";
|
|
const long aXP = 1;
|
|
const long bXP = 0;
|
|
|
|
// Base point G (Generator)
|
|
const char genXXP[] = "46E3775ECE21B0898D39BEA57050D422A0AF989E497962BAEE2CB17E0A28D5360D5476B8DC966443E37A14F1AEF37742";
|
|
const char genYXP[] = "7C8E741D2C34F4478E325469CD491603D807222C9C4AC09DDB2B31B3CE3F7CC191B3580079932BC6BEF70BE27604F65E";
|
|
|
|
// Inverse of the public key
|
|
const char pubXXP[] = "5D8DBE75198015EC41C45AAB6143542EB098F6A5CC9CE4178A1B8A1E7ABBB5BC64DF64FAF6177DC1B0988AB00BA94BF8";
|
|
const char pubYXP[] = "23A2909A0B4803C89F910C7191758B48746CEA4D5FF07667444ACDB9512080DBCA55E6EBF30433672B894F44ACE92BFA";
|
|
|
|
// The order of G was computed in 18 hours using a Pentium III 450
|
|
const char genOrderXP[] = "DB6B4C58EFBAFD";
|
|
|
|
// The private key was computed in 10 hours using a Pentium III 450
|
|
const char privateKeyXP[] = "565B0DFF8496C8";
|
|
|
|
/* Unpacks the Product Key. */
|
|
void unpackXP(ul32 *serial, ul32 *hash, ul32 *sig, ul32 *raw) {
|
|
|
|
// We're assuming that the quantity of information within the product key is at most 114 bits.
|
|
// log2(24^25) = 114.
|
|
|
|
// Serial = Bits [0..30] -> 31 bits
|
|
if (serial)
|
|
serial[0] = raw[0] & 0x7fffffff;
|
|
|
|
// Hash (e) = Bits [31..58] -> 28 bits
|
|
if (hash)
|
|
hash[0] = ((raw[0] >> 31) | (raw[1] << 1)) & 0xfffffff;
|
|
|
|
// Signature (s) = Bits [59..113] -> 55 bits
|
|
if (sig) {
|
|
sig[0] = (raw[1] >> 27) | (raw[2] << 5);
|
|
sig[1] = (raw[2] >> 27) | (raw[3] << 5);
|
|
}
|
|
}
|
|
|
|
/* Repacks the Product Key. */
|
|
void packXP(ul32 *raw, ul32 *serial, ul32 *hash, ul32 *sig) {
|
|
raw[0] = serial[0] | ((hash[0] & 1) << 31);
|
|
raw[1] = (hash[0] >> 1) | ((sig[0] & 0x1f) << 27);
|
|
raw[2] = (sig[0] >> 5) | (sig[1] << 27);
|
|
raw[3] = sig[1] >> 5;
|
|
}
|
|
|
|
/* Verify Product Key */
|
|
bool verifyXPKey(EC_GROUP *eCurve, EC_POINT *generator, EC_POINT *publicKey, char *cdKey) {
|
|
BN_CTX *context = BN_CTX_new();
|
|
|
|
// Convert Base24 CD-key to bytecode.
|
|
ul32 bKey[4]{};
|
|
ul32 pID, checkHash, sig[2];
|
|
|
|
unbase24(bKey, cdKey);
|
|
|
|
// Extract data, hash and signature from the bytecode.
|
|
unpackXP(&pID, &checkHash, sig, bKey);
|
|
|
|
// e = Hash
|
|
// s = Signature
|
|
BIGNUM *e, *s;
|
|
|
|
// Put hash word into BigNum e.
|
|
e = BN_new();
|
|
BN_set_word(e, checkHash);
|
|
|
|
// Reverse signature and create a new BigNum s.
|
|
endiannessConvert((byte *) sig, sizeof(sig));
|
|
s = BN_bin2bn((byte *)sig, sizeof(sig), nullptr);
|
|
|
|
// Create x and y.
|
|
BIGNUM *x = BN_new();
|
|
BIGNUM *y = BN_new();
|
|
|
|
// Create 2 new points on the existing elliptic curve.
|
|
EC_POINT *u = EC_POINT_new(eCurve);
|
|
EC_POINT *v = EC_POINT_new(eCurve);
|
|
|
|
// EC_POINT_mul calculates r = generator * n + q * m.
|
|
// v = s * generator + e * (-publicKey)
|
|
|
|
// u = generator * s
|
|
EC_POINT_mul(eCurve, u, nullptr, generator, s, context);
|
|
|
|
// v = publicKey * e
|
|
EC_POINT_mul(eCurve, v, nullptr, publicKey, e, context);
|
|
|
|
// v += u
|
|
EC_POINT_add(eCurve, v, u, v, context);
|
|
|
|
// EC_POINT_get_affine_coordinates() sets x and y, either of which may be nullptr, to the corresponding coordinates of p.
|
|
// x = v.x; y = v.y;
|
|
EC_POINT_get_affine_coordinates(eCurve, v, x, y, context);
|
|
|
|
|
|
byte buf[FIELD_BYTES], md[SHA_DIGEST_LENGTH], t[4];
|
|
ul32 newHash;
|
|
|
|
SHA_CTX hContext;
|
|
|
|
// h = First32(SHA-1(pID || v.x || v.y)) >> 4
|
|
SHA1_Init(&hContext);
|
|
|
|
// Chop Product ID into 4 bytes.
|
|
t[0] = (pID & 0xff); // First 8 bits
|
|
t[1] = (pID & 0xff00) >> 8; // Second 8 bits
|
|
t[2] = (pID & 0xff0000) >> 16; // Third 8 bits
|
|
t[3] = (pID & 0xff000000) >> 24; // Fourth 8 bits
|
|
|
|
// Hash chunk of data.
|
|
SHA1_Update(&hContext, t, sizeof(t));
|
|
|
|
// Empty buffer, place v.x in little-endian.
|
|
memset(buf, 0, FIELD_BYTES);
|
|
BN_bn2bin(x, buf);
|
|
endiannessConvert(buf, FIELD_BYTES);
|
|
|
|
// Hash chunk of data.
|
|
SHA1_Update(&hContext, buf, FIELD_BYTES);
|
|
|
|
// Empty buffer, place v.y in little-endian.
|
|
memset(buf, 0, FIELD_BYTES);
|
|
BN_bn2bin(y, buf);
|
|
endiannessConvert(buf, FIELD_BYTES);
|
|
|
|
// Hash chunk of data.
|
|
SHA1_Update(&hContext, buf, FIELD_BYTES);
|
|
|
|
// Store the final message from hContext in md.
|
|
SHA1_Final(md, &hContext);
|
|
|
|
// h = First32(SHA-1(pID || v.x || v.y)) >> 4
|
|
newHash = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) >> 4;
|
|
newHash &= 0xfffffff;
|
|
|
|
BN_free(e);
|
|
BN_free(s);
|
|
BN_free(x);
|
|
BN_free(y);
|
|
|
|
BN_CTX_free(context);
|
|
|
|
EC_POINT_free(u);
|
|
EC_POINT_free(v);
|
|
|
|
// If we managed to generate a key with the same hash, the key is correct.
|
|
return newHash == checkHash;
|
|
}
|
|
|
|
/* Generate a valid Product Key. */
|
|
void generateXPKey(char *pKey, EC_GROUP *eCurve, EC_POINT *generator, BIGNUM *order, BIGNUM *privateKey, ul32 *pRaw) {
|
|
EC_POINT *r = EC_POINT_new(eCurve);
|
|
BN_CTX *ctx = BN_CTX_new();
|
|
|
|
BIGNUM *c = BN_new();
|
|
BIGNUM *s = BN_new();
|
|
BIGNUM *x = BN_new();
|
|
BIGNUM *y = BN_new();
|
|
|
|
ul32 bKey[4]{};
|
|
|
|
do {
|
|
ul32 hash = 0, sig[2]{};
|
|
|
|
memset(bKey, 0, 4);
|
|
|
|
// Generate a random number c consisting of 384 bits without any constraints.
|
|
BN_rand(c, FIELD_BITS, 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]{}, t[4]{};
|
|
|
|
// h = (First-32(SHA1(pRaw, r.x, r.y)) >> 4
|
|
SHA1_Init(&hContext);
|
|
|
|
// Chop Raw Product Key into 4 bytes.
|
|
t[0] = (*pRaw & 0xff);
|
|
t[1] = (*pRaw & 0xff00) >> 8;
|
|
t[2] = (*pRaw & 0xff0000) >> 16;
|
|
t[3] = (*pRaw & 0xff000000) >> 24;
|
|
|
|
// Hash chunk of data.
|
|
SHA1_Update(&hContext, t, sizeof(t));
|
|
|
|
// Empty buffer, place r.x in little-endiannessConvert.
|
|
memset(buf, 0, FIELD_BYTES);
|
|
BN_bn2bin(x, buf);
|
|
endiannessConvert(buf, FIELD_BYTES);
|
|
|
|
// Hash chunk of data.
|
|
SHA1_Update(&hContext, buf, FIELD_BYTES);
|
|
|
|
// Empty buffer, place r.y in little-endiannessConvert.
|
|
memset(buf, 0, FIELD_BYTES);
|
|
BN_bn2bin(y, buf);
|
|
endiannessConvert(buf, FIELD_BYTES);
|
|
|
|
// Hash chunk of data.
|
|
SHA1_Update(&hContext, buf, FIELD_BYTES);
|
|
|
|
// Store the final message from hContext in md.
|
|
SHA1_Final(md, &hContext);
|
|
|
|
// h = (First-32(SHA1(pRaw, r.x, r.y)) >> 4
|
|
hash = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) >> 4;
|
|
hash &= 0xfffffff;
|
|
|
|
/* s = privateKey * hash + c; */
|
|
// s = privateKey;
|
|
BN_copy(s, privateKey);
|
|
|
|
// s *= hash;
|
|
BN_mul_word(s, hash);
|
|
|
|
// BN_mod_add() adds a to b % m and places the non-negative result in r.
|
|
// s = |s + c % order|;
|
|
BN_mod_add(s, s, c, order, ctx);
|
|
|
|
// Convert s from BigNum back to bytecode and reverse the endianness.
|
|
BN_bn2bin(s, (byte *)sig);
|
|
endiannessConvert((byte *)sig, BN_num_bytes(s));
|
|
|
|
// Pack product key.
|
|
packXP(bKey, pRaw, &hash, sig);
|
|
} while (bKey[3] >= 0x40000);
|
|
// ↑ ↑ ↑
|
|
// bKey[3] can't be longer than 18 bits, else the signature part will make
|
|
// the CD-key longer than 25 characters.
|
|
|
|
// Convert the key to Base24.
|
|
base24(pKey, bKey);
|
|
|
|
BN_free(c);
|
|
BN_free(s);
|
|
BN_free(x);
|
|
BN_free(y);
|
|
|
|
BN_CTX_free(ctx);
|
|
EC_POINT_free(r);
|
|
}
|
|
|
|
bool keyXP(char *pKey, ul32 nRaw) {
|
|
assert(nRaw <= 1'000'000'000);
|
|
|
|
// 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, genOrderXP);
|
|
BN_hex2bn(&privateKey, privateKeyXP);
|
|
|
|
EC_POINT *genPoint, *pubPoint;
|
|
EC_GROUP *eCurve = initializeEllipticCurve(
|
|
pXP,
|
|
aXP,
|
|
bXP,
|
|
genXXP,
|
|
genYXP,
|
|
pubXXP,
|
|
pubYXP,
|
|
genOrder,
|
|
privateKey,
|
|
&genPoint,
|
|
&pubPoint
|
|
);
|
|
|
|
// Shift left once.
|
|
nRaw <<= 1;
|
|
|
|
// Generate the key until it's valid. (In XP it's valid 100% of the times)
|
|
do {
|
|
generateXPKey(pKey, eCurve, genPoint, genOrder, privateKey, &nRaw);
|
|
} while (!verifyXPKey(eCurve, genPoint, pubPoint, pKey));
|
|
|
|
return true;
|
|
} |