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Server Algorithm uplift

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This commit is contained in:
Andrew 2023-06-02 17:13:57 +03:00
parent 475241e608
commit 7944a9b15f
2 changed files with 302 additions and 213 deletions
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23
src/header.h
View File

@ -24,6 +24,7 @@
#include <openssl/sha.h> #include <openssl/sha.h>
#include <openssl/rand.h> #include <openssl/rand.h>
// Algorithm macros
#define PK_LENGTH 25 #define PK_LENGTH 25
#define NULL_TERMINATOR 1 #define NULL_TERMINATOR 1
@ -32,19 +33,25 @@
#define FIELD_BITS_2003 512 #define FIELD_BITS_2003 512
#define FIELD_BYTES_2003 64 #define FIELD_BYTES_2003 64
// Type definitions
typedef uint8_t BYTE;
typedef uint16_t WORD;
typedef uint32_t DWORD;
typedef uint64_t QWORD;
// Global variables
extern char charset[]; extern char charset[];
// util.cpp // util.cpp
void endian(uint8_t *data, int length); void endian(uint8_t *data, int length);
EC_GROUP *initializeEllipticCurve( EC_GROUP *initializeEllipticCurve(
const std::string pSel, std::string pSel,
const std::string aSel, std::string aSel,
const std::string bSel, std::string bSel,
const std::string generatorXSel, std::string generatorXSel,
const std::string generatorYSel, std::string generatorYSel,
const std::string publicKeyXSel, std::string publicKeyXSel,
const std::string publicKeyYSel, std::string publicKeyYSel,
EC_POINT **genPoint, EC_POINT **genPoint,
EC_POINT **pubPoint EC_POINT **pubPoint
); );
@ -74,7 +81,5 @@ bool verifyXPKey(EC_GROUP *eCurve, EC_POINT *generator, EC_POINT *publicKey, cha
void generateXPKey(char *pKey, EC_GROUP *eCurve, EC_POINT *generator, BIGNUM *order, BIGNUM *privateKey, uint32_t *pRaw); void generateXPKey(char *pKey, EC_GROUP *eCurve, EC_POINT *generator, BIGNUM *order, BIGNUM *privateKey, uint32_t *pRaw);
// server.cpp // server.cpp
int verify2003(EC_GROUP *ec, EC_POINT *generator, EC_POINT *public_key, char *cdkey);
void generate2003(char *pkey, EC_GROUP *ec, EC_POINT *generator, BIGNUM *order, BIGNUM *priv, uint32_t *osfamily, uint32_t *prefix);
#endif //WINDOWSXPKG_HEADER_H #endif //WINDOWSXPKG_HEADER_H

492
src/server.cpp
View File

@ -2,226 +2,310 @@
char charset[] = "BCDFGHJKMPQRTVWXY2346789"; char charset[] = "BCDFGHJKMPQRTVWXY2346789";
void unpack2003(uint32_t *osfamily, uint32_t *hash, uint32_t *sig, uint32_t *prefix, uint32_t *raw) void unpackServer(DWORD *osFamily, DWORD *hash, DWORD *sig, DWORD *prefix, DWORD *raw) {
{
osfamily[0] = raw[0] & 0x7ff; // We're assuming that the quantity of information within the product key is at most 114 bits.
hash[0] = ((raw[0] >> 11) | (raw[1] << 21)) & 0x7fffffff; // log2(24^25) = 114.
sig[0] = (raw[1] >> 10) | (raw[2] << 22);
sig[1] = ((raw[2] >> 10) | (raw[3] << 22)) & 0x3fffffff; // OS Family = Bits [0..10] -> 11 bits
prefix[0] = (raw[3] >> 8) & 0x3ff; osFamily[0] = raw[0] & 0x7ff;
// Hash = Bits [11..41] -> 31 bits
hash[0] = ((raw[0] >> 11) | (raw[1] << 21)) & 0x7fffffff;
// Signature = Bits [42..103] -> 62 bits
sig[0] = (raw[1] >> 10) | (raw[2] << 22);
sig[1] = ((raw[2] >> 10) | (raw[3] << 22)) & 0x3fffffff;
// Prefix = Bits [104..113] -> 10 bits
prefix[0] = (raw[3] >> 8) & 0x3ff;
} }
void pack2003(uint32_t *raw, uint32_t *osfamily, uint32_t *hash, uint32_t *sig, uint32_t *prefix) void packServer(DWORD *raw, DWORD *osFamily, DWORD *hash, DWORD *sig, DWORD *prefix) {
{ raw[0] = osFamily[0] | (hash[0] << 11);
raw[0] = osfamily[0] | (hash[0] << 11); raw[1] = (hash[0] >> 21) | (sig[0] << 10);
raw[1] = (hash[0] >> 21) | (sig[0] << 10); raw[2] = (sig[0] >> 22) | (sig[1] << 10);
raw[2] = (sig[0] >> 22) | (sig[1] << 10); raw[3] = (sig[1] >> 22) | (prefix[0] << 8);
raw[3] = (sig[1] >> 22) | (prefix[0] << 8);
} }
int verify2003(EC_GROUP *ec, EC_POINT *generator, EC_POINT *public_key, char *cdkey)
{
char key[25];
BN_CTX *ctx = BN_CTX_new();
for (int i = 0, k = 0; i < strlen(cdkey); i++) { bool verifyServerKey(EC_GROUP *eCurve, EC_POINT *generator, EC_POINT *publicKey, char *cdKey) {
for (int j = 0; j < 24; j++) { BN_CTX *context = BN_CTX_new();
if (cdkey[i] != '-' && cdkey[i] == charset[j]) {
key[k++] = j;
break;
}
assert(j < 24);
}
if (k >= 25) break;
}
uint32_t bkey[4] = {0}; // Convert Base24 CD-key to bytecode.
uint32_t osfamily[1], hash[1], sig[2], prefix[1]; DWORD osFamily, hash, sig[2], prefix;
DWORD bKey[4]{};
unbase24(bkey, key); unbase24(bKey, cdKey);
printf("%.8ix %.8ix %.8ix %.8ix\n", bkey[3], bkey[2], bkey[1], bkey[0]); // Extract segments from the bytecode and reverse the signature.
unpack2003(osfamily, hash, sig, prefix, bkey); unpackServer(&osFamily, &hash, sig, &prefix, bKey);
endian((BYTE *)sig, 8);
printf("OS Family: %iu\nHash: %.8ix\nSig: %.8ix %.8ix\nPrefix: %.8ix\n", osfamily[0], hash[0], sig[1], sig[0], prefix[0]);
uint8_t buf[FIELD_BYTES_2003], md[20]; BYTE t[FIELD_BYTES_2003]{}, md[SHA_DIGEST_LENGTH]{};
uint32_t h1[2]; DWORD checkHash, newHash[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: %.8ix %.8ix\n", h1[1], h1[0]);
BIGNUM *s, *h, *x, *y;
x = BN_new();
y = BN_new();
endian((uint8_t *)sig, 8);
endian((uint8_t *)h1, 8);
s = BN_bin2bn((uint8_t *)sig, 8, nullptr);
h = BN_bin2bn((uint8_t *)h1, 8, nullptr);
EC_POINT *r = EC_POINT_new(ec); SHA_CTX hContext;
EC_POINT *t = EC_POINT_new(ec);
/* r = sig*(sig*generator + h1*public_key) */
EC_POINT_mul(ec, t, nullptr, generator, s, ctx);
EC_POINT_mul(ec, r, nullptr, public_key, h, ctx);
EC_POINT_add(ec, r, r, t, ctx);
EC_POINT_mul(ec, r, nullptr, r, s, ctx);
EC_POINT_get_affine_coordinates(ec, r, x, y, ctx);
uint32_t h2[1]; // H = SHA-1(5D || OS Family || Hash || Prefix || 00 00)
/* h2 = SHA-1(79 || OS Family || r.x || r.y) */ SHA1_Init(&hContext);
SHA1_Init(&h_ctx);
buf[0] = 0x79; t[0] = 0x5D;
buf[1] = osfamily[0] & 0xff; t[1] = (osFamily & 0xff);
buf[2] = (osfamily[0] & 0xff00) >> 8; t[2] = (osFamily & 0xff00) >> 8;
SHA1_Update(&h_ctx, buf, 3); t[3] = (hash & 0xff);
t[4] = (hash & 0xff00) >> 8;
memset(buf, 0, FIELD_BYTES_2003); t[5] = (hash & 0xff0000) >> 16;
BN_bn2bin(x, buf); t[6] = (hash & 0xff000000) >> 24;
endian((uint8_t *)buf, FIELD_BYTES_2003); t[7] = (prefix & 0xff);
SHA1_Update(&h_ctx, buf, FIELD_BYTES_2003); t[8] = (prefix & 0xff00) >> 8;
t[9] = 0x00;
memset(buf, 0, FIELD_BYTES_2003); t[10] = 0x00;
BN_bn2bin(y, buf);
endian((uint8_t *)buf, FIELD_BYTES_2003); SHA1_Update(&hContext, t, 11);
SHA1_Update(&h_ctx, buf, FIELD_BYTES_2003); SHA1_Final(md, &hContext);
SHA1_Final(md, &h_ctx); // First word.
h2[0] = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff; newHash[0] = md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24);
printf("Calculated hash: %.8ix\n", h2[0]);
// Second word, right shift 2 bits.
BN_free(s); newHash[1] = (md[4] | (md[5] << 8) | (md[6] << 16) | (md[7] << 24)) >> 2;
BN_free(h); newHash[1] &= 0x3FFFFFFF;
BN_free(x);
BN_free(y); endian((BYTE *)newHash, 8);
EC_POINT_free(r);
EC_POINT_free(t); BIGNUM *x = BN_new();
BN_CTX_free(ctx); BIGNUM *y = BN_new();
BIGNUM *s = BN_bin2bn((BYTE *)sig, 8, nullptr);
if (h2[0] == hash[0]) { BIGNUM *e = BN_bin2bn((BYTE *)newHash, 8, nullptr);
printf("Key VALID\n");
return 1; EC_POINT *u = EC_POINT_new(eCurve);
} EC_POINT *v = EC_POINT_new(eCurve);
else {
printf("Key invalid\n"); // EC_POINT_mul calculates r = generator * n + q * m.
return 0; // v = s * (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);
// v *= s
EC_POINT_mul(eCurve, v, nullptr, v, s, 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_GFp(eCurve, v, x, y, context);
// Hash = First31(SHA-1(79 || OS Family || v.x || v.y))
SHA1_Init(&hContext);
t[0] = 0x79;
t[1] = (osFamily & 0xff);
t[2] = (osFamily & 0xff00) >> 8;
// Hash chunk of data.
SHA1_Update(&hContext, t, 3);
// Empty buffer, place v.y in little-endian.
memset(t, 0, FIELD_BYTES_2003);
BN_bn2bin(x, t);
endian(t, FIELD_BYTES_2003);
// Hash chunk of data.
SHA1_Update(&hContext, t, FIELD_BYTES_2003);
// Empty buffer, place v.y in little-endian.
memset(t, 0, FIELD_BYTES_2003);
BN_bn2bin(y, t);
endian(t, FIELD_BYTES_2003);
// Hash chunk of data.
SHA1_Update(&hContext, t, FIELD_BYTES_2003);
// Store the final message from hContext in md.
SHA1_Final(md, &hContext);
// Hash = First31(SHA-1(79 || OS Family || v.x || v.y))
checkHash = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff;
BN_free(s);
BN_free(e);
BN_free(x);
BN_free(y);
BN_CTX_free(context);
EC_POINT_free(v);
EC_POINT_free(u);
// If we managed to generate a key with the same hash, the key is correct.
return checkHash == hash;
} }
void generate2003(char *pkey, EC_GROUP *ec, EC_POINT *generator, BIGNUM *order, BIGNUM *priv, uint32_t *osfamily, uint32_t *prefix) void generateServerKey(char *pKey, EC_GROUP *eCurve, EC_POINT *generator, BIGNUM *order, BIGNUM *privateKey, DWORD *osFamily, DWORD *prefix) {
{ EC_POINT *r = EC_POINT_new(eCurve);
BN_CTX *ctx = BN_CTX_new(); BN_CTX *ctx = BN_CTX_new();
BIGNUM *k = BN_new(); DWORD bKey[4]{},
BIGNUM *s = BN_new(); bSig[2]{};
BIGNUM *x = BN_new();
BIGNUM *y = BN_new();
BIGNUM *b = BN_new();
EC_POINT *r = EC_POINT_new(ec);
uint32_t bkey[4]; do {
uint8_t buf[FIELD_BYTES_2003], md[20]; BIGNUM *c = BN_new();
uint32_t h1[2]; BIGNUM *s = BN_new();
uint32_t hash[1], sig[2]; BIGNUM *x = BN_new();
BIGNUM *y = BN_new();
SHA_CTX h_ctx; BIGNUM *b = BN_new();
for (;;) {
/* r = k*generator */
BN_pseudo_rand(k, FIELD_BITS_2003, -1, 0);
EC_POINT_mul(ec, r, nullptr, generator, k, ctx);
EC_POINT_get_affine_coordinates_GFp(ec, r, x, y, ctx);
/* hash = 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);
endian((uint8_t *)buf, FIELD_BYTES_2003);
SHA1_Update(&h_ctx, buf, FIELD_BYTES_2003);
memset(buf, 0, FIELD_BYTES_2003);
BN_bn2bin(y, buf);
endian((uint8_t *)buf, FIELD_BYTES_2003);
SHA1_Update(&h_ctx, buf, FIELD_BYTES_2003);
SHA1_Final(md, &h_ctx);
hash[0] = (md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24)) & 0x7fffffff;
/* 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: %.8ix %.8ix\n", h1[1], h1[0]);
/* s = ( -h1*priv + sqrt( (h1*priv)^2 + 4k ) ) / 2 */
endian((uint8_t *)h1, 8);
BN_bin2bn((uint8_t *)h1, 8, b);
BN_mod_mul(b, b, priv, order, ctx);
BN_copy(s, b);
BN_mod_sqr(s, s, order, ctx);
BN_lshift(k, k, 2);
BN_add(s, s, k);
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, (uint8_t *)sig);
endian((uint8_t *)sig, BN_num_bytes(s));
if (sig[1] < 0x40000000) break;
}
pack2003(bkey, osfamily, hash, sig, prefix);
printf("OS family: %iu\nHash: %.8ix\nSig: %.8ix %.8ix\nPrefix: %.8ix\n", osfamily[0], hash[0], sig[1], sig[0], prefix[0]);
printf("%.8ix %.8ix %.8ix %.8ix\n", bkey[3], bkey[2], bkey[1], bkey[0]);
base24(pkey, bkey); DWORD hash = 0, h[2]{};
BN_free(k);
BN_free(s);
BN_free(x);
BN_free(y);
BN_free(b);
EC_POINT_free(r);
BN_CTX_free(ctx); memset(bKey, 0, 4);
memset(bSig, 0, 2);
// 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);
endian((BYTE *)buf, FIELD_BYTES_2003);
SHA1_Update(&hContext, buf, FIELD_BYTES_2003);
memset(buf, 0, FIELD_BYTES_2003);
BN_bn2bin(y, buf);
endian((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;
// H = 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;
// Input length is 11 BYTEs.
SHA1_Update(&hContext, buf, 11);
SHA1_Final(md, &hContext);
// First word.
h[0] = md[0] | (md[1] << 8) | (md[2] << 16) | (md[3] << 24);
// Second word, right shift 2 bits.
h[1] = (md[4] | (md[5] << 8) | (md[6] << 16) | (md[7] << 24)) >> 2;
h[1] &= 0x3FFFFFFF;
endian((BYTE *)h, 8);
BN_bin2bn((BYTE *)h, 8, b);
/*
* Signature * (Signature * G + H * K) = rG (mod p)
* ↓ K = kG ↓
*
* Signature * (Signature * G + H * k * G) = rG (mod p)
* Signature^2 * G + Signature * HkG = rG (mod p)
* G(Signature^2 + Signature * HkG) = G (mod p) * r
* ↓ G^(-1)(G (mod p)) = (mod n), n = order of G ↓
*
* Signature^2 + Hk * Signature = r (mod n)
* Signature = -(b +- sqrt(D)) / 2a → Signature = (-Hk +- sqrt((Hk)^2 + 4r)) / 2
*
* S = (-Hk +- sqrt((Hk)^2 + 4r)) (mod n) / 2
*
* S = s
* H = b
* k = privateKey
* n = order
* r = c
*
* s = ( ( -b * privateKey +- sqrt( (b * privateKey)^2 + 4c ) ) / 2 ) % order
*/
// b = (b * privateKey) % order
BN_mod_mul(b, b, privateKey, order, ctx);
// s = b
BN_copy(s, b);
// s = (s % order)^2
BN_mod_sqr(s, s, order, ctx);
// c <<= 2 (c = 4c)
BN_lshift(c, c, 2);
// s = s + c
BN_add(s, s, c);
// s^2 = s % order (order must be prime)
BN_mod_sqrt(s, s, order, ctx);
// s = s - b
BN_mod_sub(s, s, b, order, ctx);
// if s is odd, s = s + order
if (BN_is_odd(s)) {
BN_add(s, s, order);
}
// s >>= 1 (s = s / 2)
BN_rshift1(s, s);
// Convert s from BigNum back to bytecode and reverse the endianness.
BN_bn2bin(s, (BYTE *)bSig);
endian((BYTE *)bSig, BN_num_bytes(s));
// Pack product key.
packServer(bKey, osFamily, &hash, bSig, prefix);
BN_free(c);
BN_free(s);
BN_free(x);
BN_free(y);
BN_free(b);
} while (bSig[1] >= 0x40000000);
base24(pKey, bKey);
BN_CTX_free(ctx);
EC_POINT_free(r);
} }
int main() int main()
@ -264,7 +348,7 @@ int main()
uint32_t osfamily[1], prefix[1]; uint32_t osfamily[1], prefix[1];
osfamily[0] = 1280; osfamily[0] = 1280;
RAND_pseudo_bytes((uint8_t *)prefix, 4); RAND_bytes((uint8_t *)prefix, 4);
prefix[0] &= 0x3ff; prefix[0] &= 0x3ff;
do { do {