387 lines
12 KiB
C++
387 lines
12 KiB
C++
/**
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* This file is a part of the UMSKT Project
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*
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* Copyleft (C) 2019-2023 UMSKT Contributors (et.al.)
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Affero General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Affero General Public License for more details.
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* You should have received a copy of the GNU Affero General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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* @FileCreated by Andrew on 01/06/2023
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* @Maintainer Andrew
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*
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* @History {
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* Algorithm was initially written and open sourced by z22
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* and uploaded to GitHub by TheMCHK in August of 2019
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*
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* Endermanch (Andrew) rewrote the algorithm in May of 2023
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* }
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*/
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#include "BINK2002.h"
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/* Unpacks a Windows Server 2003-like Product Key. */
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void PIDGEN3::BINK2002::Unpack(
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QWORD (&pRaw)[2],
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BOOL &pUpgrade,
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DWORD &pChannelID,
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DWORD &pHash,
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QWORD &pSignature,
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DWORD &pAuthInfo
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) {
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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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// Upgrade = Bit 0
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pUpgrade = FIRSTNBITS(pRaw[0], 1);
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// Channel ID = Bits [1..10] -> 10 bits
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pChannelID = NEXTSNBITS(pRaw[0], 10, 1);
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// Hash = Bits [11..41] -> 31 bits
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pHash = NEXTSNBITS(pRaw[0], 31, 11);
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// Signature = Bits [42..103] -> 62 bits
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// The quad-word signature overlaps AuthInfo in bits 104 and 105,
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// hence Microsoft employs a secret technique called: Signature = HIDWORD(Signature) >> 2 | LODWORD(Signature)
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pSignature = NEXTSNBITS(pRaw[1], 30, 10) << 32 | FIRSTNBITS(pRaw[1], 10) << 22 | NEXTSNBITS(pRaw[0], 22, 42);
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// AuthInfo = Bits [104..113] -> 10 bits
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pAuthInfo = NEXTSNBITS(pRaw[1], 10, 40);
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}
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/* Packs a Windows Server 2003-like Product Key. */
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void PIDGEN3::BINK2002::Pack(
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QWORD (&pRaw)[2],
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BOOL pUpgrade,
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DWORD pChannelID,
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DWORD pHash,
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QWORD pSignature,
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DWORD pAuthInfo
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) {
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// AuthInfo [113..104] <- Signature [103..42] <- Hash [41..11] <- Channel ID [10..1] <- Upgrade [0]
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pRaw[0] = FIRSTNBITS(pSignature, 22) << 42 | (QWORD)pHash << 11 | pChannelID << 1 | pUpgrade;
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pRaw[1] = FIRSTNBITS(pAuthInfo, 10) << 40 | NEXTSNBITS(pSignature, 40, 22);
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}
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/* Verifies a Windows Server 2003-like Product Key. */
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bool PIDGEN3::BINK2002::Verify(
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EC_GROUP *eCurve,
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EC_POINT *basePoint,
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EC_POINT *publicKey,
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char (&cdKey)[25]
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) {
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BN_CTX *context = BN_CTX_new();
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QWORD bKey[2]{},
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pSignature = 0;
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DWORD pData,
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pChannelID,
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pHash,
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pAuthInfo;
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BOOL pUpgrade;
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// Convert Base24 CD-key to bytecode.
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unbase24((BYTE *)bKey, cdKey);
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// Extract product key segments from bytecode.
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Unpack(bKey, pUpgrade, pChannelID, pHash, pSignature, pAuthInfo);
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pData = pChannelID << 1 | pUpgrade;
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fmt::print(UMSKT::debug, "Validation results:\n");
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fmt::print(UMSKT::debug, " Upgrade: 0x{:08x}\n", pUpgrade);
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fmt::print(UMSKT::debug, "Channel ID: 0x{:08x}\n", pChannelID);
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fmt::print(UMSKT::debug, " Hash: 0x{:08x}\n", pHash);
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fmt::print(UMSKT::debug, " Signature: 0x{:08x}\n", pSignature);
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fmt::print(UMSKT::debug, " AuthInfo: 0x{:08x}\n", pAuthInfo);
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fmt::print(UMSKT::debug, "\n");
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BYTE msgDigest[SHA_DIGEST_LENGTH]{},
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msgBuffer[SHA_MSG_LENGTH_2003]{},
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xBin[FIELD_BYTES_2003]{},
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yBin[FIELD_BYTES_2003]{};
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// Assemble the first SHA message.
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msgBuffer[0x00] = 0x5D;
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msgBuffer[0x01] = (pData & 0x00FF);
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msgBuffer[0x02] = (pData & 0xFF00) >> 8;
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msgBuffer[0x03] = (pHash & 0x000000FF);
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msgBuffer[0x04] = (pHash & 0x0000FF00) >> 8;
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msgBuffer[0x05] = (pHash & 0x00FF0000) >> 16;
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msgBuffer[0x06] = (pHash & 0xFF000000) >> 24;
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msgBuffer[0x07] = (pAuthInfo & 0x00FF);
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msgBuffer[0x08] = (pAuthInfo & 0xFF00) >> 8;
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msgBuffer[0x09] = 0x00;
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msgBuffer[0x0A] = 0x00;
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// newSignature = SHA1(5D || Channel ID || Hash || AuthInfo || 00 00)
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SHA1(msgBuffer, 11, msgDigest);
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// Translate the byte digest into a 64-bit integer - this is our computed intermediate signature.
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// As the signature is only 62 bits long at most, we have to truncate it by shifting the high DWORD right 2 bits (per spec).
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QWORD iSignature = NEXTSNBITS(BYDWORD(&msgDigest[4]), 30, 2) << 32 | BYDWORD(msgDigest);
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/*
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*
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* Scalars:
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* e = Hash
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* s = Schnorr Signature
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*
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* Points:
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* G(x, y) = Generator (Base Point)
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* K(x, y) = Public Key
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*
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* Equation:
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* P = s(sG + eK)
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*
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*/
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BIGNUM *e = BN_lebin2bn((BYTE *)&iSignature, sizeof(iSignature), nullptr),
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*s = BN_lebin2bn((BYTE *)&pSignature, sizeof(pSignature), nullptr),
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*x = BN_new(),
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*y = BN_new();
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// Create 2 points on the elliptic curve.
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EC_POINT *p = EC_POINT_new(eCurve);
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EC_POINT *t = EC_POINT_new(eCurve);
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// t = sG
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EC_POINT_mul(eCurve, t, nullptr, basePoint, s, context);
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// p = eK
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EC_POINT_mul(eCurve, p, nullptr, publicKey, e, context);
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// p += t
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EC_POINT_add(eCurve, p, t, p, context);
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// p *= s
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EC_POINT_mul(eCurve, p, nullptr, p, s, context);
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// x = p.x; y = p.y;
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EC_POINT_get_affine_coordinates(eCurve, p, x, y, context);
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// Convert resulting point coordinates to bytes.
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BN_bn2lebin(x, xBin, FIELD_BYTES_2003);
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BN_bn2lebin(y, yBin, FIELD_BYTES_2003);
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// Assemble the second SHA message.
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msgBuffer[0x00] = 0x79;
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msgBuffer[0x01] = (pData & 0x00FF);
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msgBuffer[0x02] = (pData & 0xFF00) >> 8;
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memcpy((void *)&msgBuffer[3], (void *)xBin, FIELD_BYTES_2003);
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memcpy((void *)&msgBuffer[3 + FIELD_BYTES_2003], (void *)yBin, FIELD_BYTES_2003);
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// compHash = SHA1(79 || Channel ID || p.x || p.y)
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SHA1(msgBuffer, SHA_MSG_LENGTH_2003, msgDigest);
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// Translate the byte digest into a 32-bit integer - this is our computed hash.
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// Truncate the hash to 31 bits.
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DWORD compHash = BYDWORD(msgDigest) & BITMASK(31);
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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(p);
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EC_POINT_free(t);
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// If the computed hash checks out, the key is valid.
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return compHash == pHash;
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}
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/* Generates a Windows Server 2003-like Product Key. */
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void PIDGEN3::BINK2002::Generate(
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EC_GROUP *eCurve,
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EC_POINT *basePoint,
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BIGNUM *genOrder,
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BIGNUM *privateKey,
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DWORD pChannelID,
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DWORD pAuthInfo,
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BOOL pUpgrade,
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char (&pKey)[25]
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) {
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BN_CTX *numContext = BN_CTX_new();
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BIGNUM *c = BN_new(),
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*e = BN_new(),
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*s = BN_new(),
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*x = BN_new(),
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*y = BN_new();
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QWORD pRaw[2]{},
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pSignature = 0;
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// Data segment of the RPK.
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DWORD pData = pChannelID << 1 | pUpgrade;
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BOOL noSquare;
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do {
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EC_POINT *r = EC_POINT_new(eCurve);
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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 = cG
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EC_POINT_mul(eCurve, r, nullptr, basePoint, c, numContext);
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// Acquire its coordinates.
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// x = R.x; y = R.y;
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EC_POINT_get_affine_coordinates(eCurve, r, x, y, numContext);
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BYTE msgDigest[SHA_DIGEST_LENGTH]{},
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msgBuffer[SHA_MSG_LENGTH_2003]{},
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xBin[FIELD_BYTES_2003]{},
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yBin[FIELD_BYTES_2003]{};
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// Convert resulting point coordinates to bytes.
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BN_bn2lebin(x, xBin, FIELD_BYTES_2003);
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BN_bn2lebin(y, yBin, FIELD_BYTES_2003);
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// Assemble the first SHA message.
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msgBuffer[0x00] = 0x79;
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msgBuffer[0x01] = (pData & 0x00FF);
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msgBuffer[0x02] = (pData & 0xFF00) >> 8;
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memcpy((void *)&msgBuffer[3], (void *)xBin, FIELD_BYTES_2003);
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memcpy((void *)&msgBuffer[3 + FIELD_BYTES_2003], (void *)yBin, FIELD_BYTES_2003);
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// pHash = SHA1(79 || Channel ID || R.x || R.y)
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SHA1(msgBuffer, SHA_MSG_LENGTH_2003, msgDigest);
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// Translate the byte digest into a 32-bit integer - this is our computed hash.
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// Truncate the hash to 31 bits.
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DWORD pHash = BYDWORD(msgDigest) & BITMASK(31);
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// Assemble the second SHA message.
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msgBuffer[0x00] = 0x5D;
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msgBuffer[0x01] = (pData & 0x00FF);
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msgBuffer[0x02] = (pData & 0xFF00) >> 8;
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msgBuffer[0x03] = (pHash & 0x000000FF);
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msgBuffer[0x04] = (pHash & 0x0000FF00) >> 8;
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msgBuffer[0x05] = (pHash & 0x00FF0000) >> 16;
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msgBuffer[0x06] = (pHash & 0xFF000000) >> 24;
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msgBuffer[0x07] = (pAuthInfo & 0x00FF);
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msgBuffer[0x08] = (pAuthInfo & 0xFF00) >> 8;
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msgBuffer[0x09] = 0x00;
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msgBuffer[0x0A] = 0x00;
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// newSignature = SHA1(5D || Channel ID || Hash || AuthInfo || 00 00)
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SHA1(msgBuffer, 11, msgDigest);
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// Translate the byte digest into a 64-bit integer - this is our computed intermediate signature.
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// As the signature is only 62 bits long at most, we have to truncate it by shifting the high DWORD right 2 bits (per spec).
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QWORD iSignature = NEXTSNBITS(BYDWORD(&msgDigest[4]), 30, 2) << 32 | BYDWORD(msgDigest);
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BN_lebin2bn((BYTE *)&iSignature, sizeof(iSignature), e);
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/*
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*
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* Scalars:
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* c = Random multiplier
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* e = Intermediate Signature
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* s = Signature
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* n = Order of G
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* k = Private Key
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*
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* Points:
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* G(x, y) = Generator (Base Point)
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* R(x, y) = Random derivative of the generator
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* K(x, y) = Public Key
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*
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* Equation:
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* s(sG + eK) = R (mod p)
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* ↓ K = kG; R = cG ↓
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*
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* s(sG + ekG) = cG (mod p)
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* s(s + ek)G = cG (mod p)
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* ↓ G cancels out, the scalar arithmetic shrinks to order n ↓
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*
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* s(s + ek) = c (mod n)
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* s² + (ek)s - c = 0 (mod n)
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* ↓ This is a quadratic equation in respect to the signature ↓
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*
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* s = (-ek ± √((ek)² + 4c)) / 2 (mod n)
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*/
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// e = ek (mod n)
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BN_mod_mul(e, e, privateKey, genOrder, numContext);
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// s = e
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BN_copy(s, e);
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// s = (ek (mod n))²
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BN_mod_sqr(s, s, genOrder, numContext);
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// c *= 4 (c <<= 2)
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BN_lshift(c, c, 2);
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// s += c
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BN_add(s, s, c);
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// Around half of numbers modulo a prime are not squares -> BN_sqrt_mod fails about half of the times,
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// hence if BN_sqrt_mod returns NULL, we need to restart with a different seed.
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// s = √((ek)² + 4c (mod n))
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noSquare = BN_mod_sqrt(s, s, genOrder, numContext) == nullptr;
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// s = -ek + √((ek)² + 4c) (mod n)
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BN_mod_sub(s, s, e, genOrder, numContext);
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// If s is odd, add order to it.
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// The order is a prime, so it can't be even.
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if (BN_is_odd(s))
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// s = -ek + √((ek)² + 4c) + n
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BN_add(s, s, genOrder);
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// s /= 2 (s >>= 1)
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BN_rshift1(s, s);
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// Translate resulting scalar into a 64-bit integer (the byte order is little-endian).
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BN_bn2lebinpad(s, (BYTE *)&pSignature, BN_num_bytes(s));
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// Pack product key.
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Pack(pRaw, pUpgrade, pChannelID, pHash, pSignature, pAuthInfo);
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fmt::print(UMSKT::debug, "Generation results:\n");
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fmt::print(UMSKT::debug, " Upgrade: 0x{:08x}\n", pUpgrade);
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fmt::print(UMSKT::debug, "Channel ID: 0x{:08x}\n", pChannelID);
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fmt::print(UMSKT::debug, " Hash: 0x{:08x}\n", pHash);
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fmt::print(UMSKT::debug, " Signature: 0x{:08x}\n", pSignature);
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fmt::print(UMSKT::debug, " AuthInfo: 0x{:08x}\n", pAuthInfo);
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fmt::print(UMSKT::debug, "\n");
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EC_POINT_free(r);
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} while (pSignature > BITMASK(62) || noSquare);
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// ↑ ↑ ↑
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// The signature can't be longer than 62 bits, else it will
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// overlap with the AuthInfo segment next to it.
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// Convert bytecode to Base24 CD-key.
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base24(pKey, (BYTE *)pRaw);
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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(e);
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BN_CTX_free(numContext);
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}
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