/********************************************************************************/ /* */ /* Functions that are used for the two-phase, ECC, key-exchange protocols */ /* Written by Ken Goldman */ /* IBM Thomas J. Watson Research Center */ /* $Id: CryptEccKeyExchange.c 1658 2021-01-22 23:14:01Z kgoldman $ */ /* */ /* Licenses and Notices */ /* */ /* 1. 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Process: */ /* a) Convert xQ to an integer xqi using the convention specified in Appendix C.3. */ /* b) Calculate xqm = xqi mod 2^ceil(f/2) (where f = ceil(log2(n)). */ /* c) Calculate the associate value function avf(Q) = xqm + 2ceil(f / 2) */ /* Always returns TRUE(1). */ static BOOL avf1( bigNum bnX, // IN/OUT: the reduced value bigNum bnN // IN: the order of the curve ) { // compute f = 2^(ceil(ceil(log2(n)) / 2)) int f = (BnSizeInBits(bnN) + 1) / 2; // x' = 2^f + (x mod 2^f) BnMaskBits(bnX, f); // This is mod 2*2^f but it doesn't matter because // the next operation will SET the extra bit anyway BnSetBit(bnX, f); return TRUE; } /* 10.2.11.1.2 C_2_2_MQV() */ /* This function performs the key exchange defined in SP800-56A 6.1.1.4 Full MQV, C(2, 2, ECC MQV). */ /* CAUTION: Implementation of this function may require use of essential claims in patents not owned by TCG members. */ /* Points QsB() and QeB() are required to be on the curve of inQsA. The function will fail, possibly catastrophically, if this is not the case. */ /* Error Returns Meaning */ /* TPM_RC_NO_RESULT the value for dsA does not give a valid point on the curve */ static TPM_RC C_2_2_MQV( TPMS_ECC_POINT *outZ, // OUT: the computed point TPM_ECC_CURVE curveId, // IN: the curve for the computations TPM2B_ECC_PARAMETER *dsA, // IN: static private TPM key TPM2B_ECC_PARAMETER *deA, // IN: ephemeral private TPM key TPMS_ECC_POINT *QsB, // IN: static public party B key TPMS_ECC_POINT *QeB // IN: ephemeral public party B key ) { CURVE_INITIALIZED(E, curveId); const ECC_CURVE_DATA *C; POINT(pQeA); POINT_INITIALIZED(pQeB, QeB); POINT_INITIALIZED(pQsB, QsB); ECC_NUM(bnTa); ECC_INITIALIZED(bnDeA, deA); ECC_INITIALIZED(bnDsA, dsA); ECC_NUM(bnN); ECC_NUM(bnXeB); TPM_RC retVal; // // Parameter checks if(E == NULL) ERROR_RETURN(TPM_RC_VALUE); pAssert(outZ != NULL && pQeB != NULL && pQsB != NULL && deA != NULL && dsA != NULL); C = AccessCurveData(E); // Process: // 1. implicitsigA = (de,A + avf(Qe,A)ds,A ) mod n. // 2. P = h(implicitsigA)(Qe,B + avf(Qe,B)Qs,B). // 3. If P = O, output an error indicator. // 4. Z=xP, where xP is the x-coordinate of P. // Compute the public ephemeral key pQeA = [de,A]G if((retVal = BnPointMult(pQeA, CurveGetG(C), bnDeA, NULL, NULL, E)) != TPM_RC_SUCCESS) goto Exit; // 1. implicitsigA = (de,A + avf(Qe,A)ds,A ) mod n. // tA := (ds,A + de,A avf(Xe,A)) mod n (3) // Compute 'tA' = ('deA' + 'dsA' avf('XeA')) mod n // Ta = avf(XeA); BnCopy(bnTa, pQeA->x); avf1(bnTa, bnN); // do Ta = ds,A * Ta mod n = dsA * avf(XeA) mod n BnModMult(bnTa, bnDsA, bnTa, bnN); // now Ta = deA + Ta mod n = deA + dsA * avf(XeA) mod n BnAdd(bnTa, bnTa, bnDeA); BnMod(bnTa, bnN); // 2. P = h(implicitsigA)(Qe,B + avf(Qe,B)Qs,B). // Put this in because almost every case of h is == 1 so skip the call when // not necessary. if(!BnEqualWord(CurveGetCofactor(C), 1)) // Cofactor is not 1 so compute Ta := Ta * h mod n BnModMult(bnTa, bnTa, CurveGetCofactor(C), CurveGetOrder(C)); // Now that 'tA' is (h * 'tA' mod n) // 'outZ' = (tA)(Qe,B + avf(Qe,B)Qs,B). // first, compute XeB = avf(XeB) avf1(bnXeB, bnN); // QsB := [XeB]QsB BnPointMult(pQsB, pQsB, bnXeB, NULL, NULL, E); BnEccAdd(pQeB, pQeB, pQsB, E); // QeB := [tA]QeB = [tA](QsB + [Xe,B]QeB) and check for at infinity // If the result is not the point at infinity, return QeB BnPointMult(pQeB, pQeB, bnTa, NULL, NULL, E); if(BnEqualZero(pQeB->z)) ERROR_RETURN(TPM_RC_NO_RESULT); // Convert BIGNUM E to TPM2B E BnPointTo2B(outZ, pQeB, E); Exit: CURVE_FREE(E); return retVal; } #endif // ALG_ECMQV /* 10.2.11.1.3 C_2_2_ECDH() */ /* This function performs the two phase key exchange defined in SP800-56A, 6.1.1.2 Full Unified Model, C(2, 2, ECC CDH). */ static TPM_RC C_2_2_ECDH( TPMS_ECC_POINT *outZs, // OUT: Zs TPMS_ECC_POINT *outZe, // OUT: Ze TPM_ECC_CURVE curveId, // IN: the curve for the computations TPM2B_ECC_PARAMETER *dsA, // IN: static private TPM key TPM2B_ECC_PARAMETER *deA, // IN: ephemeral private TPM key TPMS_ECC_POINT *QsB, // IN: static public party B key TPMS_ECC_POINT *QeB // IN: ephemeral public party B key ) { CURVE_INITIALIZED(E, curveId); ECC_INITIALIZED(bnAs, dsA); ECC_INITIALIZED(bnAe, deA); POINT_INITIALIZED(ecBs, QsB); POINT_INITIALIZED(ecBe, QeB); POINT(ecZ); TPM_RC retVal; // // Parameter checks if(E == NULL) ERROR_RETURN(TPM_RC_CURVE); pAssert(outZs != NULL && dsA != NULL && deA != NULL && QsB != NULL && QeB != NULL); // Do the point multiply for the Zs value ([dsA]QsB) retVal = BnPointMult(ecZ, ecBs, bnAs, NULL, NULL, E); if(retVal == TPM_RC_SUCCESS) { // Convert the Zs value. BnPointTo2B(outZs, ecZ, E); // Do the point multiply for the Ze value ([deA]QeB) retVal = BnPointMult(ecZ, ecBe, bnAe, NULL, NULL, E); if(retVal == TPM_RC_SUCCESS) BnPointTo2B(outZe, ecZ, E); } Exit: CURVE_FREE(E); return retVal; } /* 10.2.11.1.4 CryptEcc2PhaseKeyExchange() */ /* This function is the dispatch routine for the EC key exchange functions that use two ephemeral and two static keys. */ /* Error Returns Meaning */ /* TPM_RC_SCHEME scheme is not defined */ LIB_EXPORT TPM_RC CryptEcc2PhaseKeyExchange( TPMS_ECC_POINT *outZ1, // OUT: a computed point TPMS_ECC_POINT *outZ2, // OUT: and optional second point TPM_ECC_CURVE curveId, // IN: the curve for the computations TPM_ALG_ID scheme, // IN: the key exchange scheme TPM2B_ECC_PARAMETER *dsA, // IN: static private TPM key TPM2B_ECC_PARAMETER *deA, // IN: ephemeral private TPM key TPMS_ECC_POINT *QsB, // IN: static public party B key TPMS_ECC_POINT *QeB // IN: ephemeral public party B key ) { pAssert(outZ1 != NULL && dsA != NULL && deA != NULL && QsB != NULL && QeB != NULL); // Initialize the output points so that they are empty until one of the // functions decides otherwise outZ1->x.b.size = 0; outZ1->y.b.size = 0; if(outZ2 != NULL) { outZ2->x.b.size = 0; outZ2->y.b.size = 0; } switch(scheme) { case TPM_ALG_ECDH: return C_2_2_ECDH(outZ1, outZ2, curveId, dsA, deA, QsB, QeB); break; #if ALG_ECMQV case TPM_ALG_ECMQV: return C_2_2_MQV(outZ1, curveId, dsA, deA, QsB, QeB); break; #endif #if ALG_SM2 case TPM_ALG_SM2: return SM2KeyExchange(outZ1, curveId, dsA, deA, QsB, QeB); break; #endif default: return TPM_RC_SCHEME; } } #if ALG_SM2 /* 10.2.11.1.5 ComputeWForSM2() */ /* Compute the value for w used by SM2 */ static UINT32 ComputeWForSM2( bigCurve E ) { // w := ceil(ceil(log2(n)) / 2) - 1 return (BnMsb(CurveGetOrder(AccessCurveData(E))) / 2 - 1); } /* 10.2.11.1.6 avfSm2() */ /* This function does the associated value computation required by SM2 key exchange. This is different form the avf() in the international standards because it returns a value that is half the size of the value returned by the standard avf. For example, if n is 15, Ws (w in the standard) is 2 but the W here is 1. This means that an input value of 14 (1110b) would return a value of 110b with the standard but 10b with the scheme in SM2. */ static bigNum avfSm2( bigNum bn, // IN/OUT: the reduced value UINT32 w // IN: the value of w ) { // a) set w := ceil(ceil(log2(n)) / 2) - 1 // b) set x' := 2^w + ( x & (2^w - 1)) // This is just like the avf for MQV where x' = 2^w + (x mod 2^w) BnMaskBits(bn, w); // as with avf1, this is too big by a factor of 2 but // it doesn't matter because we SET the extra bit // anyway BnSetBit(bn, w); return bn; } /* SM2KeyExchange() This function performs the key exchange defined in SM2. The first step is to compute tA = (dsA + deA avf(Xe,A)) mod n Then, compute the Z value from outZ = (h tA mod n) (QsA + [avf(QeB().x)](QeB())). The function will compute the ephemeral public key from the ephemeral private key. All points are required to be on the curve of inQsA. The function will fail catastrophically if this is not the case */ /* Error Returns Meaning */ /* TPM_RC_NO_RESULT the value for dsA does not give a valid point on the curve */ LIB_EXPORT TPM_RC SM2KeyExchange( TPMS_ECC_POINT *outZ, // OUT: the computed point TPM_ECC_CURVE curveId, // IN: the curve for the computations TPM2B_ECC_PARAMETER *dsAIn, // IN: static private TPM key TPM2B_ECC_PARAMETER *deAIn, // IN: ephemeral private TPM key TPMS_ECC_POINT *QsBIn, // IN: static public party B key TPMS_ECC_POINT *QeBIn // IN: ephemeral public party B key ) { CURVE_INITIALIZED(E, curveId); const ECC_CURVE_DATA *C; ECC_INITIALIZED(dsA, dsAIn); ECC_INITIALIZED(deA, deAIn); POINT_INITIALIZED(QsB, QsBIn); POINT_INITIALIZED(QeB, QeBIn); BN_WORD_INITIALIZED(One, 1); POINT(QeA); ECC_NUM(XeB); POINT(Z); ECC_NUM(Ta); UINT32 w; TPM_RC retVal = TPM_RC_NO_RESULT; // // Parameter checks if(E == NULL) ERROR_RETURN(TPM_RC_CURVE); C = AccessCurveData(E); pAssert(outZ != NULL && dsA != NULL && deA != NULL && QsB != NULL && QeB != NULL); // Compute the value for w w = ComputeWForSM2(E); // Compute the public ephemeral key pQeA = [de,A]G if(!BnEccModMult(QeA, CurveGetG(C), deA, E)) goto Exit; // tA := (ds,A + de,A avf(Xe,A)) mod n (3) // Compute 'tA' = ('dsA' + 'deA' avf('XeA')) mod n // Ta = avf(XeA); // do Ta = de,A * Ta = deA * avf(XeA) BnMult(Ta, deA, avfSm2(QeA->x, w)); // now Ta = dsA + Ta = dsA + deA * avf(XeA) BnAdd(Ta, dsA, Ta); BnMod(Ta, CurveGetOrder(C)); // outZ = [h tA mod n] (Qs,B + [avf(Xe,B)](Qe,B)) (4) // Put this in because almost every case of h is == 1 so skip the call when // not necessary. if(!BnEqualWord(CurveGetCofactor(C), 1)) // Cofactor is not 1 so compute Ta := Ta * h mod n BnModMult(Ta, Ta, CurveGetCofactor(C), CurveGetOrder(C)); // Now that 'tA' is (h * 'tA' mod n) // 'outZ' = ['tA'](QsB + [avf(QeB.x)](QeB)). BnCopy(XeB, QeB->x); if(!BnEccModMult2(Z, QsB, One, QeB, avfSm2(XeB, w), E)) goto Exit; // QeB := [tA]QeB = [tA](QsB + [Xe,B]QeB) and check for at infinity if(!BnEccModMult(Z, Z, Ta, E)) goto Exit; // Convert BIGNUM E to TPM2B E BnPointTo2B(outZ, Z, E); retVal = TPM_RC_SUCCESS; Exit: CURVE_FREE(E); return retVal; } #endif #endif // CC_ZGen_2Phase