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+/*******************************************************************************
+* Copyright 2016-2018 Intel Corporation
+* All Rights Reserved.
+*
+* If this software was obtained under the Intel Simplified Software License,
+* the following terms apply:
+*
+* The source code, information and material ("Material") contained herein is
+* owned by Intel Corporation or its suppliers or licensors, and title to such
+* Material remains with Intel Corporation or its suppliers or licensors. The
+* Material contains proprietary information of Intel or its suppliers and
+* licensors. The Material is protected by worldwide copyright laws and treaty
+* provisions. No part of the Material may be used, copied, reproduced,
+* modified, published, uploaded, posted, transmitted, distributed or disclosed
+* in any way without Intel's prior express written permission. No license under
+* any patent, copyright or other intellectual property rights in the Material
+* is granted to or conferred upon you, either expressly, by implication,
+* inducement, estoppel or otherwise. Any license under such intellectual
+* property rights must be express and approved by Intel in writing.
+*
+* Unless otherwise agreed by Intel in writing, you may not remove or alter this
+* notice or any other notice embedded in Materials by Intel or Intel's
+* suppliers or licensors in any way.
+*
+*
+* If this software was obtained under the Apache License, Version 2.0 (the
+* "License"), the following terms apply:
+*
+* You may not use this file except in compliance with the License. You may
+* obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
+*
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+*
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*******************************************************************************/
+
+/*
+// Intel(R) Integrated Performance Primitives. Cryptography Primitives.
+// GF(p^d) methods, if binomial generator
+//
+*/
+#include "owncp.h"
+
+#include "pcpgfpxstuff.h"
+#include "pcpgfpxmethod_com.h"
+#include "pcpgfpxmethod_binom_epid2.h"
+
+//tbcd: temporary excluded: #include <assert.h>
+
+/*
+// Intel(R) Enhanced Privacy ID (Intel(R) EPID) 2.0 specific.
+//
+// Intel(R) EPID 2.0 uses the following finite field hierarchy:
+//
+// 1) prime field GF(p),
+// p = 0xFFFFFFFFFFFCF0CD46E5F25EEE71A49F0CDC65FB12980A82D3292DDBAED33013
+//
+// 2) 2-degree extension of GF(p): GF(p^2) == GF(p)[x]/g(x), g(x) = x^2 -beta,
+// beta =-1 mod p, so "beta" represents as {1}
+//
+// 3) 3-degree extension of GF(p^2) ~ GF(p^6): GF((p^2)^3) == GF(p)[v]/g(v), g(v) = v^3 -xi,
+// xi belongs GF(p^2), xi=x+2, so "xi" represents as {2,1} ---- "2" is low- and "1" is high-order coefficients
+//
+// 4) 2-degree extension of GF((p^2)^3) ~ GF(p^12): GF(((p^2)^3)^2) == GF(p)[w]/g(w), g(w) = w^2 -vi,
+// psi belongs GF((p^2)^3), vi=0*v^2 +1*v +0, so "vi" represents as {0,1,0}---- "0", '1" and "0" are low-, middle- and high-order coefficients
+//
+// See representations in t_gfpparam.cpp
+//
+*/
+
+/*
+// Multiplication case: mul(a, vi) over GF((p^2)^3),
+// where:
+// a, belongs to GF((p^2)^3)
+// xi belongs to GF((p^2)^3), vi={0,1,0}
+//
+// The case is important in GF(((p^2)^3)^2) arithmetic for Intel(R) EPID 2.0.
+//
+*/
+__INLINE BNU_CHUNK_T* cpFq6Mul_vi(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
+{
+ gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
+ int termLen = GFP_FELEN(pGroundGFE);
+
+ const BNU_CHUNK_T* pA0 = pA;
+ const BNU_CHUNK_T* pA1 = pA+termLen;
+ const BNU_CHUNK_T* pA2 = pA+termLen*2;
+ BNU_CHUNK_T* pR0 = pR;
+ BNU_CHUNK_T* pR1 = pR+termLen;
+ BNU_CHUNK_T* pR2 = pR+termLen*2;
+
+ BNU_CHUNK_T* t = cpGFpGetPool(1, pGroundGFE);
+ //tbcd: temporary excluded: assert(NULL!=t);
+
+ cpFq2Mul_xi(t, pA2, pGroundGFE);
+ cpGFpElementCopy(pR2, pA1, termLen);
+ cpGFpElementCopy(pR1, pA0, termLen);
+ cpGFpElementCopy(pR0, t, termLen);
+
+ cpGFpReleasePool(1, pGroundGFE);
+
+ return pR;
+}
+
+/*
+// Intel(R) EPID 2.0 specific
+// ~~~~~~~~~~~~~~~
+//
+// Multiplication over GF(p^2)
+// - field polynomial: g(x) = x^2 - beta => binominal with specific value of "beta"
+// - beta = p-1
+//
+// Multiplication over GF(((p^2)^3)^2) ~ GF(p^12)
+// - field polynomial: g(w) = w^2 - vi => binominal with specific value of "vi"
+// - vi = 0*v^2 + 1*v + 0 - i.e vi={0,1,0} belongs to GF((p^2)^3)
+*/
+static BNU_CHUNK_T* cpGFpxMul_p2_binom_epid2(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, const BNU_CHUNK_T* pB, gsEngine* pGFEx)
+{
+ gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
+ mod_mul mulF = GFP_METHOD(pGroundGFE)->mul;
+ mod_add addF = GFP_METHOD(pGroundGFE)->add;
+ mod_sub subF = GFP_METHOD(pGroundGFE)->sub;
+
+ int groundElemLen = GFP_FELEN(pGroundGFE);
+
+ const BNU_CHUNK_T* pA0 = pA;
+ const BNU_CHUNK_T* pA1 = pA+groundElemLen;
+
+ const BNU_CHUNK_T* pB0 = pB;
+ const BNU_CHUNK_T* pB1 = pB+groundElemLen;
+
+ BNU_CHUNK_T* pR0 = pR;
+ BNU_CHUNK_T* pR1 = pR+groundElemLen;
+
+ BNU_CHUNK_T* t0 = cpGFpGetPool(4, pGroundGFE);
+ BNU_CHUNK_T* t1 = t0+groundElemLen;
+ BNU_CHUNK_T* t2 = t1+groundElemLen;
+ BNU_CHUNK_T* t3 = t2+groundElemLen;
+ //tbcd: temporary excluded: assert(NULL!=t0);
+
+ mulF(t0, pA0, pB0, pGroundGFE); /* t0 = a[0]*b[0] */
+ mulF(t1, pA1, pB1, pGroundGFE); /* t1 = a[1]*b[1] */
+ addF(t2, pA0, pA1, pGroundGFE); /* t2 = a[0]+a[1] */
+ addF(t3, pB0, pB1, pGroundGFE); /* t3 = b[0]+b[1] */
+
+ mulF(pR1, t2, t3, pGroundGFE); /* r[1] = (a[0]+a[1]) * (b[0]+b[1]) */
+ subF(pR1, pR1, t0, pGroundGFE); /* r[1] -= a[0]*b[0]) + a[1]*b[1] */
+ subF(pR1, pR1, t1, pGroundGFE);
+
+ /* Intel(R) EPID 2.0 specific */
+ {
+ int basicExtDegree = cpGFpBasicDegreeExtension(pGFEx);
+
+ /* deal with GF(p^2) */
+ if(basicExtDegree==2) {
+ subF(pR0, t0, t1, pGroundGFE);
+ }
+ /* deal with GF(p^6^2) */
+ else if(basicExtDegree==12) {
+ cpFq6Mul_vi(t1, t1, pGroundGFE);
+ addF(pR0, t0, t1, pGroundGFE);
+ }
+ /* deal with GF(p^x^2) - it's not Intel(R) EPID 2.0 case, just a case */
+ else {
+ cpGFpxMul_G0(t1, t1, pGFEx);
+ subF(pR0, t0, t1, pGroundGFE);
+ }
+ }
+
+ cpGFpReleasePool(4, pGroundGFE);
+ return pR;
+}
+
+/*
+// Intel(R) EPID 2.0 specific
+// ~~~~~~~~~~~~~~~
+//
+// Squaring over GF(p^2)
+// - field polynomial: g(x) = x^2 - beta => binominal with specific value of "beta"
+// - beta = p-1
+//
+// Squaring in GF(((p^2)^3)^2) ~ GF(p^12)
+// - field polynomial: g(w) = w^2 - vi => binominal with specific value of "vi"
+// - vi = 0*v^2 + 1*v + 0 - i.e vi={0,1,0} belongs to GF((p^2)^3)
+*/
+static BNU_CHUNK_T* cpGFpxSqr_p2_binom_epid2(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
+{
+ gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
+ mod_mul mulF = GFP_METHOD(pGroundGFE)->mul;
+ mod_sqr sqrF = GFP_METHOD(pGroundGFE)->sqr;
+ mod_add addF = GFP_METHOD(pGroundGFE)->add;
+ mod_sub subF = GFP_METHOD(pGroundGFE)->sub;
+
+ int groundElemLen = GFP_FELEN(pGroundGFE);
+
+ const BNU_CHUNK_T* pA0 = pA;
+ const BNU_CHUNK_T* pA1 = pA+groundElemLen;
+
+ BNU_CHUNK_T* pR0 = pR;
+ BNU_CHUNK_T* pR1 = pR+groundElemLen;
+
+ BNU_CHUNK_T* t0 = cpGFpGetPool(3, pGroundGFE);
+ BNU_CHUNK_T* t1 = t0+groundElemLen;
+ BNU_CHUNK_T* u0 = t1+groundElemLen;
+ //tbcd: temporary excluded: assert(NULL!=t0);
+
+ mulF(u0, pA0, pA1, pGroundGFE); /* u0 = a[0]*a[1] */
+
+ /* Intel(R) EPID 2.0 specific */
+ {
+ int basicExtDegree = cpGFpBasicDegreeExtension(pGFEx);
+
+ /* deal with GF(p^2) */
+ if(basicExtDegree==2) {
+ addF(t0, pA0, pA1, pGroundGFE);
+ subF(t1, pA0, pA1, pGroundGFE);
+ mulF(pR0, t0, t1, pGroundGFE);
+ addF(pR1, u0, u0, pGroundGFE); /* r[1] = 2*a[0]*a[1] */
+ }
+ /* deal with GF(p^6^2) */
+ else if(basicExtDegree==12) {
+ subF(t0, pA0, pA1, pGroundGFE);
+ cpFq6Mul_vi(t1, pA1, pGroundGFE);
+ subF(t1, pA0, t1, pGroundGFE);
+ mulF(t0, t0, t1, pGroundGFE);
+ addF(t0, t0, u0, pGroundGFE);
+ cpFq6Mul_vi(t1, u0, pGroundGFE);
+ addF(pR0, t0, t1, pGroundGFE);
+ addF(pR1, u0, u0, pGroundGFE);
+ }
+ /* just a case */
+ else {
+ sqrF(t0, pA0, pGroundGFE); /* t0 = a[0]*a[0] */
+ sqrF(t1, pA1, pGroundGFE); /* t1 = a[1]*a[1] */
+ cpGFpxMul_G0(t1, t1, pGFEx);
+ subF(pR0, t0, t1, pGroundGFE);
+ addF(pR1, u0, u0, pGroundGFE); /* r[1] = 2*a[0]*a[1] */
+ }
+ }
+
+ cpGFpReleasePool(3, pGroundGFE);
+ return pR;
+}
+
+/*
+// return specific polynomi alarith methods
+// polynomial - deg 2 binomial (Intel(R) EPID 2.0)
+*/
+static gsModMethod* gsPolyArith_binom2_epid2(void)
+{
+ static gsModMethod m = {
+ cpGFpxEncode_com,
+ cpGFpxDecode_com,
+ cpGFpxMul_p2_binom_epid2,
+ cpGFpxSqr_p2_binom_epid2,
+ NULL,
+ cpGFpxAdd_com,
+ cpGFpxSub_com,
+ cpGFpxNeg_com,
+ cpGFpxDiv2_com,
+ cpGFpxMul2_com,
+ cpGFpxMul3_com,
+ //cpGFpxInv
+ };
+ return &m;
+}
+
+/*F*
+// Name: ippsGFpxMethod_binom2_epid2
+//
+// Purpose: Returns a reference to the implementation of arithmetic operations over GF(pd).
+//
+// Returns: pointer to a structure containing
+// an implementation of arithmetic operations over GF(pd)
+// g(x) = x^2 - a0, a0 from GF(q), a0 = 1
+// g(w) = w^2 - V0, v0 from GF((q^2)^3), V0 = 0*s^2 + v + 0
+//
+//
+*F*/
+
+IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom2_epid2, (void) )
+{
+ static IppsGFpMethod method = {
+ cpID_Binom2_epid20,
+ 2,
+ NULL,
+ NULL
+ };
+ method.arith = gsPolyArith_binom2_epid2();
+ return &method;
+}
+
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