1 /******************************************************************************* 2 * Copyright 2018 Intel Corporation 3 * All Rights Reserved. 4 * 5 * If this software was obtained under the Intel Simplified Software License, 6 * the following terms apply: 7 * 8 * The source code, information and material ("Material") contained herein is 9 * owned by Intel Corporation or its suppliers or licensors, and title to such 10 * Material remains with Intel Corporation or its suppliers or licensors. The 11 * Material contains proprietary information of Intel or its suppliers and 12 * licensors. The Material is protected by worldwide copyright laws and treaty 13 * provisions. No part of the Material may be used, copied, reproduced, 14 * modified, published, uploaded, posted, transmitted, distributed or disclosed 15 * in any way without Intel's prior express written permission. No license under 16 * any patent, copyright or other intellectual property rights in the Material 17 * is granted to or conferred upon you, either expressly, by implication, 18 * inducement, estoppel or otherwise. Any license under such intellectual 19 * property rights must be express and approved by Intel in writing. 20 * 21 * Unless otherwise agreed by Intel in writing, you may not remove or alter this 22 * notice or any other notice embedded in Materials by Intel or Intel's 23 * suppliers or licensors in any way. 24 * 25 * 26 * If this software was obtained under the Apache License, Version 2.0 (the 27 * "License"), the following terms apply: 28 * 29 * You may not use this file except in compliance with the License. You may 30 * obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 31 * 32 * 33 * Unless required by applicable law or agreed to in writing, software 34 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT 35 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 36 * 37 * See the License for the specific language governing permissions and 38 * limitations under the License. 39 *******************************************************************************/ 40 41 /* 42 // Intel(R) Integrated Performance Primitives. Cryptography Primitives. 43 // internal functions for GF(p^d) methods, if binomial generator 44 // with Intel(R) Enhanced Privacy ID (Intel(R) EPID) 2.0 specific 45 // 46 */ 47 #include "owncp.h" 48 49 #include "pcpgfpxstuff.h" 50 #include "pcpgfpxmethod_com.h" 51 52 //tbcd: temporary excluded: #include <assert.h> 53 54 /* 55 // Intel(R) EPID 2.0 specific. 56 // 57 // Intel(R) EPID 2.0 uses the following finite field hierarchy: 58 // 59 // 1) prime field GF(p), 60 // p = 0xFFFFFFFFFFFCF0CD46E5F25EEE71A49F0CDC65FB12980A82D3292DDBAED33013 61 // 62 // 2) 2-degree extension of GF(p): GF(p^2) == GF(p)[x]/g(x), g(x) = x^2 -beta, 63 // beta =-1 mod p, so "beta" represents as {1} 64 // 65 // 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, 66 // xi belongs GF(p^2), xi=x+2, so "xi" represents as {2,1} ---- "2" is low- and "1" is high-order coefficients 67 // 68 // 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, 69 // 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 70 // 71 // See representations in t_gfpparam.cpp 72 // 73 */ 74 75 /* 76 // Multiplication case: mul(a, xi) over GF(p^2), 77 // where: 78 // a, belongs to GF(p^2) 79 // xi belongs to GF(p^2), xi={2,1} 80 // 81 // The case is important in GF((p^2)^3) arithmetic for Intel(R) EPID 2.0. 82 // 83 */ 84 __INLINE BNU_CHUNK_T* cpFq2Mul_xi(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx) 85 { 86 gsEngine* pGroundGFE = GFP_PARENT(pGFEx); 87 mod_mul addF = GFP_METHOD(pGroundGFE)->add; 88 mod_sub subF = GFP_METHOD(pGroundGFE)->sub; 89 90 int termLen = GFP_FELEN(pGroundGFE); 91 BNU_CHUNK_T* t0 = cpGFpGetPool(2, pGroundGFE); 92 BNU_CHUNK_T* t1 = t0+termLen; 93 94 const BNU_CHUNK_T* pA0 = pA; 95 const BNU_CHUNK_T* pA1 = pA+termLen; 96 BNU_CHUNK_T* pR0 = pR; 97 BNU_CHUNK_T* pR1 = pR+termLen; 98 99 //tbcd: temporary excluded: assert(NULL!=t0); 100 addF(t0, pA0, pA0, pGroundGFE); 101 addF(t1, pA0, pA1, pGroundGFE); 102 subF(pR0, t0, pA1, pGroundGFE); 103 addF(pR1, t1, pA1, pGroundGFE); 104 105 cpGFpReleasePool(2, pGroundGFE); 106 return pR; 107 } 108 109 /* 110 // Multiplication case: mul(a, g0) over GF(()), 111 // where: 112 // a and g0 belongs to GF(()) - field is being extension 113 // 114 // The case is important in GF(()^d) arithmetic if constructed polynomial is generic binomial g(t) = t^d +g0. 115 // 116 */ 117 static BNU_CHUNK_T* cpGFpxMul_G0(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx) 118 { 119 gsEngine* pGroundGFE = GFP_PARENT(pGFEx); 120 BNU_CHUNK_T* pGFpolynomial = GFP_MODULUS(pGFEx); /* g(x) = t^d + g0 */ 121 return GFP_METHOD(pGroundGFE)->mul(pR, pA, pGFpolynomial, pGroundGFE); 122 } 123
