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| *******************************************************************************/ |
| |
| /* |
| // Intel(R) Integrated Performance Primitives. Cryptography Primitives. |
| // GF(p^d) methods, if binomial generator over GF((p^2)^3) |
| // |
| */ |
| #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 |
| // |
| */ |
| |
| /* |
| // Intel(R) EPID 2.0 specific |
| // ~~~~~~~~~~~~~~~ |
| // |
| // Multiplication over GF((p^2)^3) |
| // - field polynomial: g(v) = v^3 - xi => binominal with specific value of "xi" |
| // - xi = x+2 |
| */ |
| static BNU_CHUNK_T* cpGFpxMul_p3_binom_epid2(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, const BNU_CHUNK_T* pB, gsEngine* pGFEx) |
| { |
| gsEngine* pGroundGFE = GFP_PARENT(pGFEx); |
| int groundElemLen = GFP_FELEN(pGroundGFE); |
| |
| mod_mul mulF = GFP_METHOD(pGroundGFE)->mul; |
| mod_add addF = GFP_METHOD(pGroundGFE)->add; |
| mod_sub subF = GFP_METHOD(pGroundGFE)->sub; |
| |
| const BNU_CHUNK_T* pA0 = pA; |
| const BNU_CHUNK_T* pA1 = pA+groundElemLen; |
| const BNU_CHUNK_T* pA2 = pA+groundElemLen*2; |
| |
| const BNU_CHUNK_T* pB0 = pB; |
| const BNU_CHUNK_T* pB1 = pB+groundElemLen; |
| const BNU_CHUNK_T* pB2 = pB+groundElemLen*2; |
| |
| BNU_CHUNK_T* pR0 = pR; |
| BNU_CHUNK_T* pR1 = pR+groundElemLen; |
| BNU_CHUNK_T* pR2 = pR+groundElemLen*2; |
| |
| BNU_CHUNK_T* t0 = cpGFpGetPool(6, pGroundGFE); |
| BNU_CHUNK_T* t1 = t0+groundElemLen; |
| BNU_CHUNK_T* t2 = t1+groundElemLen; |
| BNU_CHUNK_T* u0 = t2+groundElemLen; |
| BNU_CHUNK_T* u1 = u0+groundElemLen; |
| BNU_CHUNK_T* u2 = u1+groundElemLen; |
| //tbcd: temporary excluded: assert(NULL!=t0); |
| |
| addF(u0 ,pA0, pA1, pGroundGFE); /* u0 = a[0]+a[1] */ |
| addF(t0 ,pB0, pB1, pGroundGFE); /* t0 = b[0]+b[1] */ |
| mulF(u0, u0, t0, pGroundGFE); /* u0 = (a[0]+a[1])*(b[0]+b[1]) */ |
| mulF(t0, pA0, pB0, pGroundGFE); /* t0 = a[0]*b[0] */ |
| |
| addF(u1 ,pA1, pA2, pGroundGFE); /* u1 = a[1]+a[2] */ |
| addF(t1 ,pB1, pB2, pGroundGFE); /* t1 = b[1]+b[2] */ |
| mulF(u1, u1, t1, pGroundGFE); /* u1 = (a[1]+a[2])*(b[1]+b[2]) */ |
| mulF(t1, pA1, pB1, pGroundGFE); /* t1 = a[1]*b[1] */ |
| |
| addF(u2 ,pA2, pA0, pGroundGFE); /* u2 = a[2]+a[0] */ |
| addF(t2 ,pB2, pB0, pGroundGFE); /* t2 = b[2]+b[0] */ |
| mulF(u2, u2, t2, pGroundGFE); /* u2 = (a[2]+a[0])*(b[2]+b[0]) */ |
| mulF(t2, pA2, pB2, pGroundGFE); /* t2 = a[2]*b[2] */ |
| |
| subF(u0, u0, t0, pGroundGFE); /* u0 = a[0]*b[1]+a[1]*b[0] */ |
| subF(u0, u0, t1, pGroundGFE); |
| subF(u1, u1, t1, pGroundGFE); /* u1 = a[1]*b[2]+a[2]*b[1] */ |
| subF(u1, u1, t2, pGroundGFE); |
| subF(u2, u2, t2, pGroundGFE); /* u2 = a[2]*b[0]+a[0]*b[2] */ |
| subF(u2, u2, t0, pGroundGFE); |
| |
| /* Intel(R) EPID 2.0 specific */ |
| { |
| int basicExtDegree = cpGFpBasicDegreeExtension(pGFEx); |
| |
| /* deal with GF(p^2^3) */ |
| if(basicExtDegree==6) { |
| cpFq2Mul_xi(u1, u1, pGroundGFE); |
| cpFq2Mul_xi(t2, t2, pGroundGFE); |
| addF(pR0, t0, u1, pGroundGFE); /* r[0] = a[0]*b[0] - (a[2]*b[1]+a[1]*b[2])*beta */ |
| addF(pR1, u0, t2, pGroundGFE); /* r[1] = a[1]*b[0] + a[0]*b[1] - a[2]*b[2]*beta */ |
| } |
| /* just a case */ |
| else { |
| cpGFpxMul_G0(u1, u1, pGFEx); /* u1 = (a[1]*b[2]+a[2]*b[1]) * beta */ |
| cpGFpxMul_G0(t2, t2, pGFEx); /* t2 = a[2]*b[2] * beta */ |
| subF(pR0, t0, u1, pGroundGFE); /* r[0] = a[0]*b[0] - (a[2]*b[1]+a[1]*b[2])*beta */ |
| subF(pR1, u0, t2, pGroundGFE); /* r[1] = a[1]*b[0] + a[0]*b[1] - a[2]*b[2]*beta */ |
| } |
| } |
| |
| addF(pR2, u2, t1, pGroundGFE); /* r[2] = a[2]*b[0] + a[1]*b[1] + a[0]*b[2] */ |
| |
| cpGFpReleasePool(6, pGroundGFE); |
| return pR; |
| } |
| |
| /* |
| // Intel(R) EPID 2.0 specific |
| // ~~~~~~~~~~~~~~~ |
| // |
| // Squaring over GF((p^2)^3) |
| // - field polynomial: g(v) = v^3 - xi => binominal with specific value of "xi" |
| // - xi = x+2 |
| */ |
| static BNU_CHUNK_T* cpGFpxSqr_p3_binom_epid2(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx) |
| { |
| gsEngine* pGroundGFE = GFP_PARENT(pGFEx); |
| int groundElemLen = GFP_FELEN(pGroundGFE); |
| |
| 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; |
| |
| const BNU_CHUNK_T* pA0 = pA; |
| const BNU_CHUNK_T* pA1 = pA+groundElemLen; |
| const BNU_CHUNK_T* pA2 = pA+groundElemLen*2; |
| |
| BNU_CHUNK_T* pR0 = pR; |
| BNU_CHUNK_T* pR1 = pR+groundElemLen; |
| BNU_CHUNK_T* pR2 = pR+groundElemLen*2; |
| |
| BNU_CHUNK_T* s0 = cpGFpGetPool(5, pGroundGFE); |
| BNU_CHUNK_T* s1 = s0+groundElemLen; |
| BNU_CHUNK_T* s2 = s1+groundElemLen; |
| BNU_CHUNK_T* s3 = s2+groundElemLen; |
| BNU_CHUNK_T* s4 = s3+groundElemLen; |
| |
| addF(s2, pA0, pA2, pGroundGFE); |
| subF(s2, s2, pA1, pGroundGFE); |
| sqrF(s2, s2, pGroundGFE); |
| sqrF(s0, pA0, pGroundGFE); |
| sqrF(s4, pA2, pGroundGFE); |
| mulF(s1, pA0, pA1, pGroundGFE); |
| mulF(s3, pA1, pA2, pGroundGFE); |
| addF(s1, s1, s1, pGroundGFE); |
| addF(s3, s3, s3, pGroundGFE); |
| |
| addF(pR2, s1, s2, pGroundGFE); |
| addF(pR2, pR2, s3, pGroundGFE); |
| subF(pR2, pR2, s0, pGroundGFE); |
| subF(pR2, pR2, s4, pGroundGFE); |
| |
| /* Intel(R) EPID 2.0 specific */ |
| { |
| int basicExtDegree = cpGFpBasicDegreeExtension(pGFEx); |
| |
| /* deal with GF(p^2^3) */ |
| if(basicExtDegree==6) { |
| cpFq2Mul_xi(s4, s4, pGroundGFE); |
| cpFq2Mul_xi(s3, s3, pGroundGFE); |
| addF(pR1, s1, s4, pGroundGFE); |
| addF(pR0, s0, s3, pGroundGFE); |
| } |
| /* just a case */ |
| else { |
| cpGFpxMul_G0(s4, s4, pGFEx); |
| cpGFpxMul_G0(s3, s3, pGFEx); |
| subF(pR1, s1, s4, pGroundGFE); |
| subF(pR0, s0, s3, pGroundGFE); |
| } |
| } |
| |
| cpGFpReleasePool(5, pGroundGFE); |
| return pR; |
| } |
| |
| /* |
| // return specific polynomi alarith methods |
| // polynomial - deg 3 binomial (Intel(R) EPID 2.0) |
| */ |
| static gsModMethod* gsPolyArith_binom3_epid2(void) |
| { |
| static gsModMethod m = { |
| cpGFpxEncode_com, |
| cpGFpxDecode_com, |
| cpGFpxMul_p3_binom_epid2, |
| cpGFpxSqr_p3_binom_epid2, |
| NULL, |
| cpGFpxAdd_com, |
| cpGFpxSub_com, |
| cpGFpxNeg_com, |
| cpGFpxDiv2_com, |
| cpGFpxMul2_com, |
| cpGFpxMul3_com, |
| //cpGFpxInv |
| }; |
| return &m; |
| } |
| |
| /*F* |
| // Name: ippsGFpxMethod_binom3_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(v) = v^3 - U0, U0 from GF(q^2), U0 = u + 2 |
| // |
| // |
| *F*/ |
| |
| IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom3_epid2, (void) ) |
| { |
| static IppsGFpMethod method = { |
| cpID_Binom3_epid20, |
| 3, |
| NULL, |
| NULL |
| }; |
| method.arith = gsPolyArith_binom3_epid2(); |
| return &method; |
| } |
