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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;
}