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/*
// 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;
}