ext/ipp/sources/ippcp/src/pcpgfpxmethod_binom.c - platform/external/epid-sdk - Git at Google

 /*############################################################################
   # Copyright 1999-2018 Intel Corporation
   #
   # Licensed under the Apache License, Version 2.0 (the "License");
   # 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) Performance Primitives. Cryptography Primitives.
 //     GF(p^d) methods, if binomial generator
 //
 */
 #include "owncp.h"

 #include "pcpgfpxstuff.h"
 #include "pcpgfpxmethod_com.h"

 //gres: temporary excluded: #include <assert.h>

 static BNU_CHUNK_T* cpGFpxMul_G0(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
 {
    gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
    mod_mul mulF = GFP_METHOD(pGroundGFE)->mul;

    BNU_CHUNK_T* pGFpolynomial = GFP_MODULUS(pGFEx); /* g(x) = t^d + g0 */

    #if defined GS_DBG
    BNU_CHUNK_T* arg0 = cpGFpGetPool(1, pGroundGFE);
    BNU_CHUNK_T* arg1 = cpGFpGetPool(1, pGroundGFE);
    int groundElemLen = GFP_FELEN(pGroundGFE);
    #endif

    #if defined GS_DBG
    cpGFpxGet(arg0, groundElemLen, pA, pGroundGFE);
    cpGFpxGet(arg1, groundElemLen, pGFpolynomial, pGroundGFE);
    #endif

    mulF(pR, pA, pGFpolynomial, pGroundGFE);

    #if defined GS_DBG
    cpGFpReleasePool(2, pGroundGFE);
    #endif

    return pR;
 }

 /*
 // Multiplication in GF(p^2), if field polynomial: g(x) = x^2 + beta  => binominal
 */
 static BNU_CHUNK_T* cpGFpxMul_p2_binom(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* 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;
    //gres: temporary excluded: assert(NULL!=t0);

    #if defined GS_DBG
    BNU_CHUNK_T* arg0 = cpGFpGetPool(1, pGroundGFE);
    BNU_CHUNK_T* arg1 = cpGFpGetPool(1, pGroundGFE);
    #endif
    #if defined GS_DBG
    cpGFpxGet(arg0, groundElemLen, pA0, pGroundGFE);
    cpGFpxGet(arg1, groundElemLen, pB0, pGroundGFE);
    #endif

    mulF(t0, pA0, pB0, pGroundGFE);    /* t0 = a[0]*b[0] */

    #if defined GS_DBG
    cpGFpxGet(arg0, groundElemLen, pA1, pGroundGFE);
    cpGFpxGet(arg1, groundElemLen, pB1, pGroundGFE);
    #endif

    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] */

    #if defined GS_DBG
    cpGFpxGet(arg0, groundElemLen, t2, pGroundGFE);
    cpGFpxGet(arg1, groundElemLen, t3, pGroundGFE);
    #endif

    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);

    cpGFpxMul_G0(t1, t1, pGFEx);
    subF(pR0, t0, t1, pGroundGFE);

    #if defined GS_DBG
    cpGFpReleasePool(2, pGroundGFE);
    #endif

    cpGFpReleasePool(4, pGroundGFE);
    return pR;
 }

 /*
 // Squaring in GF(p^2), if field polynomial: g(x) = x^2 + beta  => binominal
 */
 static BNU_CHUNK_T* cpGFpxSqr_p2_binom(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;

    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;
    //gres: temporary excluded: assert(NULL!=t0);

    #if defined GS_DBG
    BNU_CHUNK_T* arg0 = cpGFpGetPool(1, pGroundGFE);
    BNU_CHUNK_T* arg1 = cpGFpGetPool(1, pGroundGFE);
    #endif
    #if defined GS_DBG
    cpGFpxGet(arg0, groundElemLen, pA0, pGroundGFE);
    cpGFpxGet(arg1, groundElemLen, pA1, pGroundGFE);
    #endif

    mulF(u0, pA0, pA1, pGroundGFE); /* u0 = a[0]*a[1] */
    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] */

    #if defined GS_DBG
    cpGFpReleasePool(2, pGroundGFE);
    #endif

    cpGFpReleasePool(3, pGroundGFE);
    return pR;
 }

 /*
 // return specific polynomi alarith methods
 // polynomial - deg 2 binomial
 */
 static gsModMethod* gsPolyArith_binom2(void)
 {
    static gsModMethod m = {
       cpGFpxEncode_com,
       cpGFpxDecode_com,
       cpGFpxMul_p2_binom,
       cpGFpxSqr_p2_binom,
       NULL,
       cpGFpxAdd_com,
       cpGFpxSub_com,
       cpGFpxNeg_com,
       cpGFpxDiv2_com,
       cpGFpxMul2_com,
       cpGFpxMul3_com,
       //cpGFpxInv
    };
    return &m;
 }

 IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom2, (void) )
 {
    static IppsGFpMethod method = {
       cpID_Binom,
       2,
       NULL,
       NULL
    };
    method.arith = gsPolyArith_binom2();
    return &method;
 }


 /*
 // Multiplication in GF(p^3), if field polynomial: g(x) = x^3 + beta  => binominal
 */
 static BNU_CHUNK_T* cpGFpxMul_p3_binom(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;
    //gres: 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);

    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;
 }

 /*
 // Squaring in GF(p^3), if field polynomial: g(x) = x^3 + beta  => binominal
 */
 static BNU_CHUNK_T* cpGFpxSqr_p3_binom(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;
    //gres: temporary excluded: assert(NULL!=s0);

    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);

    cpGFpxMul_G0(s4, s4, pGFEx);
    subF(pR1, s1,  s4, pGroundGFE);

    cpGFpxMul_G0(s3, s3, pGFEx);
    subF(pR0, s0,  s3, pGroundGFE);

    cpGFpReleasePool(5, pGroundGFE);
    return pR;
 }


 /*
 // return specific polynomi alarith methods
 // polynomial - deg 3 binomial
 */
 static gsModMethod* gsPolyArith_binom3(void)
 {
    static gsModMethod m = {
       cpGFpxEncode_com,
       cpGFpxDecode_com,
       cpGFpxMul_p3_binom,
       cpGFpxSqr_p3_binom,
       NULL,
       cpGFpxAdd_com,
       cpGFpxSub_com,
       cpGFpxNeg_com,
       cpGFpxDiv2_com,
       cpGFpxMul2_com,
       cpGFpxMul3_com,
       //cpGFpxInv
    };
    return &m;
 }
 /*
 // returns methods
 */
 IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom3, (void) )
 {
    static IppsGFpMethod method = {
       cpID_Binom,
       3,
       NULL,
       NULL
    };
    method.arith = gsPolyArith_binom3();
    return &method;
 }


 /*
 // Multiplication in GF(p^d), if field polynomial: g(x) = x^d + beta  => binominal
 */
 static BNU_CHUNK_T* cpGFpxMul_pd_binom(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, const BNU_CHUNK_T* pB, gsEngine* pGFEx)
 {
    BNU_CHUNK_T* pGFpolynomial = GFP_MODULUS(pGFEx);
    int deg = GFP_EXTDEGREE(pGFEx);
    int elemLen= GFP_FELEN(pGFEx);
    int groundElemLen = GFP_FELEN(GFP_PARENT(pGFEx));
    int d;

    BNU_CHUNK_T* R = cpGFpGetPool(4, pGFEx);
    BNU_CHUNK_T* X = R+elemLen;
    BNU_CHUNK_T* T0= X+elemLen;
    BNU_CHUNK_T* T1= T0+elemLen;
    //gres: temporary excluded: assert(NULL!=R);

    /* T0 = A * beta */
    cpGFpxMul_GFE(T0, pA, pGFpolynomial, pGFEx);
    /* T1 = A */
    cpGFpElementCopy(T1, pA, elemLen);

    /* R = A * B[0] */
    cpGFpxMul_GFE(R, pA, pB, pGFEx);

    /* R += (A*B[d]) mod g() */
    for(d=1; d<deg; d++) {
       cpGFpxMul_GFE(X, GFPX_IDX_ELEMENT(T0, deg-d, groundElemLen), GFPX_IDX_ELEMENT(pB, d, groundElemLen),  pGFEx);
       GFP_METHOD(pGFEx)->add(R, R, X, pGFEx);
    }
    cpGFpElementCopy(pR, R, elemLen);

    cpGFpReleasePool(4, pGFEx);
    return pR;
 }

 /*
 // Squaring in GF(p^d), if field polynomial: g(x) = x^d + beta  => binominal
 */
 static BNU_CHUNK_T* cpGFpxSqr_pd_binom(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
 {
    return cpGFpxMul_pd_binom(pR, pA, pA, pGFEx);
 }

 /*
 // return specific polynomial arith methods
 // polynomial - general binomial
 */
 static gsModMethod* gsPolyArith_binom(void)
 {
    static gsModMethod m = {
       cpGFpxEncode_com,
       cpGFpxDecode_com,
       cpGFpxMul_pd_binom,
       cpGFpxSqr_pd_binom,
       NULL,
       cpGFpxAdd_com,
       cpGFpxSub_com,
       cpGFpxNeg_com,
       cpGFpxDiv2_com,
       cpGFpxMul2_com,
       cpGFpxMul3_com,
       //cpGFpxInv
    };
    return &m;
 }

 IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom, (void) )
 {
    static IppsGFpMethod method = {
       cpID_Binom,
       0,
       NULL,
       NULL
    };
    method.arith = gsPolyArith_binom();
    return &method;
 }
	/*############################################################################
	# Copyright 1999-2018 Intel Corporation
	#
	# Licensed under the Apache License, Version 2.0 (the "License");
	# 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) Performance Primitives. Cryptography Primitives.
	// GF(p^d) methods, if binomial generator
	//
	*/
	#include "owncp.h"

	#include "pcpgfpxstuff.h"
	#include "pcpgfpxmethod_com.h"

	//gres: temporary excluded: #include <assert.h>

	static BNU_CHUNK_T* cpGFpxMul_G0(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
	{
	gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
	mod_mul mulF = GFP_METHOD(pGroundGFE)->mul;

	BNU_CHUNK_T* pGFpolynomial = GFP_MODULUS(pGFEx); /* g(x) = t^d + g0 */

	#if defined GS_DBG
	BNU_CHUNK_T* arg0 = cpGFpGetPool(1, pGroundGFE);
	BNU_CHUNK_T* arg1 = cpGFpGetPool(1, pGroundGFE);
	int groundElemLen = GFP_FELEN(pGroundGFE);
	#endif

	#if defined GS_DBG
	cpGFpxGet(arg0, groundElemLen, pA, pGroundGFE);
	cpGFpxGet(arg1, groundElemLen, pGFpolynomial, pGroundGFE);
	#endif

	mulF(pR, pA, pGFpolynomial, pGroundGFE);

	#if defined GS_DBG
	cpGFpReleasePool(2, pGroundGFE);
	#endif

	return pR;
	}

	/*
	// Multiplication in GF(p^2), if field polynomial: g(x) = x^2 + beta => binominal
	*/
	static BNU_CHUNK_T* cpGFpxMul_p2_binom(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* 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;
	//gres: temporary excluded: assert(NULL!=t0);

	#if defined GS_DBG
	BNU_CHUNK_T* arg0 = cpGFpGetPool(1, pGroundGFE);
	BNU_CHUNK_T* arg1 = cpGFpGetPool(1, pGroundGFE);
	#endif
	#if defined GS_DBG
	cpGFpxGet(arg0, groundElemLen, pA0, pGroundGFE);
	cpGFpxGet(arg1, groundElemLen, pB0, pGroundGFE);
	#endif

	mulF(t0, pA0, pB0, pGroundGFE); /* t0 = a[0]b[0] /

	#if defined GS_DBG
	cpGFpxGet(arg0, groundElemLen, pA1, pGroundGFE);
	cpGFpxGet(arg1, groundElemLen, pB1, pGroundGFE);
	#endif

	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] */

	#if defined GS_DBG
	cpGFpxGet(arg0, groundElemLen, t2, pGroundGFE);
	cpGFpxGet(arg1, groundElemLen, t3, pGroundGFE);
	#endif

	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);

	cpGFpxMul_G0(t1, t1, pGFEx);
	subF(pR0, t0, t1, pGroundGFE);

	#if defined GS_DBG
	cpGFpReleasePool(2, pGroundGFE);
	#endif

	cpGFpReleasePool(4, pGroundGFE);
	return pR;
	}

	/*
	// Squaring in GF(p^2), if field polynomial: g(x) = x^2 + beta => binominal
	*/
	static BNU_CHUNK_T* cpGFpxSqr_p2_binom(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;

	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;
	//gres: temporary excluded: assert(NULL!=t0);

	#if defined GS_DBG
	BNU_CHUNK_T* arg0 = cpGFpGetPool(1, pGroundGFE);
	BNU_CHUNK_T* arg1 = cpGFpGetPool(1, pGroundGFE);
	#endif
	#if defined GS_DBG
	cpGFpxGet(arg0, groundElemLen, pA0, pGroundGFE);
	cpGFpxGet(arg1, groundElemLen, pA1, pGroundGFE);
	#endif

	mulF(u0, pA0, pA1, pGroundGFE); /* u0 = a[0]a[1] /
	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] = 2a[0]a[1] */

	#if defined GS_DBG
	cpGFpReleasePool(2, pGroundGFE);
	#endif

	cpGFpReleasePool(3, pGroundGFE);
	return pR;
	}

	/*
	// return specific polynomi alarith methods
	// polynomial - deg 2 binomial
	*/
	static gsModMethod* gsPolyArith_binom2(void)
	{
	static gsModMethod m = {
	cpGFpxEncode_com,
	cpGFpxDecode_com,
	cpGFpxMul_p2_binom,
	cpGFpxSqr_p2_binom,
	NULL,
	cpGFpxAdd_com,
	cpGFpxSub_com,
	cpGFpxNeg_com,
	cpGFpxDiv2_com,
	cpGFpxMul2_com,
	cpGFpxMul3_com,
	//cpGFpxInv
	};
	return &m;
	}

	IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom2, (void) )
	{
	static IppsGFpMethod method = {
	cpID_Binom,
	2,
	NULL,
	NULL
	};
	method.arith = gsPolyArith_binom2();
	return &method;
	}


	/*
	// Multiplication in GF(p^3), if field polynomial: g(x) = x^3 + beta => binominal
	*/
	static BNU_CHUNK_T* cpGFpxMul_p3_binom(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;
	//gres: 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);

	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;
	}

	/*
	// Squaring in GF(p^3), if field polynomial: g(x) = x^3 + beta => binominal
	*/
	static BNU_CHUNK_T* cpGFpxSqr_p3_binom(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;
	//gres: temporary excluded: assert(NULL!=s0);

	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);

	cpGFpxMul_G0(s4, s4, pGFEx);
	subF(pR1, s1, s4, pGroundGFE);

	cpGFpxMul_G0(s3, s3, pGFEx);
	subF(pR0, s0, s3, pGroundGFE);

	cpGFpReleasePool(5, pGroundGFE);
	return pR;
	}


	/*
	// return specific polynomi alarith methods
	// polynomial - deg 3 binomial
	*/
	static gsModMethod* gsPolyArith_binom3(void)
	{
	static gsModMethod m = {
	cpGFpxEncode_com,
	cpGFpxDecode_com,
	cpGFpxMul_p3_binom,
	cpGFpxSqr_p3_binom,
	NULL,
	cpGFpxAdd_com,
	cpGFpxSub_com,
	cpGFpxNeg_com,
	cpGFpxDiv2_com,
	cpGFpxMul2_com,
	cpGFpxMul3_com,
	//cpGFpxInv
	};
	return &m;
	}
	/*
	// returns methods
	*/
	IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom3, (void) )
	{
	static IppsGFpMethod method = {
	cpID_Binom,
	3,
	NULL,
	NULL
	};
	method.arith = gsPolyArith_binom3();
	return &method;
	}


	/*
	// Multiplication in GF(p^d), if field polynomial: g(x) = x^d + beta => binominal
	*/
	static BNU_CHUNK_T* cpGFpxMul_pd_binom(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, const BNU_CHUNK_T* pB, gsEngine* pGFEx)
	{
	BNU_CHUNK_T* pGFpolynomial = GFP_MODULUS(pGFEx);
	int deg = GFP_EXTDEGREE(pGFEx);
	int elemLen= GFP_FELEN(pGFEx);
	int groundElemLen = GFP_FELEN(GFP_PARENT(pGFEx));
	int d;

	BNU_CHUNK_T* R = cpGFpGetPool(4, pGFEx);
	BNU_CHUNK_T* X = R+elemLen;
	BNU_CHUNK_T* T0= X+elemLen;
	BNU_CHUNK_T* T1= T0+elemLen;
	//gres: temporary excluded: assert(NULL!=R);

	/* T0 = A * beta */
	cpGFpxMul_GFE(T0, pA, pGFpolynomial, pGFEx);
	/* T1 = A */
	cpGFpElementCopy(T1, pA, elemLen);

	/* R = A * B[0] */
	cpGFpxMul_GFE(R, pA, pB, pGFEx);

	/* R += (AB[d]) mod g() /
	for(d=1; d<deg; d++) {
	cpGFpxMul_GFE(X, GFPX_IDX_ELEMENT(T0, deg-d, groundElemLen), GFPX_IDX_ELEMENT(pB, d, groundElemLen), pGFEx);
	GFP_METHOD(pGFEx)->add(R, R, X, pGFEx);
	}
	cpGFpElementCopy(pR, R, elemLen);

	cpGFpReleasePool(4, pGFEx);
	return pR;
	}

	/*
	// Squaring in GF(p^d), if field polynomial: g(x) = x^d + beta => binominal
	*/
	static BNU_CHUNK_T* cpGFpxSqr_pd_binom(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
	{
	return cpGFpxMul_pd_binom(pR, pA, pA, pGFEx);
	}

	/*
	// return specific polynomial arith methods
	// polynomial - general binomial
	*/
	static gsModMethod* gsPolyArith_binom(void)
	{
	static gsModMethod m = {
	cpGFpxEncode_com,
	cpGFpxDecode_com,
	cpGFpxMul_pd_binom,
	cpGFpxSqr_pd_binom,
	NULL,
	cpGFpxAdd_com,
	cpGFpxSub_com,
	cpGFpxNeg_com,
	cpGFpxDiv2_com,
	cpGFpxMul2_com,
	cpGFpxMul3_com,
	//cpGFpxInv
	};
	return &m;
	}

	IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom, (void) )
	{
	static IppsGFpMethod method = {
	cpID_Binom,
	0,
	NULL,
	NULL
	};
	method.arith = gsPolyArith_binom();
	return &method;
	}