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40
41 /*
42 // Intel(R) Integrated Performance Primitives. Cryptography Primitives.
43 // GF(p^d) methods, if binomial generator over GF((p^2)^3)
44 //
45 */
46 #include "owncp.h"
47
48 #include "pcpgfpxstuff.h"
49 #include "pcpgfpxmethod_com.h"
50 #include "pcpgfpxmethod_binom_epid2.h"
51
52 //tbcd: temporary excluded: #include <assert.h>
53
54 /*
55 // Intel(R) Enhanced Privacy ID (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 // Intel(R) EPID 2.0 specific
77 // ~~~~~~~~~~~~~~~
78 //
79 // Multiplication over GF((p^2)^3)
80 // - field polynomial: g(v) = v^3 - xi => binominal with specific value of "xi"
81 // - xi = x+2
82 */
cpGFpxMul_p3_binom_epid2(BNU_CHUNK_T * pR,const BNU_CHUNK_T * pA,const BNU_CHUNK_T * pB,gsEngine * pGFEx)83 static BNU_CHUNK_T* cpGFpxMul_p3_binom_epid2(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, const BNU_CHUNK_T* pB, gsEngine* pGFEx)
84 {
85 gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
86 int groundElemLen = GFP_FELEN(pGroundGFE);
87
88 mod_mul mulF = GFP_METHOD(pGroundGFE)->mul;
89 mod_add addF = GFP_METHOD(pGroundGFE)->add;
90 mod_sub subF = GFP_METHOD(pGroundGFE)->sub;
91
92 const BNU_CHUNK_T* pA0 = pA;
93 const BNU_CHUNK_T* pA1 = pA+groundElemLen;
94 const BNU_CHUNK_T* pA2 = pA+groundElemLen*2;
95
96 const BNU_CHUNK_T* pB0 = pB;
97 const BNU_CHUNK_T* pB1 = pB+groundElemLen;
98 const BNU_CHUNK_T* pB2 = pB+groundElemLen*2;
99
100 BNU_CHUNK_T* pR0 = pR;
101 BNU_CHUNK_T* pR1 = pR+groundElemLen;
102 BNU_CHUNK_T* pR2 = pR+groundElemLen*2;
103
104 BNU_CHUNK_T* t0 = cpGFpGetPool(6, pGroundGFE);
105 BNU_CHUNK_T* t1 = t0+groundElemLen;
106 BNU_CHUNK_T* t2 = t1+groundElemLen;
107 BNU_CHUNK_T* u0 = t2+groundElemLen;
108 BNU_CHUNK_T* u1 = u0+groundElemLen;
109 BNU_CHUNK_T* u2 = u1+groundElemLen;
110 //tbcd: temporary excluded: assert(NULL!=t0);
111
112 addF(u0 ,pA0, pA1, pGroundGFE); /* u0 = a[0]+a[1] */
113 addF(t0 ,pB0, pB1, pGroundGFE); /* t0 = b[0]+b[1] */
114 mulF(u0, u0, t0, pGroundGFE); /* u0 = (a[0]+a[1])*(b[0]+b[1]) */
115 mulF(t0, pA0, pB0, pGroundGFE); /* t0 = a[0]*b[0] */
116
117 addF(u1 ,pA1, pA2, pGroundGFE); /* u1 = a[1]+a[2] */
118 addF(t1 ,pB1, pB2, pGroundGFE); /* t1 = b[1]+b[2] */
119 mulF(u1, u1, t1, pGroundGFE); /* u1 = (a[1]+a[2])*(b[1]+b[2]) */
120 mulF(t1, pA1, pB1, pGroundGFE); /* t1 = a[1]*b[1] */
121
122 addF(u2 ,pA2, pA0, pGroundGFE); /* u2 = a[2]+a[0] */
123 addF(t2 ,pB2, pB0, pGroundGFE); /* t2 = b[2]+b[0] */
124 mulF(u2, u2, t2, pGroundGFE); /* u2 = (a[2]+a[0])*(b[2]+b[0]) */
125 mulF(t2, pA2, pB2, pGroundGFE); /* t2 = a[2]*b[2] */
126
127 subF(u0, u0, t0, pGroundGFE); /* u0 = a[0]*b[1]+a[1]*b[0] */
128 subF(u0, u0, t1, pGroundGFE);
129 subF(u1, u1, t1, pGroundGFE); /* u1 = a[1]*b[2]+a[2]*b[1] */
130 subF(u1, u1, t2, pGroundGFE);
131 subF(u2, u2, t2, pGroundGFE); /* u2 = a[2]*b[0]+a[0]*b[2] */
132 subF(u2, u2, t0, pGroundGFE);
133
134 /* Intel(R) EPID 2.0 specific */
135 {
136 int basicExtDegree = cpGFpBasicDegreeExtension(pGFEx);
137
138 /* deal with GF(p^2^3) */
139 if(basicExtDegree==6) {
140 cpFq2Mul_xi(u1, u1, pGroundGFE);
141 cpFq2Mul_xi(t2, t2, pGroundGFE);
142 addF(pR0, t0, u1, pGroundGFE); /* r[0] = a[0]*b[0] - (a[2]*b[1]+a[1]*b[2])*beta */
143 addF(pR1, u0, t2, pGroundGFE); /* r[1] = a[1]*b[0] + a[0]*b[1] - a[2]*b[2]*beta */
144 }
145 /* just a case */
146 else {
147 cpGFpxMul_G0(u1, u1, pGFEx); /* u1 = (a[1]*b[2]+a[2]*b[1]) * beta */
148 cpGFpxMul_G0(t2, t2, pGFEx); /* t2 = a[2]*b[2] * beta */
149 subF(pR0, t0, u1, pGroundGFE); /* r[0] = a[0]*b[0] - (a[2]*b[1]+a[1]*b[2])*beta */
150 subF(pR1, u0, t2, pGroundGFE); /* r[1] = a[1]*b[0] + a[0]*b[1] - a[2]*b[2]*beta */
151 }
152 }
153
154 addF(pR2, u2, t1, pGroundGFE); /* r[2] = a[2]*b[0] + a[1]*b[1] + a[0]*b[2] */
155
156 cpGFpReleasePool(6, pGroundGFE);
157 return pR;
158 }
159
160 /*
161 // Intel(R) EPID 2.0 specific
162 // ~~~~~~~~~~~~~~~
163 //
164 // Squaring over GF((p^2)^3)
165 // - field polynomial: g(v) = v^3 - xi => binominal with specific value of "xi"
166 // - xi = x+2
167 */
cpGFpxSqr_p3_binom_epid2(BNU_CHUNK_T * pR,const BNU_CHUNK_T * pA,gsEngine * pGFEx)168 static BNU_CHUNK_T* cpGFpxSqr_p3_binom_epid2(BNU_CHUNK_T* pR, const BNU_CHUNK_T* pA, gsEngine* pGFEx)
169 {
170 gsEngine* pGroundGFE = GFP_PARENT(pGFEx);
171 int groundElemLen = GFP_FELEN(pGroundGFE);
172
173 mod_mul mulF = GFP_METHOD(pGroundGFE)->mul;
174 mod_sqr sqrF = GFP_METHOD(pGroundGFE)->sqr;
175 mod_add addF = GFP_METHOD(pGroundGFE)->add;
176 mod_sub subF = GFP_METHOD(pGroundGFE)->sub;
177
178 const BNU_CHUNK_T* pA0 = pA;
179 const BNU_CHUNK_T* pA1 = pA+groundElemLen;
180 const BNU_CHUNK_T* pA2 = pA+groundElemLen*2;
181
182 BNU_CHUNK_T* pR0 = pR;
183 BNU_CHUNK_T* pR1 = pR+groundElemLen;
184 BNU_CHUNK_T* pR2 = pR+groundElemLen*2;
185
186 BNU_CHUNK_T* s0 = cpGFpGetPool(5, pGroundGFE);
187 BNU_CHUNK_T* s1 = s0+groundElemLen;
188 BNU_CHUNK_T* s2 = s1+groundElemLen;
189 BNU_CHUNK_T* s3 = s2+groundElemLen;
190 BNU_CHUNK_T* s4 = s3+groundElemLen;
191
192 addF(s2, pA0, pA2, pGroundGFE);
193 subF(s2, s2, pA1, pGroundGFE);
194 sqrF(s2, s2, pGroundGFE);
195 sqrF(s0, pA0, pGroundGFE);
196 sqrF(s4, pA2, pGroundGFE);
197 mulF(s1, pA0, pA1, pGroundGFE);
198 mulF(s3, pA1, pA2, pGroundGFE);
199 addF(s1, s1, s1, pGroundGFE);
200 addF(s3, s3, s3, pGroundGFE);
201
202 addF(pR2, s1, s2, pGroundGFE);
203 addF(pR2, pR2, s3, pGroundGFE);
204 subF(pR2, pR2, s0, pGroundGFE);
205 subF(pR2, pR2, s4, pGroundGFE);
206
207 /* Intel(R) EPID 2.0 specific */
208 {
209 int basicExtDegree = cpGFpBasicDegreeExtension(pGFEx);
210
211 /* deal with GF(p^2^3) */
212 if(basicExtDegree==6) {
213 cpFq2Mul_xi(s4, s4, pGroundGFE);
214 cpFq2Mul_xi(s3, s3, pGroundGFE);
215 addF(pR1, s1, s4, pGroundGFE);
216 addF(pR0, s0, s3, pGroundGFE);
217 }
218 /* just a case */
219 else {
220 cpGFpxMul_G0(s4, s4, pGFEx);
221 cpGFpxMul_G0(s3, s3, pGFEx);
222 subF(pR1, s1, s4, pGroundGFE);
223 subF(pR0, s0, s3, pGroundGFE);
224 }
225 }
226
227 cpGFpReleasePool(5, pGroundGFE);
228 return pR;
229 }
230
231 /*
232 // return specific polynomi alarith methods
233 // polynomial - deg 3 binomial (Intel(R) EPID 2.0)
234 */
gsPolyArith_binom3_epid2(void)235 static gsModMethod* gsPolyArith_binom3_epid2(void)
236 {
237 static gsModMethod m = {
238 cpGFpxEncode_com,
239 cpGFpxDecode_com,
240 cpGFpxMul_p3_binom_epid2,
241 cpGFpxSqr_p3_binom_epid2,
242 NULL,
243 cpGFpxAdd_com,
244 cpGFpxSub_com,
245 cpGFpxNeg_com,
246 cpGFpxDiv2_com,
247 cpGFpxMul2_com,
248 cpGFpxMul3_com,
249 //cpGFpxInv
250 };
251 return &m;
252 }
253
254 /*F*
255 // Name: ippsGFpxMethod_binom3_epid2
256 //
257 // Purpose: Returns a reference to the implementation of arithmetic operations over GF(pd).
258 //
259 // Returns: pointer to a structure containing
260 // an implementation of arithmetic operations over GF(pd)
261 // g(v) = v^3 - U0, U0 from GF(q^2), U0 = u + 2
262 //
263 //
264 *F*/
265
266 IPPFUN( const IppsGFpMethod*, ippsGFpxMethod_binom3_epid2, (void) )
267 {
268 static IppsGFpMethod method = {
269 cpID_Binom3_epid20,
270 3,
271 NULL,
272 NULL
273 };
274 method.arith = gsPolyArith_binom3_epid2();
275 return &method;
276 }
277