static Matrix_t *makekernel(const Poly_t *pol)
{
Matrix_t *materg;
PTR rowptr;
FEL *xbuf, *pbuf = pol->Data;
long pdeg = pol->Degree;
int k, xshift;
long fl = pol->Field;
materg = MatAlloc(fl,pdeg,pdeg);
rowptr = materg->Data;
xbuf = NALLOC(FEL,pdeg+1);
for (k = 0; k <= pdeg; ++k)
xbuf[k] = FF_ZERO;
xbuf[0] = FF_ONE;
for (k = 0; k < pdeg; ++k)
{
int l;
for (l = 0; l < pdeg; ++l)
FfInsert(rowptr,l,xbuf[l]);
FfInsert(rowptr,k,FfSub(xbuf[k],FF_ONE));
FfStepPtr(&rowptr);
for (xshift = (int) fl; xshift > 0; )
{
FEL f;
int d;
/* Find leading pos */
for (l = pdeg-1; xbuf[l] == FF_ZERO && l >= 0; --l);
/* Shift left as much as possible */
if ((d = pdeg - l) > xshift) d = xshift;
for (; l >= 0; l--) xbuf[l+d] = xbuf[l];
for (l = d-1; l >= 0; --l) xbuf[l] = FF_ZERO;
xshift -= d;
if (xbuf[pdeg] == FF_ZERO) continue;
/* Reduce with pol */
f = FfNeg(FfDiv(xbuf[pdeg],pbuf[pdeg]));
for (l = pdeg-1; l >= 0; --l)
xbuf[l] = FfAdd(xbuf[l],FfMul(pbuf[l],f));
xbuf[pdeg] = FF_ZERO;
}
}
SysFree(xbuf);
return MatNullSpace__(materg);
}
static void TestScalarProduct1(PTR a, PTR b, int size)
{
int count;
for (count = 0; count < 10; ++count) {
int i;
FEL expected = FF_ZERO;
FfMulRow(a,FF_ZERO);
FfMulRow(b,FF_ZERO);
for (i = 0; i < size; ++i) {
FEL f1 = FTab[MtxRandomInt(FfOrder)];
FEL f2 = FTab[MtxRandomInt(FfOrder)];
FfInsert(a,i,f1);
FfInsert(b,i,f2);
expected = FfAdd(expected,FfMul(f1,f2));
}
ASSERT_EQ_INT(FfScalarProduct(a,b), expected);
}
}
void FfAddMulRow(PTR row1, PTR row2, FEL f)
{ register long i;
register FEL *p1, *p2;
CHECKFEL(f);
if (f == FF_ZERO) return;
if (f == FF_ONE)
{ FfAddRow(row1,row2);
return;
}
p1 = row1;
p2 = row2;
for (i = FfNoc; i != 0; --i)
{ *p1 = FfAdd(*p1,FfMul(*p2,f));
++p1;
++p2;
}
}
EpidStatus EpidSignBasic(MemberCtx const* ctx, void const* msg, size_t msg_len,
void const* basename, size_t basename_len,
BasicSignature* sig, BigNumStr* rnd_bsn) {
EpidStatus sts = kEpidErr;
EcPoint* B = NULL;
EcPoint* t = NULL; // temp value in G1
EcPoint* k = NULL;
EcPoint* e = NULL;
FfElement* R2 = NULL;
FfElement* p2y = NULL;
FfElement* t1 = NULL;
FfElement* t2 = NULL;
FfElement* a = NULL;
FfElement* b = NULL;
FfElement* rx = NULL;
FfElement* ra = NULL;
FfElement* rb = NULL;
struct p2x_t {
uint32_t i;
uint8_t bsn[1];
}* p2x = NULL;
FfElement* t3 = NULL; // temporary for multiplication
FfElement* c = NULL;
uint8_t* digest = NULL;
PreComputedSignature curr_presig = {0};
if (!ctx || !sig) {
return kEpidBadArgErr;
}
if (!msg && (0 != msg_len)) {
// if message is non-empty it must have both length and content
return kEpidBadArgErr;
}
if (!basename && (0 != basename_len)) {
// if basename is non-empty it must have both length and content
return kEpidBadArgErr;
}
if (!ctx->epid2_params) {
return kEpidBadArgErr;
}
do {
FiniteField* Fp = ctx->epid2_params->Fp;
SignCommitOutput commit_out = {0};
FpElemStr c_str = {0};
EcGroup* G1 = ctx->epid2_params->G1;
FiniteField* GT = ctx->epid2_params->GT;
FiniteField* Fq = ctx->epid2_params->Fq;
PairingState* ps_ctx = ctx->epid2_params->pairing_state;
const BigNumStr kOne = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1};
BigNumStr t1_str = {0};
BigNumStr t2_str = {0};
size_t digest_size = 0;
uint16_t* rf_ctr = (uint16_t*)&ctx->rf_ctr;
FfElement const* x = ctx->x;
if (basename) {
if (!IsBasenameAllowed(ctx->allowed_basenames, basename, basename_len)) {
sts = kEpidBadArgErr;
BREAK_ON_EPID_ERROR(sts);
}
}
sts = NewEcPoint(G1, &B);
BREAK_ON_EPID_ERROR(sts);
sts = NewEcPoint(G1, &k);
BREAK_ON_EPID_ERROR(sts);
sts = NewEcPoint(G1, &t);
BREAK_ON_EPID_ERROR(sts);
sts = NewEcPoint(G1, &e);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(GT, &R2);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fq, &p2y);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &t1);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &t2);
BREAK_ON_EPID_ERROR(sts);
p2x = (struct p2x_t*)SAFE_ALLOC(sizeof(struct p2x_t) + basename_len - 1);
if (!p2x) {
sts = kEpidMemAllocErr;
break;
}
sts = NewFfElement(Fp, &a);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &b);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &rx);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &ra);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &rb);
BREAK_ON_EPID_ERROR(sts);
sts = MemberGetPreSig((MemberCtx*)ctx, &curr_presig);
BREAK_ON_EPID_ERROR(sts);
// 3. If the pre-computed signature pre-sigma exists, the member
// loads (B, K, T, a, b, rx, rf, ra, rb, R1, R2) from
// pre-sigma. Refer to Section 4.4 for the computation of
// these values.
sts = ReadFfElement(Fp, &curr_presig.a, sizeof(curr_presig.a), a);
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(Fp, &curr_presig.b, sizeof(curr_presig.b), b);
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(Fp, &curr_presig.rx, sizeof(curr_presig.rx), rx);
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(Fp, &curr_presig.ra, sizeof(curr_presig.ra), ra);
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(Fp, &curr_presig.rb, sizeof(curr_presig.rb), rb);
BREAK_ON_EPID_ERROR(sts);
// If the basename is provided, use it, otherwise use presig B
if (basename) {
// 3.a. The member computes (B, i2, y2) = G1.tpmHash(bsn).
sts = EcHash(G1, basename, basename_len, ctx->hash_alg, B, &p2x->i);
BREAK_ON_EPID_ERROR(sts);
p2x->i = htonl(p2x->i);
sts = WriteEcPoint(G1, B, &commit_out.B, sizeof(commit_out.B));
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(Fq, &commit_out.B.y, sizeof(commit_out.B.y), p2y);
BREAK_ON_EPID_ERROR(sts);
// b.i. (KTPM, LTPM, ETPM, counterTPM) = TPM2_Commit(P1=h1,(s2, y2) = (i2
// || bsn, y2)).
// b.ii.K = KTPM.
if (0 !=
memcpy_S((void*)p2x->bsn, basename_len, basename, basename_len)) {
sts = kEpidBadArgErr;
break;
}
sts =
Tpm2Commit(ctx->tpm2_ctx, ctx->h1, p2x, sizeof(p2x->i) + basename_len,
p2y, k, t, e, (uint16_t*)&ctx->rf_ctr);
BREAK_ON_EPID_ERROR(sts);
sts = WriteEcPoint(G1, k, &commit_out.K, sizeof(commit_out.K));
BREAK_ON_EPID_ERROR(sts);
// c.i. The member computes R1 = LTPM.
sts = WriteEcPoint(G1, t, &commit_out.R1, sizeof(commit_out.R1));
BREAK_ON_EPID_ERROR(sts);
// c.ii. e12rf = pairing(ETPM, g2)
sts = Pairing(ps_ctx, e, ctx->epid2_params->g2, R2);
BREAK_ON_EPID_ERROR(sts);
// c.iii. R2 = GT.sscmMultiExp(ea2, t1, e12rf, 1, e22, t2, e2w,ra).
// 4.i. The member computes t1 = (- rx) mod p.
sts = FfNeg(Fp, rx, t1);
BREAK_ON_EPID_ERROR(sts);
// 4.j. The member computes t2 = (rb - a * rx) mod p.
sts = FfMul(Fp, a, rx, t2);
BREAK_ON_EPID_ERROR(sts);
sts = FfNeg(Fp, t2, t2);
BREAK_ON_EPID_ERROR(sts);
sts = FfAdd(Fp, rb, t2, t2);
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(Fp, t1, &t1_str, sizeof(t1_str));
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(Fp, t2, &t2_str, sizeof(t2_str));
BREAK_ON_EPID_ERROR(sts);
{
FfElement const* points[4];
BigNumStr const* exponents[4];
points[0] = ctx->ea2;
points[1] = R2;
points[2] = ctx->e22;
points[3] = ctx->e2w;
exponents[0] = &t1_str;
exponents[1] = &kOne;
exponents[2] = &t2_str;
exponents[3] = (BigNumStr*)&curr_presig.ra;
sts = FfMultiExp(GT, points, exponents, COUNT_OF(points), R2);
BREAK_ON_EPID_ERROR(sts);
}
sts = WriteFfElement(GT, R2, &commit_out.R2, sizeof(commit_out.R2));
BREAK_ON_EPID_ERROR(sts);
// d. The member over-writes the counterTPM, B, K, R1 and R2 values.
} else {
if (!rnd_bsn) {
sts = kEpidBadArgErr;
break;
}
sts = ReadEcPoint(G1, &curr_presig.B, sizeof(curr_presig.B), B);
BREAK_ON_EPID_ERROR(sts);
commit_out.B = curr_presig.B;
commit_out.K = curr_presig.K;
commit_out.R1 = curr_presig.R1;
((MemberCtx*)ctx)->rf_ctr = curr_presig.rf_ctr;
commit_out.R2 = curr_presig.R2;
*rnd_bsn = curr_presig.rnd_bsn;
}
commit_out.T = curr_presig.T;
sts = HashSignCommitment(Fp, ctx->hash_alg, &ctx->pub_key, &commit_out, msg,
msg_len, &c_str);
BREAK_ON_EPID_ERROR(sts);
digest_size = EpidGetHashSize(ctx->hash_alg);
digest = (uint8_t*)SAFE_ALLOC(digest_size);
if (!digest) {
sts = kEpidNoMemErr;
break;
}
memcpy_S(digest + digest_size - sizeof(c_str), sizeof(c_str), &c_str,
sizeof(c_str));
sts = NewFfElement(Fp, &t3);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(Fp, &c);
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(Fp, &c_str, sizeof(c_str), c);
BREAK_ON_EPID_ERROR(sts);
// 7. The member computes sx = (rx + c * x) mod p.
sts = FfMul(Fp, c, x, t3);
BREAK_ON_EPID_ERROR(sts);
sts = FfAdd(Fp, rx, t3, t3);
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(Fp, t3, &sig->sx, sizeof(sig->sx));
BREAK_ON_EPID_ERROR(sts);
// 8. The member computes sf = (rf + c * f) mod p.
sts = Tpm2Sign(ctx->tpm2_ctx, digest, digest_size, *rf_ctr, NULL, t3);
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(Fp, t3, &sig->sf, sizeof(sig->sf));
BREAK_ON_EPID_ERROR(sts);
// 9. The member computes sa = (ra + c * a) mod p.
sts = FfMul(Fp, c, a, t3);
BREAK_ON_EPID_ERROR(sts);
sts = FfAdd(Fp, ra, t3, t3);
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(Fp, t3, &sig->sa, sizeof(sig->sa));
BREAK_ON_EPID_ERROR(sts);
// 10. The member computes sb = (rb + c * b) mod p.
sts = FfMul(Fp, c, b, t3);
BREAK_ON_EPID_ERROR(sts);
sts = FfAdd(Fp, rb, t3, t3);
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(Fp, t3, &sig->sb, sizeof(sig->sb));
BREAK_ON_EPID_ERROR(sts);
sig->B = commit_out.B;
sig->K = commit_out.K;
sig->T = commit_out.T;
sig->c = c_str;
sts = kEpidNoErr;
} while (0);
if (sts != kEpidNoErr) {
(void)Tpm2ReleaseCounter(ctx->tpm2_ctx, (uint16_t)ctx->rf_ctr);
(void)Tpm2ReleaseCounter(ctx->tpm2_ctx, curr_presig.rf_ctr);
} else if (basename) {
(void)Tpm2ReleaseCounter(ctx->tpm2_ctx, curr_presig.rf_ctr);
}
EpidZeroMemory(&curr_presig, sizeof(curr_presig));
DeleteEcPoint(&B);
DeleteEcPoint(&k);
DeleteEcPoint(&t);
DeleteEcPoint(&e);
DeleteFfElement(&R2);
DeleteFfElement(&p2y);
DeleteFfElement(&t1);
DeleteFfElement(&t2);
DeleteFfElement(&a);
DeleteFfElement(&b);
DeleteFfElement(&rx);
DeleteFfElement(&ra);
DeleteFfElement(&rb);
SAFE_FREE(p2x);
DeleteFfElement(&t3);
DeleteFfElement(&c);
SAFE_FREE(digest);
return sts;
}
static factor_t *factorsquarefree(const Poly_t *pol)
{
long int e,j,k,ltmp,tdeg,exp;
Poly_t *t0, *t, *w, *v;
FEL *tbuf, *t0buf;
factor_t *list;
int nfactors = 0;
/* Initialize variables
-------------------- */
FfSetField(pol->Field);
for (exp = 0, ltmp = FfOrder; ltmp % FfChar == 0; ++exp, ltmp /= FfChar);
t0 = PolDup(pol);
e = 1;
/* Allocate the list of factors. The can be at most <pol->Degree>
factors, but we need one extra entry to terminate the list.
----------------------------------------------------------- */
list = NALLOC(factor_t,pol->Degree + 1);
/* Main loop
--------- */
while (t0->Degree > 0)
{
Poly_t *der = PolDerive(PolDup(t0));
t = PolGcd(t0,der);
PolFree(der);
v = PolDivMod(t0,t);
PolFree(t0);
for (k = 0; v->Degree > 0; )
{
Poly_t *tmp;
if ( ++k % FfChar == 0 )
{
tmp = PolDivMod(t,v);
PolFree(t);
t = tmp;
k++;
}
w = PolGcd(t,v);
list[nfactors].p = PolDivMod(v,w);
list[nfactors].n = e * k;
if (list[nfactors].p->Degree > 0)
++nfactors; /* add to output */
else
PolFree(list[nfactors].p); /* discard const. */
PolFree(v);
v = w;
tmp = PolDivMod(t,v);
PolFree(t);
t = tmp;
}
PolFree(v);
/* shrink the polynomial */
tdeg = t->Degree;
e *= FfChar;
if ( tdeg % FfChar != 0 )
printf("error in t, degree not div. by prime \n");
t0 = PolAlloc(FfOrder,tdeg/FfChar);
t0buf = t0->Data;
tbuf = t->Data;
for (j = t0->Degree; j >= 0; --j)
{
FEL el, el1;
long lexp;
el = *tbuf;
tbuf += FfChar;
el1 = el;
/* this is a bug, it should apply the e-1 power of the
frobenius K. Lux 16th 11 1996 */
/* replace el1 by el1^(FfChar^(exp-1)) */
for ( lexp = 0; lexp < exp-1; lexp++ )
{
long n;
/* replace el1 by el1^FfChar */
el = el1;
for ( n = FfChar-1; 0 < n; n-- ) {
el1 = FfMul(el1,el);
}
}
*t0buf = el1;
++t0buf;
}
PolFree(t);
}
PolFree(t0);
/* Terminate the list
------------------ */
list[nfactors].p = NULL;
list[nfactors].n = 0;
return list;
}
EpidStatus EpidComputePreSig(MemberCtx const* ctx,
PreComputedSignature* precompsig) {
EpidStatus res = kEpidNotImpl;
EcPoint* B = NULL;
EcPoint* K = NULL;
EcPoint* T = NULL;
EcPoint* R1 = NULL;
FfElement* R2 = NULL;
FfElement* a = NULL;
FfElement* b = NULL;
FfElement* rx = NULL;
FfElement* rf = NULL;
FfElement* ra = NULL;
FfElement* rb = NULL;
FfElement* t1 = NULL;
FfElement* t2 = NULL;
FfElement* f = NULL;
if (!ctx || !precompsig) return kEpidBadArgErr;
if (!ctx->epid2_params || !ctx->pub_key || !ctx->priv_key)
return kEpidBadArgErr;
do {
// handy shorthands:
EcGroup* G1 = ctx->epid2_params->G1;
FiniteField* GT = ctx->epid2_params->GT;
FiniteField* Fp = ctx->epid2_params->Fp;
EcPoint* h2 = ctx->pub_key->h2;
EcPoint* A = ctx->priv_key->A;
FfElement* x = ctx->priv_key->x;
BigNumStr f_str = {0};
BigNumStr a_str = {0};
BigNumStr t1_str = {0};
BigNumStr rf_str = {0};
BigNumStr t2_str = {0};
BigNumStr ra_str = {0};
static const BigNumStr one = {
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}};
if (!G1 || !GT || !Fp || !h2 || !A || !x || !ctx->priv_key->f ||
!ctx->e12 || !ctx->e22 || !ctx->e2w || !ctx->ea2) {
res = kEpidBadArgErr;
BREAK_ON_EPID_ERROR(res);
}
f = ctx->priv_key->f;
// The following variables B, K, T, R1 (elements of G1), R2
// (elements of GT), a, b, rx, rf, ra, rb, t1, t2 (256-bit
// integers) are used.
res = NewEcPoint(G1, &B);
BREAK_ON_EPID_ERROR(res);
res = NewEcPoint(G1, &K);
BREAK_ON_EPID_ERROR(res);
res = NewEcPoint(G1, &T);
BREAK_ON_EPID_ERROR(res);
res = NewEcPoint(G1, &R1);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(GT, &R2);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &a);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &b);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &rx);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &rf);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &ra);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &rb);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &t1);
BREAK_ON_EPID_ERROR(res);
res = NewFfElement(Fp, &t2);
BREAK_ON_EPID_ERROR(res);
// 1. The member expects the pre-computation is done (e12, e22, e2w,
// ea2). Refer to Section 3.5 for the computation of these
// values.
// 2. The member verifies gid in public key matches gid in private
// key.
// 3. The member computes B = G1.getRandom().
res = EcGetRandom(G1, ctx->rnd_func, ctx->rnd_param, B);
BREAK_ON_EPID_ERROR(res);
// 4. The member computes K = G1.sscmExp(B, f).
res = WriteFfElement(Fp, f, &f_str, sizeof(f_str));
BREAK_ON_EPID_ERROR(res);
res = EcExp(G1, B, &f_str, K);
BREAK_ON_EPID_ERROR(res);
// 5. The member chooses randomly an integers a from [1, p-1].
res = FfGetRandom(Fp, &one, ctx->rnd_func, ctx->rnd_param, a);
BREAK_ON_EPID_ERROR(res);
// 6. The member computes T = G1.sscmExp(h2, a).
res = WriteFfElement(Fp, a, &a_str, sizeof(a_str));
BREAK_ON_EPID_ERROR(res);
res = EcExp(G1, h2, &a_str, T);
BREAK_ON_EPID_ERROR(res);
// 7. The member computes T = G1.mul(T, A).
res = EcMul(G1, T, A, T);
BREAK_ON_EPID_ERROR(res);
// 8. The member computes b = (a * x) mod p.
res = FfMul(Fp, a, x, b);
BREAK_ON_EPID_ERROR(res);
// 9. The member chooses rx, rf, ra, rb randomly from [1, p-1].
res = FfGetRandom(Fp, &one, ctx->rnd_func, ctx->rnd_param, rx);
BREAK_ON_EPID_ERROR(res);
res = FfGetRandom(Fp, &one, ctx->rnd_func, ctx->rnd_param, rf);
BREAK_ON_EPID_ERROR(res);
res = FfGetRandom(Fp, &one, ctx->rnd_func, ctx->rnd_param, ra);
BREAK_ON_EPID_ERROR(res);
res = FfGetRandom(Fp, &one, ctx->rnd_func, ctx->rnd_param, rb);
BREAK_ON_EPID_ERROR(res);
// 10. The member computes t1 = (- rx) mod p.
res = FfNeg(Fp, rx, t1);
BREAK_ON_EPID_ERROR(res);
// 11. The member computes t2 = (rb - a * rx) mod p.
res = FfMul(Fp, a, rx, t2);
BREAK_ON_EPID_ERROR(res);
res = FfNeg(Fp, t2, t2);
BREAK_ON_EPID_ERROR(res);
res = FfAdd(Fp, rb, t2, t2);
BREAK_ON_EPID_ERROR(res);
// 12. The member computes R1 = G1.sscmExp(B, rf).
res = WriteFfElement(Fp, rf, &rf_str, sizeof(rf_str));
BREAK_ON_EPID_ERROR(res);
res = EcExp(G1, B, &rf_str, R1);
BREAK_ON_EPID_ERROR(res);
// 13. The member computes R2 = GT.sscmMultiExp(ea2, t1, e12, rf,
// e22, t2, e2w, ra).
res = WriteFfElement(Fp, t1, &t1_str, sizeof(t1_str));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, t2, &t2_str, sizeof(t2_str));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, ra, &ra_str, sizeof(ra_str));
BREAK_ON_EPID_ERROR(res);
{
FfElement const* points[4];
BigNumStr const* exponents[4];
points[0] = ctx->ea2;
points[1] = ctx->e12;
points[2] = ctx->e22;
points[3] = ctx->e2w;
exponents[0] = &t1_str;
exponents[1] = &rf_str;
exponents[2] = &t2_str;
exponents[3] = &ra_str;
res = FfMultiExp(GT, points, exponents, COUNT_OF(points), R2);
BREAK_ON_EPID_ERROR(res);
}
// 14. The member sets and outputs pre-sigma = (B, K, T, a, b, rx,
// rf, ra, rb, R1, R2).
res = WriteEcPoint(G1, B, &precompsig->B, sizeof(precompsig->B));
BREAK_ON_EPID_ERROR(res);
res = WriteEcPoint(G1, K, &precompsig->K, sizeof(precompsig->K));
BREAK_ON_EPID_ERROR(res);
res = WriteEcPoint(G1, T, &precompsig->T, sizeof(precompsig->T));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, a, &precompsig->a, sizeof(precompsig->a));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, b, &precompsig->b, sizeof(precompsig->b));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, rx, &precompsig->rx, sizeof(precompsig->rx));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, rf, &precompsig->rf, sizeof(precompsig->rf));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, ra, &precompsig->ra, sizeof(precompsig->ra));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(Fp, rb, &precompsig->rb, sizeof(precompsig->rb));
BREAK_ON_EPID_ERROR(res);
res = WriteEcPoint(G1, R1, &precompsig->R1, sizeof(precompsig->R1));
BREAK_ON_EPID_ERROR(res);
res = WriteFfElement(GT, R2, &precompsig->R2, sizeof(precompsig->R2));
BREAK_ON_EPID_ERROR(res);
// 15. The member stores pre-sigma in the secure storage of the
// member.
res = kEpidNoErr;
} while (0);
f = NULL;
DeleteEcPoint(&B);
DeleteEcPoint(&K);
DeleteEcPoint(&T);
DeleteEcPoint(&R1);
DeleteFfElement(&R2);
DeleteFfElement(&a);
DeleteFfElement(&b);
DeleteFfElement(&rx);
DeleteFfElement(&rf);
DeleteFfElement(&ra);
DeleteFfElement(&rb);
DeleteFfElement(&t1);
DeleteFfElement(&t2);
return (res);
}
EpidStatus EpidRequestJoin(GroupPubKey const* pub_key, IssuerNonce const* ni,
FpElemStr const* f, BitSupplier rnd_func,
void* rnd_param, HashAlg hash_alg,
JoinRequest* join_request) {
EpidStatus sts;
static const BigNumStr one = {
{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}};
BigNumStr r_str;
JoinPCommitValues commit_values;
Epid2Params_* params = NULL;
FfElement* r_el = NULL;
FfElement* f_el = NULL;
FfElement* c_el = NULL;
FfElement* cf_el = NULL;
FfElement* s_el = NULL;
EcPoint* f_pt = NULL;
EcPoint* r_pt = NULL;
EcPoint* h1_pt = NULL;
if (!pub_key || !ni || !f || !rnd_func || !join_request) {
return kEpidBadArgErr;
}
if (kSha256 != hash_alg && kSha384 != hash_alg && kSha512 != hash_alg) {
return kEpidBadArgErr;
}
do {
sts = CreateEpid2Params(¶ms);
BREAK_ON_EPID_ERROR(sts);
if (!params->Fp || !params->G1) {
sts = kEpidBadArgErr;
break;
}
sts = NewFfElement(params->Fp, &r_el);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(params->Fp, &f_el);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(params->Fp, &c_el);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(params->Fp, &cf_el);
BREAK_ON_EPID_ERROR(sts);
sts = NewFfElement(params->Fp, &s_el);
BREAK_ON_EPID_ERROR(sts);
sts = NewEcPoint(params->G1, &f_pt);
BREAK_ON_EPID_ERROR(sts);
sts = NewEcPoint(params->G1, &h1_pt);
BREAK_ON_EPID_ERROR(sts);
sts = NewEcPoint(params->G1, &r_pt);
BREAK_ON_EPID_ERROR(sts);
sts = ReadFfElement(params->Fp, (uint8_t const*)f, sizeof(*f), f_el);
BREAK_ON_EPID_ERROR(sts);
sts = ReadEcPoint(params->G1, (uint8_t*)&pub_key->h1, sizeof(pub_key->h1),
h1_pt);
BREAK_ON_EPID_ERROR(sts);
// Step 1. The member chooses a random integer r from [1, p-1].
sts = FfGetRandom(params->Fp, &one, rnd_func, rnd_param, r_el);
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(params->Fp, r_el, (uint8_t*)&r_str, sizeof(r_str));
// Step 2. The member computes F = G1.sscmExp(h1, f).
sts = EcExp(params->G1, h1_pt, (BigNumStr const*)f, f_pt);
BREAK_ON_EPID_ERROR(sts);
// Step 3. The member computes R = G1.sscmExp(h1, r).
sts = EcExp(params->G1, h1_pt, (BigNumStr const*)&r_str, r_pt);
BREAK_ON_EPID_ERROR(sts);
// Step 4. The member computes c = Fp.hash(p || g1 || g2 || h1 || h2 || w ||
// F || R || NI). Refer to Section 7.1 for hash operation over a prime
// field.
sts = WriteBigNum(params->p, sizeof(commit_values.p),
(uint8_t*)&commit_values.p);
BREAK_ON_EPID_ERROR(sts);
sts = WriteEcPoint(params->G1, params->g1, (uint8_t*)&commit_values.g1,
sizeof(commit_values.g1));
BREAK_ON_EPID_ERROR(sts);
sts = WriteEcPoint(params->G2, params->g2, (uint8_t*)&commit_values.g2,
sizeof(commit_values.g2));
BREAK_ON_EPID_ERROR(sts);
commit_values.h1 = pub_key->h1;
commit_values.h2 = pub_key->h2;
commit_values.w = pub_key->w;
sts = WriteEcPoint(params->G1, f_pt, (uint8_t*)&commit_values.F,
sizeof(commit_values.F));
BREAK_ON_EPID_ERROR(sts);
sts = WriteEcPoint(params->G1, r_pt, (uint8_t*)&commit_values.R,
sizeof(commit_values.R));
BREAK_ON_EPID_ERROR(sts);
commit_values.NI = *ni;
sts = FfHash(params->Fp, (uint8_t*)&commit_values, sizeof(commit_values),
hash_alg, c_el);
BREAK_ON_EPID_ERROR(sts);
// Step 5. The member computes s = (r + c * f) mod p.
sts = FfMul(params->Fp, c_el, f_el, cf_el);
BREAK_ON_EPID_ERROR(sts);
sts = FfAdd(params->Fp, r_el, cf_el, s_el);
BREAK_ON_EPID_ERROR(sts);
// Step 6. The output join request is (F, c, s).
sts = WriteFfElement(params->Fp, c_el, (uint8_t*)&join_request->c,
sizeof(join_request->c));
BREAK_ON_EPID_ERROR(sts);
sts = WriteFfElement(params->Fp, s_el, (uint8_t*)&join_request->s,
sizeof(join_request->s));
BREAK_ON_EPID_ERROR(sts);
sts = WriteEcPoint(params->G1, f_pt, (uint8_t*)&join_request->F,
sizeof(join_request->F));
BREAK_ON_EPID_ERROR(sts);
sts = kEpidNoErr;
} while (0);
DeleteEcPoint(&h1_pt);
DeleteEcPoint(&r_pt);
DeleteEcPoint(&f_pt);
DeleteFfElement(&s_el);
DeleteFfElement(&cf_el);
DeleteFfElement(&c_el);
DeleteFfElement(&f_el);
DeleteFfElement(&r_el);
DeleteEpid2Params(¶ms);
return sts;
}
EpidStatus NewG2(Epid2Params const* param, BigNum* p, BigNum* q,
FiniteField* Fq, FiniteField* Fq2, EcGroup** G2) {
EpidStatus result = kEpidErr;
EcGroup* ec = NULL;
FfElement* a = NULL;
FfElement* b = NULL;
FfElement* fq_param_b = NULL;
FfElement* x = NULL;
FfElement* y = NULL;
BigNum* order = NULL;
BigNum* cofactor = NULL;
if (!param || !Fq || !Fq2 || !G2) {
return kEpidBadArgErr;
}
do {
// 2. Set xi = (xi0, xi1) an element of Fq2.
// 3. Let b', xi' be a temporary variable in Fq2.
// 4. Compute xi' = Fq2.inverse(xi).
// 5. Compute b' = Fq2.mul(xi', b).
result = NewFfElement(Fq2, &b);
if (kEpidNoErr != result) {
break;
}
result = ReadFfElement(Fq2, ¶m->xi, sizeof(param->xi), b);
if (kEpidNoErr != result) {
break;
}
result = FfInv(Fq2, b, b);
if (kEpidNoErr != result) {
break;
}
result = NewFfElement(Fq, &fq_param_b);
if (kEpidNoErr != result) {
break;
}
result = ReadFfElement(Fq, ¶m->b, sizeof(param->b), fq_param_b);
if (kEpidNoErr != result) {
break;
}
result = FfMul(Fq2, b, fq_param_b, b); // ??? overflow fq2*fq
if (kEpidNoErr != result) {
break;
}
// 6. Set g2.x = (g2.x[0], g2.x[1]) an element of Fq2.
// 7. Set g2.y = (g2.y[0], g2.y[1]) an element of Fq2.
result = NewFfElement(Fq2, &x);
if (kEpidNoErr != result) {
break;
}
result = ReadFfElement(Fq2, ¶m->g2.x, sizeof(param->g2.x), x);
if (kEpidNoErr != result) {
break;
}
result = NewFfElement(Fq2, &y);
if (kEpidNoErr != result) {
break;
}
result = ReadFfElement(Fq2, ¶m->g2.y, sizeof(param->g2.y), y);
if (kEpidNoErr != result) {
break;
}
// 8. set h = 2q - p, aka cofactor
result = NewBigNum(2 * sizeof(param->q), &cofactor);
if (kEpidNoErr != result) {
break;
}
result = BigNumAdd(q, q, cofactor);
if (kEpidNoErr != result) {
break;
}
result = BigNumSub(cofactor, p, cofactor);
if (kEpidNoErr != result) {
break;
}
// 9. set n = p * h, AKA order
result = NewBigNum(2 * sizeof(param->q), &order);
if (kEpidNoErr != result) {
break;
}
result = BigNumMul(p, cofactor, order);
if (kEpidNoErr != result) {
break;
}
// set a to identity, NewFfElement does it by default
result = NewFfElement(Fq2, &a);
if (kEpidNoErr != result) {
break;
}
// 10. Set G2 = E(Fq2).init(p, param(Fq2), n, h, 0, b', g2.x, g2.y)
result = NewEcGroup(Fq2, a, b, x, y, order, cofactor, &ec);
if (kEpidNoErr != result) {
break;
}
*G2 = ec;
result = kEpidNoErr;
} while (0);
DeleteBigNum(&cofactor);
DeleteBigNum(&order);
DeleteFfElement(&y);
DeleteFfElement(&x);
DeleteFfElement(&b);
DeleteFfElement(&a);
DeleteFfElement(&fq_param_b);
return result;
}
