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mce_qd: fixup to working state

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This commit is contained in:
Mirek Kratochvil 2012-11-05 22:14:48 +01:00
parent 6d5b4c1feb
commit 736fd10e05
4 changed files with 180 additions and 141 deletions
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15
include/codecrypt.h
View file

@ -31,6 +31,9 @@ typedef unsigned int uint;
/*
* vector over GF(2). We rely on STL's vector<bool> == bit_vector
* specialization for space efficiency.
*
* TODO. This is great, but some operations (ESPECIALLY add()) could be done
* blockwise for speed. Investigate/implement that.
*/
class polynomial;
class gf2m;
@ -136,6 +139,7 @@ public:
void generate_random (uint n, prng&);
//TODO permute_inv is easy, do it everywhere
template<class A, class R> void permute (const A&a, R&r) const {
r.resize (a.size() );
for (uint i = 0; i < size(); ++i) r[item (i) ] = a[i];
@ -216,6 +220,7 @@ public:
uint eval (uint, gf2m&) const;
uint head() {
int t;
if ( (t = degree() ) >= 0) return item (t);
else return 0;
}
@ -387,7 +392,7 @@ public:
gf2m fld; //we fix q=2^fld.m=fld.n, n=q/2
uint T; //the QD's t parameter is 2^T.
permutation block_perm; //order of blocks
//TODO this is derivable from hperm.
//TODO block_count is (easily) derivable from hperm.
uint block_count; //blocks >= block_count are shortened-out
permutation hperm; //block permutation of H block used to get G
std::vector<uint> block_perms; //dyadic permutations of blocks
@ -395,10 +400,10 @@ public:
//derivable stuff
std::vector<uint> Hsig; //signature of canonical H matrix
std::vector<uint> support; //computed goppa support
polynomial g; //computed goppa polynomial
std::vector<polynomial> sqInv;
//blocks of signature lines of pre-permuted check matrix
std::vector<std::vector<bvector> > Hc;
uint omega;
//cols of check matrix of g^2(x)
std::vector<polynomial> Hc;
//pre-permuted positions of support rows
std::vector<uint> support_pos;

2
lib/mce.cpp
View file

@ -70,7 +70,7 @@ int privkey::decrypt (const bvector&in, bvector&out)
Pinv.permute (in, not_permuted);
//prepare for decoding
permutation hpermInv;
permutation hpermInv; //TODO pre-invert it in prepare()
hperm.compute_inversion (hpermInv);
bvector canonical, syndrome;

220
lib/mce_qd.cpp
View file

@ -38,13 +38,12 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
priv.T = T;
uint t = 1 << T;
std::cout << "generate" << std::endl;
//convenience
gf2m&fld = priv.fld;
std::vector<uint>&Hsig = priv.Hsig;
std::vector<uint>&essence = priv.essence;
std::vector<uint>&support = priv.support;
polynomial&g = priv.g;
polynomial g;
//prepare for data
Hsig.resize (fld.n / 2);
@ -58,7 +57,6 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
std::set<uint> used;
used.clear();
std::cout << "attempt..." << std::endl;
//first off, compute the H signature
Hsig[0] = choose_random (fld.n, rng, used);
@ -88,27 +86,28 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
}
}
//from now on, we fix 'omega' from the paper to zero.
std::cout << "goppa..." << std::endl;
//assemble goppa polynomial.
used.clear();
g.clear();
g.resize (1, 1); //g(x)=1 so we can multiply it
polynomial tmp;
tmp.resize (2, 1); //tmp(x)=x-1
bool consistent = true;
for (uint i = 0; i < t; ++i) {
//tmp(x)=x-z=x-(1/h_i)
tmp[0] = fld.inv (Hsig[i]);
if (used.count (tmp[0]) ) {
consistent = false;
break;
}
used.insert (tmp[0]);
g.mult (tmp, fld);
std::cout << "computing g... " << g;
}
if (!consistent) continue; //retry
std::cout << "Goppa poly " << g;
std::cout << "support..." << std::endl;
//compute the support, retry if it has two equal elements.
used.clear();
bool consistent = true;
for (uint i = 0; i < fld.n / 2; ++i) {
support[i] = fld.add (
fld.inv (Hsig[i]),
@ -119,19 +118,17 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
break;
}
//as we are having z's in used, this is not necessary.
//TODO verify, then TODO maybe delete.
if (g.eval (support[i], fld) == 0) {
std::cout << "support zero!" << std::endl;
consistent = false;
break;
}
std::cout << "support at " << i << ": " << support[i] << std::endl;
used.insert (support[i]);
}
if (!consistent) continue; //retry
std::cout << "blocks..." << std::endl;
//now the blocks.
uint block_size = 1 << T,
h_block_count = (fld.n / 2) / block_size;
@ -147,16 +144,13 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
bl[i][j] = Hsig[i * block_size + j];
}
std::cout << "permuting blocks..." << std::endl;
//permute them
priv.block_perm.generate_random (h_block_count, rng);
priv.block_perm.permute (bl, blp);
std::cout << "discarding blocks..." << std::endl;
//discard blocks
blp.resize (block_count);
std::cout << "permuting dyadic blocks..." << std::endl;
//permute individual blocks
priv.block_perms.resize (block_count);
bl.resize (blp.size() );
@ -169,7 +163,6 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
//try several permutations to construct G
uint attempts = 0;
for (attempts = 0; attempts < block_count; ++attempts) {
std::cout << "generating G..." << std::endl;
/*
* try computing the redundancy block of G
@ -207,12 +200,15 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
*/
priv.hperm.generate_random (block_count, rng);
permutation hpermInv;
priv.hperm.compute_inversion (hpermInv);
std::vector<std::vector<bvector> > hblocks;
bvector tmp;
bool failed;
uint i, j, k, l;
//prepare blocks of h
hblocks.resize (block_count);
for (i = 0; i < block_count; ++i)
@ -220,14 +216,14 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
//fill them from Hsig
for (i = 0; i < block_count; ++i) {
tmp.from_poly_cotrace (bl[priv.hperm[i]], fld);
tmp.from_poly_cotrace (bl[hpermInv[i]], fld);
for (j = 0; j < fld.m; ++j)
tmp.get_block (j * block_size,
block_size,
hblocks[i][j]);
}
/* now do a modified gaussian elimination on hblocks */
/* do a modified QD-blockwise gaussian elimination on hblocks */
failed = false;
tmp.resize (block_size);
for (i = 0; i < fld.m; ++i) { //gauss step
@ -247,9 +243,8 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
//now normalize the row
for (j = i; j < fld.m; ++j) {
uint l = hblocks
[block_count - fld.m + i]
[j].hamming_weight();
l = hblocks [block_count - fld.m + i]
[j].hamming_weight();
if (l == 0) continue; //zero is just okay :]
if (! (l % 2) ) //singular, make it regular by adding the i-th row
for (k = 0;
@ -258,13 +253,21 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
hblocks[k][j].add
(hblocks[k][i]);
//now a matrix is regular, we can easily make it I
//now a matrix is regular, we can easily make it I.
//first, multiply the row
for (k = 0; k < block_count; ++k) {
//don't overwrite the matrix we're counting with
if (k == block_count - fld.m + i) continue;
fwht_dyadic_multiply
(hblocks[block_count - fld.m + i][j],
hblocks[k][j], tmp);
hblocks[k][j] = tmp;
}
//change the block on the diagonal
fwht_dyadic_multiply
(hblocks[block_count - fld.m + i][j],
hblocks[block_count - fld.m + i][j], tmp);
hblocks[block_count - fld.m + i][j] = tmp;
//and zero the column below diagonal
if (j > i) for (k = 0; k < block_count; ++k)
@ -276,8 +279,9 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
if (failed) continue;
for (i = 0; i < fld.m; ++i) { //jordan step
//normalize diagonal (it's already nonsingular)
for (k = 0; k < block_count; ++k) {
//normalize diagonal
for (k = 0; k < block_count - i; ++k) {
//we can safely rewrite the diagonal here (nothing's behind it)
fwht_dyadic_multiply
(hblocks[block_count - i - 1][fld.m - i - 1],
hblocks[k][fld.m - i - 1], tmp);
@ -294,7 +298,8 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
hblocks[k][fld.m - j - 1].add
(hblocks[k][fld.m - i - 1]);
}
for (k = 0; k < block_count; ++k) {
for (k = 0; k < block_count - i; ++k) {
//overwrite is also safe here
fwht_dyadic_multiply
(hblocks[block_count - i - 1]
[fld.m - j - 1],
@ -308,8 +313,6 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
}
}
if (failed) continue;
pub.qd_sigs.resize (block_count - fld.m);
for (uint i = 0; i < block_count - fld.m; ++i) {
pub.qd_sigs[i].resize (block_size * fld.m);
@ -334,7 +337,6 @@ int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
int privkey::prepare()
{
uint s, i, j;
std::cout << "prepare" << std::endl;
//compute H signature from essence
Hsig.resize (fld.n / 2);
Hsig[0] = fld.inv (essence[fld.m - 1]);
@ -353,93 +355,104 @@ int privkey::prepare()
) ) );
}
//compute the support
//goppa polynomial with omega=0
std::set<uint> used;
used.clear();
polynomial g, tmp;
g.clear();
g.resize (1, 1); //g(x)=1
tmp.clear();
tmp.resize (2, 1); //tmp(x)=x+1
for (i = 0; i < (1 << T); ++i) {
tmp[0] = fld.inv (Hsig[i]); //tmp(x)=x+1/h_i
if (used.count (tmp[0]) )
return 1;
used.insert (tmp[0]);
g.mult (tmp, fld);
}
//compute the support with omega=0
support.resize (fld.n / 2);
std::set<uint> used_support;
for (i = 0; i < fld.n / 2; ++i) {
support[i] = fld.add
(fld.inv (Hsig[i]),
essence[fld.m - 1]);
//support consistency check
if (used_support.count (support[i]) )
if (used.count (support[i]) )
return 1;
used_support.insert (support[i]);
used.insert (support[i]);
}
//prepare permuted Hsig (so that it can be applied directly)
//and prepare reverse support position lookup data
//choose omega
omega = fld.n;
for (i = 0; i < fld.n; ++i)
if (!used.count (i) ) {
omega = i;
break;
}
if (omega == fld.n) return 1;
//modify support to omega-ized version
for (i = 0; i < support.size(); ++i)
support[i] = fld.add (support[i], omega);
//modify g to omega-ized version
g.clear();
tmp.clear();
g.resize (1, 1); //g(x)=1
tmp.resize (2, 1); //tmp(x)=x+1
for (i = 0; i < (1 << T); ++i) {
tmp[0] = fld.add (fld.inv (Hsig[i]), omega);
g.mult (tmp, fld);
}
// prepare permuted support, from that prepare permuted check matrix
// (so that it can be applied directly)
uint block_size = 1 << T;
uint pos, blk_perm;
polynomial tmp_blk, tmp_pblk;
bvector cotrace, tmp_block;
std::vector<uint> sbl1, sbl2, permuted_support;
tmp_blk.resize (block_size);
tmp_pblk.resize (block_size);
Hc.resize (fld.m);
for (i = 0; i < fld.m; ++i) {
Hc[i].resize (block_count);
}
permuted_support.resize (block_size * block_count);
sbl1.resize (block_size);
sbl2.resize (block_size);
permuted_support.resize (block_size * block_count);
//go through all the blocks of original H and convert them if they
//aren't discarded.
//permute support
for (i = 0; i < (fld.n / 2) / block_size; ++i) {
pos = block_perm[i];
if (pos >= block_count) continue; //was discarded
blk_perm = block_perms[pos];
pos = hperm[pos];
//permute i-th block of H to pos-th block of Hc,
//also move the support.
for (j = 0; j < block_size; ++j) {
tmp_blk[j] = Hsig[j + i * block_size];
//permute i-th block of support
for (j = 0; j < block_size; ++j)
sbl1[j] = support[j + i * block_size];
}
permutation::permute_dyadic (blk_perm, tmp_blk, tmp_pblk);
permutation::permute_dyadic (blk_perm, sbl1, sbl2);
//store support to permuted support
for (j = 0; j < block_size; ++j)
permuted_support[j + pos * block_size] = sbl2[j];
//cotrace permuted H block to Hc
cotrace.from_poly_cotrace (tmp_pblk, fld);
for (j = 0; j < fld.m; ++j)
cotrace.get_block (j * block_size, block_size, Hc[j][pos]);
}
//convert the support result to actual lookup
//prepare Hc
Hc.resize (block_size * block_count);
for (i = 0; i < block_size * block_count; ++i) {
Hc[i].resize (block_size * 2);
Hc[i][0] = fld.inv (g.eval (permuted_support[i], fld) );
Hc[i][0] = fld.mult (Hc[i][0], Hc[i][0]);
for (j = 1; j < 2 * block_size; ++j)
Hc[i][j] = fld.mult (permuted_support[i],
Hc[i][j - 1]);
}
//convert the permuted support to actual lookup
support_pos.clear();
//fld.n in support lookup means that it isn't there (we don't have -1)
support_pos.resize (fld.n, fld.n);
for (i = 0; i < block_size * block_count; ++i)
support_pos[permuted_support[i]] = i;
for (i = 0; i < support_pos.size(); ++i) {
std::cout << "support " << i << " has position " << support_pos[i] << std::endl;
}
//goppa polynomial
g.clear();
g.resize (1, 1);
polynomial tmp;
tmp.resize (2, 1);
uint t = 1 << T;
for (i = 0; i < t; ++i) {
tmp[0] = fld.inv (Hsig[i]);
g.mult (tmp, fld);
}
//sqInv
g.compute_square_root_matrix (sqInv, fld);
return 0;
}
@ -475,9 +488,7 @@ int pubkey::encrypt (const bvector & in, bvector & out, prng & rng)
//block result
fwht_dyadic_multiply (p, g, r);
//std::cout << "DYADIC MULTIPLY: " << p << g << r << "---" << std::endl;
cksum.add_offset (r, t * j);
//std::cout << "CKSUM NOW: " << cksum;
}
}
@ -503,29 +514,17 @@ int pubkey::encrypt (const bvector & in, bvector & out, prng & rng)
int privkey::decrypt (const bvector & in, bvector & out)
{
if (in.size() != cipher_size() ) return 2;
polynomial synd;
uint i;
//multiply line-by-line block-by-block by H
uint block_size = 1 << T;
bvector synd_vec;
bvector hp, cp, res;
uint i, j, k;
synd_vec.resize (block_size * fld.m);
cp.resize (block_size);
res.resize (block_size);
for (i = 0; i < block_count; ++i) {
in.get_block (i * block_size, block_size, cp);
for (j = 0; j < fld.m; ++j) {
fwht_dyadic_multiply (Hc[j][i], cp, res);
synd_vec.add_offset (res, j * block_size);
}
}
synd.clear();
for (i = 0; i < cipher_size(); ++i)
if (in[i]) synd.add (Hc[i], fld);
//decoding
polynomial synd, loc;
synd_vec.to_poly_cotrace (synd, fld);
compute_error_locator (synd, fld, g, sqInv, loc);
polynomial loc;
//compute_alternant_error_locator (synd, fld, g, loc);
compute_alternant_error_locator (synd, fld, 1 << T, loc);
bvector ev;
if (!evaluate_error_locator_trace (loc, ev, fld) )
@ -536,9 +535,14 @@ int privkey::decrypt (const bvector & in, bvector & out)
out.resize (plain_size() );
//flip error positions of out.
for (i = 0; i < ev.size(); ++i) if (ev[i]) {
if (support_pos[i] == fld.n) return 1; //couldn't decode TODO is it true?
if (i < plain_size() )
out[i] = !out[i];
uint epos = support_pos[fld.inv (i)];
if (epos == fld.n) {
//found unexpected support, die.
out.clear();
return 1;
}
if (epos < plain_size() )
out[epos] = !out[epos];
}
return 0;

84
src/main.cpp
View file

@ -26,52 +26,82 @@ int main()
ccr::mce_qd::privkey priv;
ccr::mce_qd::pubkey pub;
ccr::mce_qd::generate (pub, priv, r, 5, 1, 1);
priv.prepare();
ccr::mce_qd::generate (pub, priv, r, 11, 5, 2);
cout << "cipher size: " << priv.cipher_size() << ' ' << pub.cipher_size() << endl;
cout << "plain size: " << priv.plain_size() << ' ' << pub.plain_size() << endl;
priv.prepare();
ccr::bvector plain;
plain.resize (pub.plain_size(), 0);
plain[0] = 1;
plain[1] = 1;
plain[2] = 1;
//plain[1] = 1;
//plain[2] = 1;
cout << "PLAINTEXT" << endl;
cout << plain;
ccr::bvector cipher;
//pub.encrypt (plain, cipher, r);
pub.encrypt (plain, cipher, r, 10);
pub.encrypt (plain, cipher, r);
cout << "CIPHERTEXT" << endl;
cout << cipher;
ccr::bvector result;
priv.decrypt (cipher, result);
ccr::bvector decrypted;
priv.decrypt (cipher, decrypted);
cout << "DECRYPTED" << endl;
cout << result;
#endif
cout << decrypted;
/* signature test */
ccr::bvector hash, signature;
hash.resize (priv.hash_size(), 0);
hash[0] = 1;
hash[1] = 1;
hash[2] = 1;
cout << "SIGNING" << endl << hash;
priv.sign (hash, signature, 2, priv.hash_size() *priv.hash_size(), r);
cout << "SIGNATURE" << endl << signature;
if (pub.verify (signature, hash, 2) )
cout << "VERIFY FAIL" << endl;
else cout << "VERIFY OK" << endl;
return 0;
}
#if 0
cout << "PUBLIC KEY" << endl;
cout << pub.t << endl;
cout << pub.G;
/* mce encryption test */
ccr::bvector plain;
plain.resize (pub.plain_size(), 0);
plain[0] = 1;
plain[1] = 1;
plain[2] = 1;
cout << "PLAINTEXT" << endl;
cout << plain;
ccr::bvector cipher;
//pub.encrypt (plain, cipher, r);
pub.encrypt (plain, cipher, r, 10);
cout << "CIPHERTEXT" << endl;
cout << cipher;
ccr::bvector result;
priv.decrypt (cipher, result);
cout << "DECRYPTED" << endl;
cout << result;
/* signature test */
ccr::bvector hash, signature;
hash.resize (priv.hash_size(), 0);
hash[0] = 1;
hash[1] = 1;
hash[2] = 1;
cout << "SIGNING" << endl << hash;
priv.sign (hash, signature, 2, priv.hash_size() *priv.hash_size(), r);
cout << "SIGNATURE" << endl << signature;
if (pub.verify (signature, hash, 2) )
cout << "VERIFY FAIL" << endl;
else cout << "VERIFY OK" << endl;
return 0;
}
#endif