581 lines
14 KiB
C++
581 lines
14 KiB
C++
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/*
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* This file is part of Codecrypt.
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*
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* Codecrypt is free software: you can redistribute it and/or modify it
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* under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or (at
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* your option) any later version.
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*
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* Codecrypt is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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* License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with Codecrypt. If not, see <http://www.gnu.org/licenses/>.
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*/
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#include "codecrypt.h"
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using namespace ccr;
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using namespace ccr::cfs_qd;
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#include "decoding.h"
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#include "qd_utils.h"
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#include <set>
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int cfs_qd::generate (pubkey&pub, privkey&priv, prng&rng,
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uint m, uint T, uint t, uint block_discard)
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{
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priv.fld.create (m);
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priv.T = T;
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uint block_size = 1 << T;
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if (t > block_size) return 2;
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priv.t = t;
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//convenience
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gf2m&fld = priv.fld;
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std::vector<uint>&essence = priv.essence;
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std::vector<uint> support, Hsig;
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polynomial g;
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uint i, j;
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//prepare for data
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Hsig.resize (fld.n);
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support.resize (fld.n);
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essence.resize (m + 1);
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//note that q=2^m, algo. n=q/2, log n = m-1
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//retry generating until goppa code is produced.
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for (;;) {
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std::cout << "attempt" << std::endl;
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std::set<uint> used;
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used.clear();
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//first off, compute the H signature
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Hsig[0] = choose_random (fld.n, rng, used);
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essence[m] = fld.inv (Hsig[0]);
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//essence[m] is now used as precomputed 1/h_0
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for (uint s = 0; s < m; ++s) {
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i = 1 << s; //i = 2^s
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Hsig[i] = choose_random (fld.n, rng, used);
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essence[s] = fld.add (essence[m], fld.inv (Hsig[i]) );
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used.insert (fld.inv (essence[s]) );
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for (j = 1; j < i; ++j) {
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uint hij = fld.inv
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(fld.add
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(fld.inv (Hsig[i]),
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fld.add (
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fld.inv (Hsig[j]),
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essence[m]
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) ) );
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if ( (!Hsig[i]) || (!Hsig[j]) ) hij = 0;
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Hsig[i + j] = hij;
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if (hij) {
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used.insert (Hsig[i + j]);
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/*used.insert (fld.inv
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(fld.add
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(fld.inv (Hsig[i + j]),
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essence[m]) ) );*/
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}
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}
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}
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std::cout << "Gen Hsig: ";
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for (i = 0; i < fld.n; ++i) std::cout << Hsig[i] << ' ';
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std::cout << std::endl;
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//let's play with blocks.
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uint block_size = 1 << T,
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h_block_count = fld.n / block_size,
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block_count = h_block_count - block_discard;
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//check if we have enough good blocks.
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std::vector<bool> block_status;
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uint badblocks;
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block_status.resize (h_block_count);
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badblocks = 0;
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for (i = 0; i < h_block_count; ++i) {
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block_status[i] = true;
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for (j = 0; j < block_size; ++j)
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if (!Hsig[i * block_size + j]) {
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block_status[i] = false;
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break;
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}
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if (!block_status[i]) ++badblocks;
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}
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std::cout << "badblocks: " << badblocks << std::endl;
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if (badblocks > block_discard) continue; //don't have enough good blocks
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if (!block_status[0]) continue; //cannot assemble goppa poly
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std::cout << "lol contd." << std::endl;
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//reconstruct g
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used.clear();
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g.clear();
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g.resize (1, 1); //g(x)=1 so we can multiply it
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polynomial tmp;
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tmp.resize (2, 1); //tmp(x)=x-1
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bool consistent = true;
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for (i = 0; i < t; ++i) {
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//tmp(x)=x-z=x-(1/h_i) where h_i is squared!
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tmp[0] = fld.inv (Hsig[i]);
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if (used.count (tmp[0]) ) {
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consistent = false;
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break;
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}
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used.insert (tmp[0]);
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g.mult (tmp, fld);
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}
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if (!consistent) continue; //retry
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std::cout << "lol have g: " << g;
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//compute the support, retry if it has two equal elements.
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for (i = 0; i < fld.n; ++i) {
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if (!block_status[i / block_size]) continue;
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support[i] = fld.add (
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fld.inv (Hsig[i]),
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essence[m]);
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std::cout << "support " << i << " = " << support[i] << std::endl;
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if (used.count (support[i]) ) {
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std::cout << "support inconsistent at " << i << std::endl;
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++badblocks;
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block_status[i / block_size] = false;
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break;
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}
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used.insert (support[i]);
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}
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std::cout << "bad: " << badblocks << std::endl;
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if (badblocks > block_discard) continue;
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//assemble blocks to bl
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std::vector<polynomial> bl, blp;
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bl.resize (h_block_count);
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for (i = 0; i < h_block_count; ++i) {
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bl[i].resize (block_size);
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for (j = 0; j < block_size; ++j)
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bl[i][j] = Hsig[i * block_size + j];
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}
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//permute the blocks. first move the damaged to discard area
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priv.block_perm.generate_identity (h_block_count);
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uint oks = h_block_count;
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for (i = 0; i < oks; ++i)
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if (!block_status[i]) {
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std::cout << "removing one" << std::endl;
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--oks;
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priv.block_perm[i] = oks;
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priv.block_perm[oks] = i;
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//swap block statuses as well
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bool tmp = block_status[i];
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block_status[i] = block_status[oks];
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block_status[oks] = tmp;
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--i;
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}
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std::cout << "BLOCK " << priv.block_perm;
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permutation rest_perm;
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rest_perm.generate_random (oks, rng);
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//permute the undamaged part of block_perm by hand TODO FIXME
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//for (i = 0; i < oks; ++i) rest_perm[i] = priv.block_perm[rest_perm[i]];
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//for (i = 0; i < oks; ++i) priv.block_perm[i] = rest_perm[i];
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//now we can safely permute and discard blocks
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priv.block_perm.permute (bl, blp);
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blp.resize (block_count);
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//permute individual blocks
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priv.block_perms.resize (block_count);
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bl.resize (blp.size() );
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for (i = 0; i < block_count; ++i) {
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priv.block_perms[i] = rng.random (block_size);
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permutation::permute_dyadic (priv.block_perms[i],
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blp[i], bl[i]);
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}
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//construct H
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pub.qd_sigs.resize (fld.m);
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bvector col;
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bvector block;
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for (i = 0; i < fld.m; ++i)
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pub.qd_sigs[i].resize (block_count * block_size);
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for (i = 0; i < block_count; ++i) {
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col.from_poly_cotrace (bl[i], fld);
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for (j = 0; j < fld.m; ++j) {
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col.get_block (j * block_size,
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block_size, block);
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pub.qd_sigs[j].set_block
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(block, block_size * i);
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}
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}
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//finish the pubkey
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pub.T = T;
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pub.t = t;
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return 0;
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}
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}
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int privkey::prepare()
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{
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uint s, i, j, k;
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std::vector<uint> Hsig, support;
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uint omega;
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uint block_count = block_perms.size(),
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block_size = 1 << T;
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//compute H signature from essence
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Hsig.resize (fld.n);
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Hsig[0] = fld.inv (essence[fld.m]);
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for (s = 0; s < fld.m; ++s) {
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i = 1 << s; //i = 2^s
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Hsig[i] = fld.inv (fld.add (essence[s], essence[fld.m]) );
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for (j = 1; j < i; ++j)
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Hsig[i + j] = fld.inv
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(fld.add
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(fld.inv (Hsig[i]),
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fld.add (
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fld.inv (Hsig[j]),
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essence[fld.m]
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) ) );
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}
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std::cout << "Gen Hsig: ";
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for (i = 0; i < fld.n; ++i) std::cout << Hsig[i] << ' ';
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std::cout << std::endl;
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//goppa polynomial with omega=0
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std::set<uint> used;
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used.clear();
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polynomial tmp;
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g.clear();
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g.resize (1, 1); //g(x)=1
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tmp.clear();
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tmp.resize (2, 1); //tmp(x)=x+1
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for (i = 0; i < t; ++i) {
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tmp[0] = fld.inv (Hsig[i]); //tmp(x)=x+1/h_i
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if (used.count (tmp[0]) )
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return 1;
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std::cout << tmp[0] << std::endl;
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used.insert (tmp[0]);
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g.mult (tmp, fld);
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}
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std::cout << "HERE 1" << std::endl;
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//compute the support with omega=0
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support.resize (fld.n);
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for (i = 0; i < fld.n; ++i) {
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//don't compute with discarded support
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if (block_perm[i / block_size] >= block_count) continue;
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support[i] = fld.add
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(fld.inv (Hsig[i]),
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essence[fld.m]);
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std::cout << "support " << i << " = " << support[i] << std::endl;
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if (used.count (support[i]) ) //invalid support
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return 1;
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used.insert (support[i]);
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}
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std::cout << "HERE LOLOLOLOLOL" << std::endl;
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//choose omega
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omega = fld.n;
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for (i = 0; i < fld.n; ++i)
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if (!used.count (i) ) {
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omega = i;
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break;
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}
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if (omega == fld.n) return 1;
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//modify support to omega-ized version
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for (i = 0; i < support.size(); ++i)
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support[i] = fld.add (support[i], omega);
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//modify g to omega-ized version
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g.clear();
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tmp.clear();
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g.resize (1, 1); //g(x)=1
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tmp.resize (2, 1); //tmp(x)=x+1
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for (i = 0; i < t; ++i) {
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tmp[0] = fld.add (fld.inv (Hsig[i]), omega);
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g.mult (tmp, fld);
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}
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g.compute_square_root_matrix (sqInv, fld);
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// prepare permuted support, from that prepare permuted check matrix
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// (so that it can be applied directly)
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uint pos;
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std::vector<uint> sbl1, sbl2, permuted_support;
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sbl1.resize (block_size);
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sbl2.resize (block_size);
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permuted_support.resize (block_size * block_count);
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//permute support
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for (i = 0; i < fld.n / block_size; ++i) {
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pos = block_perm[i];
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if (pos >= block_count) continue; //was discarded
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//permute i-th block of support
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for (j = 0; j < block_size; ++j)
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sbl1[j] = support[j + i * block_size];
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permutation::permute_dyadic (block_perms[pos], sbl1, sbl2);
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//store support to permuted support
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for (j = 0; j < block_size; ++j)
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permuted_support[j + pos * block_size] = sbl2[j];
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}
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//convert the permuted support to actual lookup
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support_pos.clear();
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//fld.n in support lookup means that it isn't there (we don't have -1)
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support_pos.resize (fld.n, fld.n);
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for (i = 0; i < block_size * block_count; ++i)
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support_pos[permuted_support[i]] = i;
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/*
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* TODO move this to separate function
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*
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* prepare the matrix to compute decodable syndrome from QD matrix. From Barreto's slides:
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*
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* A is public check matrix
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* H is private check matrix producing decodable syndromes
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*
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* H=SA for some S
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* therefore if
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*
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* synd = A * codeword
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*
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* then
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*
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* S*synd = H*codeword
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*
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* and S = H * A^T * (A * A^T)^-1
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*/
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std::vector<std::vector<uint> > ma, mb, tmpa, tmph;
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std::vector<uint> t1, t2;
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/*
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* First, precompute the matrices A and H
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*/
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tmpa.resize (t);
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tmph.resize (t);
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for (i = 0; i < t; ++i) {
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tmpa[i].resize (fld.n);
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tmph[i].resize (fld.n);
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}
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for (i = 0; i < t; ++i)
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permutation::permute_dyadic (i, Hsig, tmpa[i]);
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std::cout << "TMPA" << std::endl;
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for (i = 0; i < t; ++i) {
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for (j = 0; j < fld.n; ++j) std::cout << tmpa[i][j] << ' ';
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std::cout << std::endl;
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}
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polynomial tmpcol;
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for (i = 0; i < fld.n; ++i) {
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tmpcol.resize (2);
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tmpcol[0] = support[i];
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tmpcol[1] = 1;
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tmpcol.inv (g, fld);
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tmpcol.resize (t, 0);
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for (j = 0; j < t; ++j) tmph[j][i] = tmpcol[j];
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}
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/*
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* compute H * H^T to ma and A * H^T to mb.
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*/
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ma.resize (t);
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mb.resize (t);
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for (i = 0; i < t; ++i) {
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ma[i].resize (t, 0);
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mb[i].resize (t, 0);
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}
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for (i = 0; i < t; ++i) for (j = 0; j < t; ++j) {
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for (k = 0; k < fld.n; ++k) {
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ma[i][j] = fld.add (ma[i][j], fld.mult (tmph[i][k], tmph[j][k]) );
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mb[i][j] = fld.add (mb[i][j], fld.mult (tmpa[i][k], tmph[j][k]) );
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}
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}
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std::cout << "MA" << std::endl;
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for (i = 0; i < t; ++i) {
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for (j = 0; j < t; ++j) std::cout << ma[i][j] << ' ';
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std::cout << std::endl;
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}
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std::cout << "MB" << std::endl;
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for (i = 0; i < t; ++i) {
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for (j = 0; j < t; ++j) std::cout << mb[i][j] << ' ';
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std::cout << std::endl;
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}
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/*
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* now invert mb into ma as (mb|ma) to (I|ma*mb^-1)
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*
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* (result will be transposed, but that's actually good for our purpose)
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*/
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uint x;
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//gauss step
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for (i = 0; i < t; ++i) {
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//find pivot
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for (j = i; j < t; ++j) if (mb[j][i] != 0) break;
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if (j >= t) return 1; //no pivot -> not invertible
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if (j > i) {
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ma[j].swap (ma[i]);
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mb[j].swap (mb[i]);
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}
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//normalize
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x = fld.inv (mb[i][i]);
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for (j = 0; j < t; ++j) {
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ma[i][j] = fld.mult (ma[i][j], x);
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mb[i][j] = fld.mult (mb[i][j], x);
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}
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//zero rows below
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for (j = i + 1; j < t; ++j) {
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x = mb[j][i];
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if (x == 0) continue;
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for (k = 0; k < t; ++k) {
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ma[j][k] = fld.add (ma[j][k], fld.mult (x, ma[i][k]) );
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mb[j][k] = fld.add (mb[j][k], fld.mult (x, mb[i][k]) );
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}
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}
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}
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//jordan step
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std::cout << "jordan step..." << std::endl;
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for (i = 0; i < t; ++i) {
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for (j = i + 1; j < t; ++j) {
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x = mb[t - j - 1][t - i - 1];
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if (x == 0) continue;
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for (k = 0; k < t; ++k) {
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ma[t - j - 1][k] = fld.add (ma[t - j - 1][k], fld.mult (x, ma[t - i - 1][k]) );
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mb[t - j - 1][k] = fld.add (mb[t - j - 1][k], fld.mult (x, mb[t - i - 1][k]) );
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}
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}
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}
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//result is now transposed in ma.
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syndS.resize (t);
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for (i = 0; i < t; ++i) {
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syndS[i].resize (t);
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for (j = 0; j < t; ++j) syndS[i][j] = ma[i][j];
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|
}
|
|
|
|
std::cout << "SyndS is OKAY!" << std::endl;
|
|
|
|
polynomial decsynd, loc;
|
|
for (i = 0; i < t; ++i)
|
|
decsynd.add_mult (syndS[i], Hsig[i], fld);
|
|
compute_goppa_error_locator (decsynd, fld, g, sqInv, loc);
|
|
std::cout << "TEST LOCATOR: " << loc;
|
|
|
|
return 0;
|
|
}
|
|
|
|
int privkey::sign (const bvector& hash, bvector&signature,
|
|
uint delta, uint attempts, prng&rng)
|
|
{
|
|
if (hash.size() != hash_size() ) return 2;
|
|
|
|
polynomial synd, decsynd, tmp, loc;
|
|
bvector ev, h2;
|
|
|
|
uint i;
|
|
|
|
for (uint att = 0; att < attempts; ++att) {
|
|
h2 = hash;
|
|
for (i = 0; i < delta; ++i) {
|
|
uint p = rng.random (h2.size() );
|
|
h2[p] = !h2[p];
|
|
}
|
|
|
|
h2.to_poly_cotrace (synd, fld);
|
|
|
|
std::cout << "SYND" << synd;
|
|
|
|
decsynd.clear();
|
|
for (i = 0; i < t; ++i)
|
|
decsynd.add_mult (syndS[i], synd[i], fld);
|
|
|
|
std::cout << "SYND PREP" << decsynd;
|
|
|
|
compute_goppa_error_locator (decsynd, fld, g, sqInv, loc);
|
|
if (!evaluate_error_locator_trace (loc, ev, fld) ) continue;
|
|
//we might have it!
|
|
std::cout << ev;
|
|
signature.clear();
|
|
signature.resize (signature_size(), 0);
|
|
|
|
for (i = 0; i < fld.n; ++i) if (ev[i]) {
|
|
uint epos = support_pos[i];
|
|
if (epos == fld.n) break; //bad luck, undecodable
|
|
signature[epos] = 1;
|
|
}
|
|
if (i == fld.n) return 0;
|
|
}
|
|
return 1; //no attempts left.
|
|
}
|
|
|
|
int pubkey::verify (const bvector&signature, const bvector&hash, uint delta)
|
|
{
|
|
if (signature.size() != signature_size() ) return 2;
|
|
if (hash.size() != hash_size() ) return 2;
|
|
|
|
uint i, j;
|
|
uint block_size = 1 << T;
|
|
bvector synd, b1, b2;
|
|
|
|
synd.resize (t * qd_sigs.size(), 0);
|
|
//compute the syndrome
|
|
for (i = 0; i < signature_size(); ++i) {
|
|
if (!signature[i]) continue;
|
|
|
|
//this is actually quite fast, as it happens only several times
|
|
for (j = 0; j < qd_sigs.size(); ++j) {
|
|
qd_sigs[j].get_block ( (i / block_size) *block_size,
|
|
block_size, b1);
|
|
permutation::permute_dyadic (i % block_size, b1, b2);
|
|
b2.resize (t);
|
|
synd.add_offset (b2, t * j);
|
|
}
|
|
}
|
|
|
|
std::cout << "SYNDROME: " << synd;
|
|
synd.add (hash);
|
|
std::cout << "DIFF: " << synd;
|
|
if (synd.hamming_weight() > delta) return 1;
|
|
|
|
return 0;
|
|
}
|