551 lines
14 KiB
C++
551 lines
14 KiB
C++
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#include "codecrypt.h"
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using namespace ccr;
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using namespace ccr::mce_qd;
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#include "decoding.h"
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#include "fwht.h"
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#include <set>
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static uint sample_from_u (gf2m&fld, prng&rng, std::set<uint>&used)
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{
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uint x;
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for (;;) {
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x = rng.random (fld.n);
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if (used.count (x) ) continue;
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used.insert (x);
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return x;
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}
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}
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static uint choose_random (uint limit, prng&rng, std::set<uint>used)
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{
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if (used.size() >= limit - 1) return 0; //die
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for (;;) {
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uint a = 1 + rng.random (limit - 1);
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if (used.count (a) ) continue;
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used.insert (a);
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return a;
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}
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}
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int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
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uint m, 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 t = 1 << T;
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//convenience
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gf2m&fld = priv.fld;
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std::vector<uint>&Hsig = priv.Hsig;
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std::vector<uint>&essence = priv.essence;
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std::vector<uint>&support = priv.support;
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polynomial g;
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//prepare for data
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Hsig.resize (fld.n / 2);
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support.resize (fld.n / 2);
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essence.resize (m);
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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::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 - 1] = fld.inv (Hsig[0]);
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//essence[m-1] is now used as precomputed 1/h_0
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for (uint s = 0; s < m - 1; ++s) {
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uint 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 - 1], fld.inv (Hsig[i]) );
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used.insert (fld.inv (essence[s]) );
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for (uint 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[m - 1]
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) ) );
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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 - 1]) ) );
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}
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}
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//assemble goppa polynomial.
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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 (uint i = 0; i < t; ++i) {
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//tmp(x)=x-z=x-(1/h_i)
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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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//compute the support, retry if it has two equal elements.
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for (uint i = 0; i < fld.n / 2; ++i) {
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support[i] = fld.add (
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fld.inv (Hsig[i]),
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essence[m - 1]);
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if (used.count (support[i]) ) {
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consistent = false;
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break;
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}
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//as we are having z's in used, this is not necessary.
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//TODO verify, then TODO maybe delete.
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if (g.eval (support[i], fld) == 0) {
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consistent = 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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if (!consistent) continue; //retry
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//now the blocks.
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uint block_size = 1 << T,
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h_block_count = (fld.n / 2) / block_size;
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uint& block_count = priv.block_count;
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block_count = h_block_count - block_discard;
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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 (uint i = 0; i < h_block_count; ++i) {
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bl[i].resize (block_size);
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for (uint 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 them
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priv.block_perm.generate_random (h_block_count, rng);
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priv.block_perm.permute (bl, blp);
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//discard blocks
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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 (uint 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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//try several permutations to construct G
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uint attempts = 0;
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for (attempts = 0; attempts < block_count; ++attempts) {
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/*
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* try computing the redundancy block of G
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*
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* First, co-trace H, then compute G in form
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*
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* G^T = [I | X]
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*
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* Since H*G^T = [L | R] * [I | X] = L + R*X = 0
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* we have the solution: X = R^1 * L
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* (thanks to Rafael Misoczki)
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*
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* Inversion is done the quasi-dyadic way:
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*
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* - because for QD matrix m=delta(h) the product
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* m*m = sum(h) * I, binary QD matrix m is either
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* inversion of itself (m*m=I) or isn't invertible
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* and m*m=0. sum(h), the "count of ones in QD
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* signature mod 2", easily determines the result.
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*
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* - Using blockwise invertions/multiplications,
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* gaussian elimination needed to invert the right
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* square of H can be performed in O(m^2*block_count)
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* matrix operations. Matrix operations are either
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* addition (O(t) on QDs), multiplication(O(t log t)
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* on QDs) or inversion (O(t), as shown above).
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* Whole proces is therefore quite fast.
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*
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* Gaussian elimination on the QD signature should
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* result in something like this: (for m=3, t=4)
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*
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* 1010 0101 1001 1000 0000 0000
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* 0101 1100 1110 0000 1000 0000
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* 0111 1110 0100 0000 0000 1000
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*/
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priv.hperm.generate_random (block_count, rng);
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permutation hpermInv;
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priv.hperm.compute_inversion (hpermInv);
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std::vector<std::vector<bvector> > hblocks;
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bvector tmp;
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bool failed;
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uint i, j, k, l;
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//prepare blocks of h
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hblocks.resize (block_count);
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for (i = 0; i < block_count; ++i)
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hblocks[i].resize (fld.m);
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//fill them from Hsig
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for (i = 0; i < block_count; ++i) {
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tmp.from_poly_cotrace (bl[hpermInv[i]], fld);
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for (j = 0; j < fld.m; ++j)
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tmp.get_block (j * block_size,
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block_size,
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hblocks[i][j]);
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}
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/* do a modified QD-blockwise gaussian elimination on hblocks */
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failed = false;
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tmp.resize (block_size);
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for (i = 0; i < fld.m; ++i) { //gauss step
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//first, find a nonsingular matrix in the column
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for (j = i; j < fld.m; ++j)
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if (hblocks[block_count - fld.m + i][j]
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.hamming_weight() % 2) break;
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if (j >= fld.m) { //none found, break;
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failed = true;
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break;
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}
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//bring it to correct position (swap it to i-th row)
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if (j > i) for (k = 0; k < block_count; ++k)
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hblocks[k][i].swap
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(hblocks[k][j]);
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//now normalize the row
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for (j = i; j < fld.m; ++j) {
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l = hblocks [block_count - fld.m + i]
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[j].hamming_weight();
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if (l == 0) continue; //zero is just okay :]
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if (! (l % 2) ) //singular, make it regular by adding the i-th row
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for (k = 0;
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k < block_count;
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++k)
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hblocks[k][j].add
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(hblocks[k][i]);
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//now a matrix is regular, we can easily make it I.
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//first, multiply the row
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for (k = 0; k < block_count; ++k) {
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//don't overwrite the matrix we're counting with
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if (k == block_count - fld.m + i) continue;
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fwht_dyadic_multiply
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(hblocks[block_count - fld.m + i][j],
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hblocks[k][j], tmp);
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hblocks[k][j] = tmp;
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}
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//change the block on the diagonal
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fwht_dyadic_multiply
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(hblocks[block_count - fld.m + i][j],
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hblocks[block_count - fld.m + i][j], tmp);
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hblocks[block_count - fld.m + i][j] = tmp;
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//and zero the column below diagonal
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if (j > i) for (k = 0; k < block_count; ++k)
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hblocks[k][j].add
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(hblocks[k][i]);
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}
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}
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if (failed) continue;
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for (i = 0; i < fld.m; ++i) { //jordan step
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//normalize diagonal
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for (k = 0; k < block_count - i; ++k) {
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//we can safely rewrite the diagonal here (nothing's behind it)
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fwht_dyadic_multiply
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(hblocks[block_count - i - 1][fld.m - i - 1],
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hblocks[k][fld.m - i - 1], tmp);
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hblocks[k][fld.m - i - 1] = tmp;
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}
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//now make zeroes above
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for (j = i + 1; j < fld.m; ++j) {
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l = hblocks[block_count - i - 1]
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[fld.m - j - 1].hamming_weight();
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if (l == 0) continue; //already zero
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if (! (l % 2) ) { //nonsingular, fix it by adding diagonal
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for (k = 0; k < block_count; ++k)
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hblocks[k][fld.m - j - 1].add
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(hblocks[k][fld.m - i - 1]);
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}
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for (k = 0; k < block_count - i; ++k) {
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//overwrite is also safe here
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fwht_dyadic_multiply
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(hblocks[block_count - i - 1]
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[fld.m - j - 1],
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hblocks[k][fld.m - j - 1], tmp);
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hblocks[k][fld.m - j - 1] = tmp;
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}
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//I+I=0
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for (k = 0; k < block_count; ++k)
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hblocks[k][fld.m - j - 1].add
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(hblocks[k][fld.m - i - 1]);
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}
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}
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pub.qd_sigs.resize (block_count - fld.m);
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for (uint i = 0; i < block_count - fld.m; ++i) {
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pub.qd_sigs[i].resize (block_size * fld.m);
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for (uint j = 0; j < fld.m; ++j)
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pub.qd_sigs[i].set_block
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(hblocks[i][j], block_size * j);
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}
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break;
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}
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if (attempts == block_count) //generating G failed, retry all
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continue;
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//finish the pubkey
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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;
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//compute H signature from essence
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Hsig.resize (fld.n / 2);
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Hsig[0] = fld.inv (essence[fld.m - 1]);
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for (s = 0; s < fld.m - 1; ++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 - 1]) );
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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 - 1]
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) ) );
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}
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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 g, 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 < (1 << 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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used.insert (tmp[0]);
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g.mult (tmp, fld);
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}
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//compute the support with omega=0
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support.resize (fld.n / 2);
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for (i = 0; i < fld.n / 2; ++i) {
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support[i] = fld.add
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(fld.inv (Hsig[i]),
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essence[fld.m - 1]);
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//support consistency check
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if (used.count (support[i]) )
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return 1;
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used.insert (support[i]);
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}
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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 < (1 << 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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// 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 block_size = 1 << T;
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uint pos, blk_perm;
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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 / 2) / 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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blk_perm = block_perms[pos];
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pos = hperm[pos];
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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 (blk_perm, 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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//prepare Hc
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Hc.resize (block_size * block_count);
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for (i = 0; i < block_size * block_count; ++i) {
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Hc[i].resize (block_size * 2);
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Hc[i][0] = fld.inv (g.eval (permuted_support[i], fld) );
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Hc[i][0] = fld.mult (Hc[i][0], Hc[i][0]);
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for (j = 1; j < 2 * block_size; ++j)
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Hc[i][j] = fld.mult (permuted_support[i],
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Hc[i][j - 1]);
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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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return 0;
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}
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int pubkey::encrypt (const bvector & in, bvector & out, prng & rng)
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{
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uint t = 1 << T;
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bvector p, g, r, cksum;
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uint i, j, k;
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/*
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* shortened checksum pair of G is computed blockwise accordingly to
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* the t-sized square dyadic blocks.
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*/
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//some checks
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if (!qd_sigs.size() ) return 1;
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if (qd_sigs[0].size() % t) return 1;
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uint blocks = qd_sigs[0].size() / t;
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cksum.resize (qd_sigs[0].size(), 0);
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p.resize (t);
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g.resize (t);
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r.resize (t);
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for (i = 0; i < qd_sigs.size(); ++i) {
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//plaintext block
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in.get_block (i * t, t, p);
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for (j = 0; j < blocks; ++j) {
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//checksum block
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qd_sigs[i].get_block (j * t, t, g);
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//block result
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fwht_dyadic_multiply (p, g, r);
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cksum.add_offset (r, t * j);
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}
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}
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//generate t errors
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bvector e;
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e.resize (cipher_size(), 0);
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for (uint n = t; n > 0;) {
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uint p = rng.random (e.size() );
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if (!e[p]) {
|
|
e[p] = 1;
|
|
--n;
|
|
}
|
|
}
|
|
|
|
//compute ciphertext
|
|
out = in;
|
|
out.insert (out.end(), cksum.begin(), cksum.end() );
|
|
out.add (e);
|
|
|
|
return 0;
|
|
}
|
|
|
|
int privkey::decrypt (const bvector & in, bvector & out)
|
|
{
|
|
if (in.size() != cipher_size() ) return 2;
|
|
polynomial synd;
|
|
uint i;
|
|
|
|
synd.clear();
|
|
for (i = 0; i < cipher_size(); ++i)
|
|
if (in[i]) synd.add (Hc[i], fld);
|
|
|
|
//decoding
|
|
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) )
|
|
return 1; //couldn't decode
|
|
//TODO evaluator should return error positions, not bvector. fix it everywhere!
|
|
|
|
out = in;
|
|
out.resize (plain_size() );
|
|
//flip error positions of out.
|
|
for (i = 0; i < ev.size(); ++i) if (ev[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;
|
|
}
|
|
|