310 lines
6.7 KiB
C++
310 lines
6.7 KiB
C++
|
|
#include "codecrypt.h"
|
|
|
|
using namespace ccr;
|
|
using namespace ccr::mce_qd;
|
|
|
|
#include "decoding.h"
|
|
|
|
#include <set>
|
|
|
|
static uint sample_from_u (gf2m&fld, prng&rng, std::set<uint>&used)
|
|
{
|
|
uint x;
|
|
for (;;) {
|
|
x = rng.random (fld.n);
|
|
if (used.count (x) ) continue;
|
|
used.insert (x);
|
|
return x;
|
|
}
|
|
}
|
|
|
|
static uint choose_random (uint limit, prng&rng, std::set<uint>used)
|
|
{
|
|
if (used.size() >= limit - 1) return 0; //die
|
|
for (;;) {
|
|
uint a = 1 + rng.random (limit - 1);
|
|
if (used.count (a) ) continue;
|
|
used.insert (a);
|
|
return a;
|
|
}
|
|
}
|
|
|
|
int mce_qd::generate (pubkey&pub, privkey&priv, prng&rng,
|
|
uint m, uint T, uint block_discard)
|
|
{
|
|
priv.fld.create (m);
|
|
priv.T = T;
|
|
uint t = 1 << T;
|
|
|
|
//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;
|
|
|
|
//prepare for data
|
|
Hsig.resize (fld.n / 2);
|
|
support.resize (fld.n / 2);
|
|
essence.resize (m);
|
|
//note that q=2^m, algo. n=q/2, log n = m-1
|
|
|
|
//retry generating until goppa code is produced.
|
|
for (;;) {
|
|
|
|
std::set<uint> used;
|
|
used.clear();
|
|
|
|
//first off, compute the H signature
|
|
|
|
Hsig[0] = choose_random (fld.n, rng, used);
|
|
essence[m-1] = fld.inv (Hsig[0]);
|
|
//essence[m-1] is now used as precomputed 1/h_0
|
|
|
|
for (uint s = 0; s < m - 1; ++s) {
|
|
uint i = 1 << s; //i = 2^s
|
|
|
|
Hsig[i] = choose_random (fld.n, rng, used);
|
|
essence[s] = fld.add (essence[m-1], fld.inv (Hsig[i]) );
|
|
used.insert (fld.inv (essence[s]) );
|
|
|
|
for (uint j = 1; j < i; ++j) {
|
|
Hsig[i+j] = fld.inv
|
|
(fld.add
|
|
(fld.inv (Hsig[i]),
|
|
fld.add (
|
|
fld.inv (Hsig[j]),
|
|
essence[m-1]
|
|
) ) );
|
|
used.insert (Hsig[i+j]);
|
|
used.insert (fld.inv
|
|
(fld.add
|
|
(fld.inv (Hsig[i+j]),
|
|
essence[m-1]) ) );
|
|
}
|
|
}
|
|
|
|
//from now on, we fix 'omega' from the paper to zero.
|
|
|
|
//assemble goppa polynomial.
|
|
g.clear();
|
|
g.resize (1, 1); //g(x)=1 so we can multiply it
|
|
polynomial tmp;
|
|
tmp.resize (2, 1); //tmp(x)=x-1
|
|
for (uint i = 0; i < t; ++i) {
|
|
//tmp(x)=x-z=x-(1/h_i)
|
|
tmp[0] = fld.inv (Hsig[i]);
|
|
g.mult (tmp, fld);
|
|
}
|
|
|
|
//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]),
|
|
essence[m-1]);
|
|
|
|
if (used.count (support[i]) ) {
|
|
consistent = false;
|
|
break;
|
|
}
|
|
|
|
if (g.eval (support[i], fld) == 0) {
|
|
consistent = false;
|
|
break;
|
|
}
|
|
|
|
|
|
used.insert (support[i]);
|
|
}
|
|
if (!consistent) continue; //retry
|
|
|
|
//now the blocks.
|
|
uint block_size = 1 << T,
|
|
h_block_count = (fld.n / 2) / block_size;
|
|
uint& block_count = priv.block_count;
|
|
block_count = h_block_count - block_discard;
|
|
|
|
//assemble blocks to bl
|
|
std::vector<std::vector<uint> > bl, blp;
|
|
bl.resize (h_block_count);
|
|
for (uint i = 0; i < h_block_count; ++i)
|
|
bl[i] = std::vector<uint>
|
|
(Hsig.begin() + i * block_size,
|
|
Hsig.begin() + (i + 1) * block_size);
|
|
|
|
//permute them
|
|
priv.block_perm.generate_random (h_block_count, rng);
|
|
priv.block_perm.permute (bl, blp);
|
|
|
|
//discard blocks
|
|
blp.resize (block_count);
|
|
|
|
//permute individual blocks
|
|
priv.block_perms.resize (block_count);
|
|
bl.resize (blp.size() );
|
|
for (uint i = 0; i < block_count; ++i) {
|
|
priv.block_perms[i] = rng.random (block_size);
|
|
permutation::permute_dyadic (priv.block_perms[i],
|
|
blp[i], bl[i]);
|
|
}
|
|
|
|
//co-trace blocks to binary H^, retry creating G using hperm.
|
|
matrix Hc;
|
|
polynomial col;
|
|
Hc.resize (block_count * block_size);
|
|
|
|
matrix r, ri, l;
|
|
|
|
for (;;) {
|
|
priv.hperm.generate_random (block_count, rng);
|
|
|
|
for (uint i = 0; i < block_count; ++i)
|
|
for (uint j = 0; j < block_size; ++j) {
|
|
permutation::permute_dyadic
|
|
(j, bl[priv.hperm[i]], col);
|
|
Hc[i*block_size + j].from_poly_cotrace
|
|
(col, fld);
|
|
}
|
|
|
|
/*
|
|
* try computing the redundancy block of G
|
|
*
|
|
* Since H*G^T = [L | R] * [I | X] = L + R*X = 0
|
|
* we have the solution: X = R^1 * L
|
|
*/
|
|
|
|
Hc.get_right_square (r);
|
|
if (!r.compute_inversion (ri) )
|
|
continue; //retry with other hperm
|
|
Hc.strip_right_square (l);
|
|
ri.mult (l);
|
|
break;
|
|
}
|
|
|
|
/*
|
|
* Redundancy-checking part of G is now (transposed) in ri.
|
|
* Get QD signatures by getting every t'th row (transposed).
|
|
*/
|
|
|
|
pub.T = T;
|
|
pub.qd_sigs.resize (ri.width() / t);
|
|
for (uint i = 0; i < ri.width(); i += t)
|
|
pub.qd_sigs[i/t] = ri[i];
|
|
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
int privkey::prepare()
|
|
{
|
|
//compute H signature from essence
|
|
Hsig.resize (fld.n / 2);
|
|
Hsig[0] = fld.inv (essence[fld.m-1]);
|
|
for (uint s = 0; s < fld.m - 1; ++s) {
|
|
uint i = 1 << s; //i = 2^s
|
|
|
|
//TODO verify this
|
|
Hsig[i] = fld.inv (fld.add (essence[s], essence[fld.m-1]) );
|
|
|
|
for (uint j = 1; j < i; ++j)
|
|
Hsig[i+j] = fld.inv
|
|
(fld.add
|
|
(fld.inv (Hsig[i]),
|
|
fld.add (
|
|
fld.inv (Hsig[j]),
|
|
essence[fld.m-1]
|
|
) ) );
|
|
}
|
|
|
|
//compute the support
|
|
support.resize (fld.n / 2);
|
|
for (uint i = 0; i < fld.n / 2; ++i) {
|
|
support[i] = fld.add
|
|
(fld.inv (Hsig[i]),
|
|
essence[fld.m-1]);
|
|
|
|
}
|
|
|
|
//goppa polynomial
|
|
g.clear();
|
|
g.resize (1, 1);
|
|
polynomial tmp;
|
|
tmp.resize (2, 1);
|
|
uint t = 1 << T;
|
|
for (uint 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;
|
|
}
|
|
|
|
#include "fwht.h"
|
|
|
|
int pubkey::encrypt (const bvector& in, bvector&out, prng&rng)
|
|
{
|
|
uint t = 1 << T;
|
|
bvector p, g, r, cksum;
|
|
|
|
/*
|
|
* shortened checksum pair of G is computed blockwise accordingly to
|
|
* the t-sized square dyadic blocks.
|
|
*/
|
|
|
|
//some checks
|
|
if (!qd_sigs.size() ) return 1;
|
|
if (qd_sigs[0].size() % t) return 1;
|
|
|
|
uint blocks = qd_sigs[0].size() / t;
|
|
cksum.resize (qd_sigs[0].size(), 0);
|
|
|
|
p.resize (t);
|
|
g.resize (t);
|
|
r.resize (t);
|
|
|
|
for (uint i = 0; i < qd_sigs.size(); ++i) {
|
|
//plaintext block
|
|
for (uint k = 0; k < t; ++k) p[k] = in[k+i*t];
|
|
|
|
for (uint j = 0; j < blocks; ++j) {
|
|
//checksum block
|
|
for (uint k = 0; k < t; ++k) g[k] = qd_sigs[i][k+j*t];
|
|
|
|
//block result
|
|
fwht_dyadic_multiply (p, g, r);
|
|
cksum.add_offset (r, t * j);
|
|
}
|
|
}
|
|
|
|
//generate t errors
|
|
bvector e;
|
|
e.resize (cipher_size(), 0);
|
|
for (uint n = t; n > 0;) {
|
|
uint p = rng.random (e.size() );
|
|
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)
|
|
{
|
|
//TODO decoding
|
|
return 0;
|
|
}
|
|
|