int privkey::decrypt (const bvector & in, bvector & out, bvector & errors)
{
if (in.size() != cipher_size() ) return 2;
polynomial synd;
uint i, j, tmp;
/*
* compute the syndrome from alternant check matrix
* that is H_alt = Vdm(L) * Diag(g(L_i)^{-2})
*/
uint h_size = 1 << (T + 1); //= 2*block_size
synd.clear();
synd.resize (h_size, 0);
for (i = 0; i < cipher_size(); ++i) if (in[i]) {
tmp = fld.inv (g.eval (permuted_support[i], fld) );
tmp = fld.mult (tmp, tmp); //g(Li)^{-2}
synd[0] = fld.add (synd[0], tmp);
for (j = 1; j < h_size; ++j) {
tmp = fld.mult (tmp, permuted_support[i]);
synd[j] = fld.add (synd[j], tmp);
}
}
//decoding
polynomial 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() );
errors.clear();
errors.resize (cipher_size(), 0);
//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 >= cipher_size() ) return 1;
errors[epos] = 1;
if (epos < plain_size() )
out[epos] = !out[epos];
}
return 0;
}
bool evaluate_error_locator_trace (polynomial&sigma, bvector&ev, gf2m&fld)
{
ev.clear();
ev.resize (fld.n, 0);
std::vector<polynomial> trace_aux, trace; //trace cache
trace_aux.resize (fld.m);
trace.resize (fld.m);
trace_aux[0] = polynomial();
trace_aux[0].resize (2, 0);
trace_aux[0][1] = 1; //trace_aux[0] = x
trace[0] = trace_aux[0]; //trace[0] = x
for (uint i = 1; i < fld.m; ++i) {
trace_aux[i] = trace_aux[i - 1];
trace_aux[i].square (fld);
trace_aux[i].mod (sigma, fld);
trace[0].add (trace_aux[i], fld);
}
std::set<std::pair<uint, polynomial> > stk; //"stack"
stk.insert (make_pair (0, sigma));
bool failed = false;
while (!stk.empty()) {
uint i = stk.begin()->first;
polynomial cur = stk.begin()->second;
stk.erase (stk.begin());
int deg = cur.degree();
if (deg <= 0) continue;
if (deg == 1) { //found a linear factor
ev[fld.mult (cur[0], fld.inv (cur[1])) ] = 1;
continue;
}
if (i >= fld.m) {
failed = true;
continue;
}
if (trace[i].zero()) {
//compute the trace if it isn't cached
uint a = fld.exp (i);
for (uint j = 0; j < fld.m; ++j) {
trace[i].add_mult (trace_aux[j], a, fld);
a = fld.mult (a, a);
}
}
polynomial t;
t = cur.gcd (trace[i], fld);
polynomial q, r;
cur.divmod (t, q, r, fld);
stk.insert (make_pair (i + 1, t));
stk.insert (make_pair (i + 1, q));
}
return !failed;
}