mirror of
https://github.com/biergaizi/codecrypt
synced 2024-06-28 09:53:46 +00:00
algebraic decoding
This commit is contained in:
Mirek Kratochvil
parent
b715459593
commit
0963baefa1
@ -26,6 +26,8 @@ typedef int sint;
|
||||
* vector over GF(2). We rely on STL's vector<bool> == bit_vector
|
||||
* specialization for efficiency.
|
||||
*/
|
||||
class polynomial;
|
||||
class gf2m;
|
||||
class bvector : public std::vector<bool>
|
||||
{
|
||||
protected:
|
||||
@ -34,6 +36,8 @@ public:
|
||||
uint hamming_weight();
|
||||
void add (const bvector&);
|
||||
bool operator* (const bvector&); //dot product
|
||||
bool zero() const;
|
||||
void to_poly (polynomial&, gf2m&);
|
||||
};
|
||||
|
||||
/*
|
||||
@ -115,6 +119,7 @@ public:
|
||||
uint mult (uint, uint);
|
||||
uint exp (uint, sint);
|
||||
uint inv (uint);
|
||||
uint sq_root (uint);
|
||||
};
|
||||
|
||||
/*
|
||||
@ -129,13 +134,26 @@ public:
|
||||
void strip();
|
||||
int degree() const;
|
||||
bool zero() const;
|
||||
void shift (uint);
|
||||
|
||||
uint eval (uint, gf2m&) const;
|
||||
void add (const polynomial&, gf2m&);
|
||||
void mod (const polynomial&, gf2m&);
|
||||
void mult (const polynomial&, gf2m&);
|
||||
void add_mult (const polynomial&, uint mult, gf2m&);
|
||||
void mod (const polynomial&, gf2m&);
|
||||
void div (polynomial&, polynomial&, gf2m&);
|
||||
void divmod (polynomial&, polynomial&, polynomial&, gf2m&);
|
||||
void square (gf2m&);
|
||||
void inv (polynomial&, gf2m&);
|
||||
void make_monic (gf2m&);
|
||||
|
||||
void sqrt (vector<polynomial>&, gf2m&);
|
||||
polynomial gcd (polynomial, gf2m&);
|
||||
void mod_to_fracton (polynomial&, polynomial&, polynomial&, gf2m&);
|
||||
|
||||
bool is_irreducible (gf2m&) const;
|
||||
void generate_random_irreducible (uint s, gf2m&, prng&);
|
||||
|
||||
bool compute_square_root_matrix (std::vector<polynomial>&, gf2m&);
|
||||
void compute_goppa_check_matrix (matrix&, gf2m&);
|
||||
};
|
||||
|
||||
@ -25,3 +25,16 @@ bool bvector::operator* (const bvector&a)
|
||||
return r;
|
||||
}
|
||||
|
||||
bool bvector::zero() const
|
||||
{
|
||||
for (uint i = 0; i < size(); ++i) if (item (i) ) return false;
|
||||
return true;
|
||||
}
|
||||
|
||||
void bvector::to_poly (polynomial&r, gf2m&fld)
|
||||
{
|
||||
r.clear();
|
||||
r.resize ( (size() % fld.m) ? 1 : 0 + (size() / fld.m), 0);
|
||||
for (uint i = 0; i < size(); ++i)
|
||||
if (item (i) ) r[i/fld.m] |= 1 << (i % fld.m);
|
||||
}
|
||||
|
||||
30
lib/decoding.cpp
Normal file
30
lib/decoding.cpp
Normal file
@ -0,0 +1,30 @@
|
||||
|
||||
#include "decoding.h"
|
||||
|
||||
void syndrome_decode (bvector&syndrome, gf2m&fld, polynomial& goppa,
|
||||
std::vector<polynomial>& sqInv, bvector&ev)
|
||||
|
||||
{
|
||||
ev.resize (fld.n, 0);
|
||||
if (syndrome.zero() ) return;
|
||||
|
||||
polynomial p;
|
||||
syndrome.to_poly (p, fld);
|
||||
p.inv (goppa, fld); // p=S^-1 mod goppa
|
||||
|
||||
p[1] = fld.add (1, p[1]); //p is now tau
|
||||
p.sqrt (sqInv, fld); //tau = sqrt(T+x) mod goppa
|
||||
|
||||
polynomial a, b;
|
||||
p.mod_to_fracton (a, b, goppa, fld);
|
||||
a.square (fld);
|
||||
b.square (fld);
|
||||
b.shift (1);
|
||||
a.add (b, fld); //new a = a^2 + x b^2
|
||||
|
||||
a.make_monic (fld); //now it is the error locator.
|
||||
|
||||
for (uint i = 0; i < fld.n; ++i) {
|
||||
if (0 == a.eval (i, fld) ) ev[i] = 1;
|
||||
}
|
||||
}
|
||||
14
lib/decoding.h
Normal file
14
lib/decoding.h
Normal file
@ -0,0 +1,14 @@
|
||||
|
||||
#ifndef _decoding_h_
|
||||
#define _decoding_h_
|
||||
|
||||
#include "codecrypt.h"
|
||||
|
||||
using namespace ccr;
|
||||
void syndrome_decode (bvector&syndrome,
|
||||
gf2m&fld,
|
||||
polynomial& gp,
|
||||
std::vector<polynomial>& sqInv,
|
||||
bvector&ev);
|
||||
|
||||
#endif
|
||||
@ -117,3 +117,9 @@ uint gf2m::inv (uint a)
|
||||
return exp (a, n - 2);
|
||||
}
|
||||
|
||||
uint gf2m::sq_root (uint a)
|
||||
{
|
||||
for (uint i = 0; i < m; ++i)
|
||||
a = mult (a, a);
|
||||
return a;
|
||||
}
|
||||
|
||||
@ -62,8 +62,8 @@ bool matrix::compute_inversion (matrix&res)
|
||||
if (m[i][i] != 1) {
|
||||
for (j = i + 1; j < s; ++j) if (m[j][i] == 1) break;
|
||||
if (j == s) return false; //noninvertible
|
||||
m[i].add (m[j]);
|
||||
r[i].add (r[j]);
|
||||
m[i].swap (m[j]);
|
||||
r[i].swap (r[j]);
|
||||
}
|
||||
//remove 1's below
|
||||
for (j = i + 1; j < s; ++j) if (m[j][i]) {
|
||||
|
||||
@ -69,7 +69,6 @@ int pubkey::encrypt (const bvector& in, bvector&out, prng&rng)
|
||||
|
||||
int privkey::decrypt (const bvector&in, bvector&out)
|
||||
{
|
||||
|
||||
return -1; //TODO
|
||||
}
|
||||
|
||||
|
||||
@ -28,6 +28,14 @@ void polynomial::add (const polynomial&f, gf2m&fld)
|
||||
for (int i = 0; i <= df; ++i) item (i) = fld.add (item (i), f[i]);
|
||||
}
|
||||
|
||||
void polynomial::add_mult (const polynomial&f, uint mult, gf2m&fld)
|
||||
{
|
||||
int df = f.degree();
|
||||
if (df > degree() ) resize (df + 1);
|
||||
for (int i = 0; i <= df; ++i)
|
||||
item (i) = fld.add (item (i), fld.mult (mult, f[i]) );
|
||||
}
|
||||
|
||||
void polynomial::mod (const polynomial&f, gf2m&fld)
|
||||
{
|
||||
int df = f.degree();
|
||||
@ -226,3 +234,103 @@ void polynomial::compute_goppa_check_matrix (matrix&r, gf2m&fld)
|
||||
r[i][j] = (h[j/fld.m][i] >> (j % fld.m) ) & 1;
|
||||
}
|
||||
}
|
||||
|
||||
void polynomial::make_monic (gf2m&fld)
|
||||
{
|
||||
int d = degree();
|
||||
if (d < 0) return;
|
||||
uint m = fld.inv (item (d) );
|
||||
for (uint i = 0; i <= d; ++i) item (i) = fld.mult (item (i), m);
|
||||
}
|
||||
|
||||
void polynomial::shift (uint n)
|
||||
{
|
||||
if (degree() < 0) return;
|
||||
insert (begin(), n, 0);
|
||||
}
|
||||
|
||||
void polynomial::square (gf2m&fld)
|
||||
{
|
||||
polynomial a = *this;
|
||||
this->mult (a, fld);
|
||||
}
|
||||
|
||||
void polynomial::sqrt (vector<polynomial>& sqInv, gf2m&fld)
|
||||
{
|
||||
polynomial a = *this;
|
||||
clear();
|
||||
for (uint i = 0; i < a.size(); ++i) add_mult (sqInv[i], a[i], fld);
|
||||
for (uint i = 0; i < size(); ++i) item (i) = fld.sq_root (item (i) );
|
||||
}
|
||||
|
||||
void polynomial::div (polynomial&p, polynomial&m, gf2m&fld)
|
||||
{
|
||||
int degp = p.degree();
|
||||
if (degp < 0) return;
|
||||
|
||||
uint headInv = fld.inv (p[degp]);
|
||||
polynomial A = *this;
|
||||
A.mod (m, fld);
|
||||
clear();
|
||||
int da;
|
||||
while ( (da = A.degree() ) >= degp) {
|
||||
int rp = da - degp;
|
||||
if (size() < rp + 1) resize (rp + 1, 0);
|
||||
item (rp) = fld.mult (headInv, A[da]);
|
||||
for (uint i = 0; i <= degp; ++i)
|
||||
A[i+rp] = fld.add (A[i+rp], fld.mult (item (rp), p[i]) );
|
||||
}
|
||||
}
|
||||
|
||||
void polynomial::divmod (polynomial&d, polynomial&res, polynomial&rem, gf2m&fld)
|
||||
{
|
||||
int degd = d.degree();
|
||||
if (degd < 0) return;
|
||||
|
||||
uint headInv = fld.inv (d[degd]);
|
||||
rem = *this;
|
||||
res.clear();
|
||||
int t;
|
||||
while ( (t = rem.degree() ) >= degd) {
|
||||
int rp = t - degd;
|
||||
if (res.size() < rp + 1) res.resize (rp + 1, 0);
|
||||
res[rp] = fld.mult (headInv, rem[t]);
|
||||
for (uint i = 0; i <= degd; ++i)
|
||||
rem[i+rp] = fld.add (rem[i+rp], fld.mult (res[rp], d[i]) );
|
||||
}
|
||||
}
|
||||
|
||||
void polynomial::inv (polynomial&m, gf2m&fld)
|
||||
{
|
||||
polynomial a = *this;
|
||||
this->resize (2);
|
||||
item (0) = 0;
|
||||
item (1) = 1;
|
||||
div (a, m, fld);
|
||||
}
|
||||
|
||||
void polynomial::mod_to_fracton (polynomial&a, polynomial&b, polynomial&m, gf2m&fld)
|
||||
{
|
||||
int deg = m.degree() / 2;
|
||||
polynomial a0, a1, b0, b1, t1, t2;
|
||||
a0 = m;
|
||||
a0.make_monic (fld);
|
||||
a1 = *this;
|
||||
a1.mod (m, fld);
|
||||
b0.resize (1, 0);
|
||||
b1.resize (1, 1);
|
||||
while (a1.degree() > deg) {
|
||||
|
||||
a0.divmod (a1, t1, t2, fld);
|
||||
a0.swap (a1);
|
||||
a1.swap (t2);
|
||||
|
||||
t1.mult (b1);
|
||||
t1.mod (m);
|
||||
t1.add (b0);
|
||||
b0.swap (b1);
|
||||
b1.swap (t1);
|
||||
}
|
||||
a = a1;
|
||||
b = b1;
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user