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polynomial fixes

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irreducibility, goppa check matrix
This commit is contained in:
Mirek Kratochvil 2012-04-08 14:09:44 +02:00
parent b4381c473e
commit 781ea21513
2 changed files with 29 additions and 26 deletions
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1
include/codecrypt.h
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@ -134,6 +134,7 @@ public:
void strip(); void strip();
int degree() const; int degree() const;
bool zero() const; bool zero() const;
bool one() const;
void shift (uint); void shift (uint);
uint eval (uint, gf2m&) const; uint eval (uint, gf2m&) const;

54
lib/polynomial.cpp
View file

@ -21,6 +21,12 @@ bool polynomial::zero() const
return true; return true;
} }
bool polynomial::one() const
{
if (degree() != 0) return false;
return item (0) == 1;
}
void polynomial::add (const polynomial&f, gf2m&fld) void polynomial::add (const polynomial&f, gf2m&fld)
{ {
int df = f.degree(); int df = f.degree();
@ -107,14 +113,17 @@ bool polynomial::is_irreducible (gf2m&fld) const
uint d = degree(); uint d = degree();
for (uint i = 1; i <= d / 2; ++i) { for (uint i = 1; i <= d / 2; ++i) {
for (uint j = 0; j < fld.m; ++j) {
t = xi;
t.mult (xi, fld);
t.mod (*this, fld);
xi.swap (t);
}
t = xi; t = xi;
t.mult (xi, fld); //because mult would destroy xi on xi.mult(xi)
t.mod (*this, fld);
xi = t;
t.add (xmodf, fld); t.add (xmodf, fld);
t = t.gcd (*this, fld); t = t.gcd (*this, fld);
if (t.degree() > 0) //gcd(f,x^2^i - x mod f) is polynomial if (t.degree() > 0) //gcd(f,x^2^i - x mod f) != const
return false; return false;
} }
return true; return true;
@ -124,7 +133,7 @@ void polynomial::generate_random_irreducible (uint s, gf2m&fld, prng& rng)
{ {
resize (s + 1); resize (s + 1);
item (s) = 1; //degree s item (s) = 1; //degree s
item (0) = 1 + rng.random (fld.n - 1); //not divisible by x^1 item (0) = 1 + rng.random (fld.n - 1);
for (uint i = 1; i < s; ++i) item (i) = rng.random (fld.n); for (uint i = 1; i < s; ++i) item (i) = rng.random (fld.n);
while (!is_irreducible (fld) ) { while (!is_irreducible (fld) ) {
uint pos = rng.random (s); uint pos = rng.random (s);
@ -216,32 +225,26 @@ void polynomial::compute_goppa_check_matrix (matrix&r, gf2m&fld)
{ {
if (degree() < 0) return; //wrongly initialized polynomial if (degree() < 0) return; //wrongly initialized polynomial
uint t = degree(); uint t = degree();
vector<vector<uint> > yz, h; vector<vector<uint> > h;
uint i, j, k; uint i, j;
yz.resize (t);
h.resize (t); //construction from Sendrier's slides with maximal support L=[0..fld.n)
for (i = 0; i < t; ++i) { h.resize (fld.n);
yz[i].resize (fld.n); for (i = 0; i < fld.n; ++i) {
h[i].resize (fld.n, 0); h[i].resize (t);
h[i][0] = fld.inv (eval (i, fld) );
if(h[i][0]==0) std::cout << "BLE" << std::endl;
} }
//create Y*Z //compute support powers
for (i = 0; i < fld.n; ++i) yz[0][i] = fld.inv (eval (i, fld) ); for (j = 0; j < fld.n; ++j) for (i = 1; i < t; ++i)
for (i = 1; i < t; ++i) for (j = 0; j < fld.n; ++j) h[j][i] = fld.mult (h[j][i-1], j);
yz[i][j] = fld.mult (yz[i-1][j], j);
//X*Y*Z = h
for (i = 0; i < t; ++i)
for (j = 0; j < fld.n; ++j)
for (k = 0; k <= i; ++k)
h[i][j] = fld.add (h[i][j], fld.mult
(yz[k][j],
item (t + k - i) ) );
//now convert to binary //now convert to binary
r.resize (fld.n); r.resize (fld.n);
for (i = 0; i < fld.n; ++i) { for (i = 0; i < fld.n; ++i) {
r[i].resize (fld.m * t, 0); r[i].resize (fld.m * t);
for (j = 0; j < fld.m * t; ++j) for (j = 0; j < fld.m * t; ++j)
r[i][j] = (h[j/fld.m][i] >> (j % fld.m) ) & 1; r[i][j] = (h[i][j/fld.m] >> (j % fld.m) ) & 1;
} }
} }
@ -278,7 +281,6 @@ void polynomial::div (polynomial&p, polynomial&m, gf2m&fld)
polynomial r0, r1, s0, s1, s2, q1, q2; polynomial r0, r1, s0, s1, s2, q1, q2;
r0 = m; r0 = m;
r1 = p; r1 = p;
r1.mod (m, fld); r1.mod (m, fld);