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/*
* (C) Copyright Projet SECRET, INRIA, Rocquencourt
* (C) Bhaskar Biswas and Nicolas Sendrier
*
* (C) 2014 cryptosource GmbH
* (C) 2014 Falko Strenzke fstrenzke@cryptosource.de
* (C) 2015 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*
*/
#include <botan/mceliece.h>
#include <botan/internal/mce_internal.h>
#include <botan/internal/code_based_util.h>
#include <botan/polyn_gf2m.h>
#include <botan/loadstor.h>
namespace Botan {
namespace {
class binary_matrix final
{
public:
binary_matrix(size_t m_rown, size_t m_coln);
void row_xor(size_t a, size_t b);
secure_vector<size_t> row_reduced_echelon_form();
/**
* return the coefficient out of F_2
*/
uint32_t coef(size_t i, size_t j)
{
return (m_elem[(i) * m_rwdcnt + (j) / 32] >> (j % 32)) & 1;
}
void set_coef_to_one(size_t i, size_t j)
{
m_elem[(i) * m_rwdcnt + (j) / 32] |= (static_cast<uint32_t>(1) << ((j) % 32)) ;
}
void toggle_coeff(size_t i, size_t j)
{
m_elem[(i) * m_rwdcnt + (j) / 32] ^= (static_cast<uint32_t>(1) << ((j) % 32)) ;
}
size_t rows() const { return m_rown; }
size_t columns() const { return m_coln; }
private:
size_t m_rown; // number of rows.
size_t m_coln; // number of columns.
size_t m_rwdcnt; // number of words in a row
public:
// TODO this should be private
std::vector<uint32_t> m_elem;
};
binary_matrix::binary_matrix(size_t rown, size_t coln)
{
m_coln = coln;
m_rown = rown;
m_rwdcnt = 1 + ((m_coln - 1) / 32);
m_elem = std::vector<uint32_t>(m_rown * m_rwdcnt);
}
void binary_matrix::row_xor(size_t a, size_t b)
{
for(size_t i = 0; i != m_rwdcnt; i++)
{
m_elem[a*m_rwdcnt+i] ^= m_elem[b*m_rwdcnt+i];
}
}
//the matrix is reduced from LSB...(from right)
secure_vector<size_t> binary_matrix::row_reduced_echelon_form()
{
secure_vector<size_t> perm(m_coln);
for(size_t i = 0; i != m_coln; i++)
{
perm[i] = i; // initialize permutation.
}
uint32_t failcnt = 0;
size_t max = m_coln - 1;
for(size_t i = 0; i != m_rown; i++, max--)
{
bool found_row = false;
for(size_t j = i; !found_row && j != m_rown; j++)
{
if(coef(j, max))
{
if(i != j) //not needed as ith row is 0 and jth row is 1.
{
row_xor(i, j);//xor to the row.(swap)?
}
found_row = true;
}
}
//if no row with a 1 found then swap last column and the column with no 1 down.
if(!found_row)
{
perm[m_coln - m_rown - 1 - failcnt] = static_cast<int>(max);
failcnt++;
if(!max)
{
perm.resize(0);
}
i--;
}
else
{
perm[i+m_coln - m_rown] = max;
for(size_t j=i+1;j<m_rown;j++)//fill the column downwards with 0's
{
if(coef(j, max))
{
row_xor(j,i);//check the arg. order.
}
}
//fill the column with 0's upwards too.
for(size_t j = i; j != 0; --j)
{
if(coef(j - 1, max))
{
row_xor(j - 1, i);
}
}
}
}//end for(i)
return perm;
}
void randomize_support(std::vector<gf2m>& L, RandomNumberGenerator& rng)
{
for(size_t i = 0; i != L.size(); ++i)
{
gf2m rnd = random_gf2m(rng);
// no rejection sampling, but for useful code-based parameters with n <= 13 this seem tolerable
std::swap(L[i], L[rnd % L.size()]);
}
}
std::unique_ptr<binary_matrix> generate_R(std::vector<gf2m> &L, polyn_gf2m* g, std::shared_ptr<GF2m_Field> sp_field, size_t code_length, size_t t)
{
//L- Support
//t- Number of errors
//n- Length of the Goppa code
//m- The extension degree of the GF
//g- The generator polynomial.
const size_t r = t * sp_field->get_extension_degree();
binary_matrix H(r, code_length);
for(size_t i = 0; i != code_length; i++)
{
gf2m x = g->eval(lex_to_gray(L[i]));//evaluate the polynomial at the point L[i].
x = sp_field->gf_inv(x);
gf2m y = x;
for(size_t j=0;j<t;j++)
{
for(size_t k=0;k<sp_field->get_extension_degree();k++)
{
if(y & (1<<k))
{
//the co-eff. are set in 2^0,...,2^11 ; 2^0,...,2^11 format along the rows/cols?
H.set_coef_to_one(j*sp_field->get_extension_degree()+ k,i);
}
}
y = sp_field->gf_mul(y,lex_to_gray(L[i]));
}
}//The H matrix is fed.
secure_vector<size_t> perm = H.row_reduced_echelon_form();
if(perm.size() == 0)
{
throw Invalid_State("McEliece keygen failed - could not bring matrix to row reduced echelon form");
}
std::unique_ptr<binary_matrix> result(new binary_matrix(code_length-r, r)) ;
for(size_t i = 0; i < result->rows(); ++i)
{
for(size_t j = 0; j < result->columns(); ++j)
{
if(H.coef(j, perm[i]))
{
result->toggle_coeff(i,j);
}
}
}
std::vector<gf2m> Laux(code_length);
for(size_t i = 0; i < code_length; ++i)
{
Laux[i] = L[perm[i]];
}
for(size_t i = 0; i < code_length; ++i)
{
L[i] = Laux[i];
}
return result;
}
}
McEliece_PrivateKey generate_mceliece_key(RandomNumberGenerator & rng, size_t ext_deg, size_t code_length, size_t t)
{
const size_t codimension = t * ext_deg;
if(code_length <= codimension)
{
throw Invalid_Argument("invalid McEliece parameters");
}
std::shared_ptr<GF2m_Field> sp_field(new GF2m_Field(ext_deg));
//pick the support.........
std::vector<gf2m> L(code_length);
for(size_t i = 0; i != L.size(); i++)
{
L[i] = static_cast<gf2m>(i);
}
randomize_support(L, rng);
polyn_gf2m g(sp_field); // create as zero
bool success = false;
std::unique_ptr<binary_matrix> R;
do
{
// create a random irreducible polynomial
g = polyn_gf2m(t, rng, sp_field);
try
{
R = generate_R(L, &g, sp_field, code_length, t);
success = true;
}
catch(const Invalid_State &)
{
}
} while (!success);
std::vector<polyn_gf2m> sqrtmod = polyn_gf2m::sqrt_mod_init( g);
std::vector<polyn_gf2m> F = syndrome_init(g, L, static_cast<int>(code_length));
// Each F[i] is the (precomputed) syndrome of the error vector with
// a single '1' in i-th position.
// We do not store the F[i] as polynomials of degree t , but
// as binary vectors of length ext_deg * t (this will
// speed up the syndrome computation)
//
std::vector<uint32_t> H(bit_size_to_32bit_size(codimension) * code_length);
uint32_t* sk = H.data();
for(size_t i = 0; i < code_length; ++i)
{
for(size_t l = 0; l < t; ++l)
{
const size_t k = (l * ext_deg) / 32;
const uint8_t j = (l * ext_deg) % 32;
sk[k] ^= static_cast<uint32_t>(F[i].get_coef(l)) << j;
if(j + ext_deg > 32)
{
sk[k + 1] ^= F[i].get_coef(l) >> (32 - j);
}
}
sk += bit_size_to_32bit_size(codimension);
}
// We need the support L for decoding (decryption). In fact the
// inverse is needed
std::vector<gf2m> Linv(code_length) ;
for(size_t i = 0; i != Linv.size(); ++i)
{
Linv[L[i]] = static_cast<gf2m>(i);
}
std::vector<uint8_t> pubmat(R->m_elem.size() * 4);
for(size_t i = 0; i < R->m_elem.size(); i++)
{
store_le(R->m_elem[i], &pubmat[i*4]);
}
return McEliece_PrivateKey(g, H, sqrtmod, Linv, pubmat);
}
}