/**
@brief Test sieve by checking if function returns correct vector.
@param A input lattice
@param b shortest vector
@return
*/
template <class ZT> int test_sieve_alg(ZZ_mat<ZT> &A, IntVect &b, int alg)
{
GaussSieve<ZT, FP_NR<double>> gsieve(A, alg, 0, 0);
Z_NR<ZT> goal_norm;
goal_norm = 0;
gsieve.set_goal_norm2(goal_norm);
if (gsieve.alg == 3)
gsieve.run_3sieve();
else if (gsieve.alg == 4)
gsieve.run_4sieve();
else
gsieve.run_2sieve();
NumVect<Z_NR<ZT>> v = gsieve.return_first();
Z_NR<ZT> tmp;
Z_NR<ZT> norm_s;
Z_NR<ZT> norm_b;
for (int i = 0; i < A.get_cols(); i++)
{
tmp.mul(v[i], v[i]);
norm_s.add(norm_s, tmp);
tmp.mul(b[i], b[i]);
norm_b.add(norm_b, tmp);
}
if (norm_s != norm_b)
return 1;
return 0;
}
template <> int hkz(Options &o, ZZ_mat<mpz_t> &b)
{
const char *format = o.output_format ? o.output_format : "b";
int flags = 0;
if (o.verbose)
flags |= HKZ_VERBOSE;
string dump_gso_filename;
if (o.bkz_flags & BKZ_DUMP_GSO) {
dump_gso_filename = o.bkz_dump_gso_filename;
flags |= BKZ_DUMP_GSO;
}
//int status = hkz_reduction(b, flags, o.float_type, o.precision, dump_gso_filename);
int status = hkz_reduction(b, flags, o.float_type, o.precision);
for (int i = 0; format[i]; i++)
{
if (format[i] == 'b')
{
if (format[i + 1] == 'k')
{
b.print_comma(cout);
i++;
}
else
cout << b << endl;
}
}
if (status != RED_SUCCESS)
{
cerr << "Failure: " << get_red_status_str(status) << endl;
}
return status;
}
/**
@brief Test if dual SVP reduction returns reduced basis.
@param A input lattice
@param b shortest dual vector
@return
*/
template <class ZT> int test_dsvp_reduce(ZZ_mat<ZT> &A, IntVect &b)
{
IntMatrix u;
int d = A.get_rows();
Float normb;
if (dual_length(normb, A, b))
{
return 1;
}
int status =
lll_reduction(A, u, LLL_DEF_DELTA, LLL_DEF_ETA, LM_WRAPPER, FT_DEFAULT, 0, LLL_DEFAULT);
if (status != RED_SUCCESS)
{
cerr << "LLL reduction failed: " << get_red_status_str(status) << endl;
return status;
}
IntMatrix empty_mat;
MatGSO<Integer, Float> gso(A, empty_mat, empty_mat, GSO_INT_GRAM);
LLLReduction<Integer, Float> lll_obj(gso, LLL_DEF_DELTA, LLL_DEF_ETA, LLL_DEFAULT);
vector<Strategy> strategies;
BKZParam dummy(d, strategies);
BKZReduction<Float> bkz_obj(gso, lll_obj, dummy);
bool clean = true;
bkz_obj.svp_reduction_ex(0, d, dummy, clean, true);
status = bkz_obj.status;
if (status != RED_SUCCESS)
{
cerr << "Failure: " << get_red_status_str(status) << endl;
return status;
}
Float norm_sol;
Integer zero;
zero = 0;
IntVect e_n(d, zero);
e_n[d - 1] = 1;
if (dual_length(norm_sol, A, e_n))
{
return 1;
}
Float error;
error = 1;
error.mul_2si(error, -(int)error.get_prec());
normb += error;
if (norm_sol > normb)
{
cerr << "Last dual vector too long by more than " << error << endl;
return 1;
}
return 0;
}
/**
@brief Compute the norm of a dual vector (specified by coefficients in the dual basis).
@param A input lattice
@param b coefficients of shortest dual vector
@return
*/
template <class ZT> int dual_length(Float &norm, ZZ_mat<ZT> &A, const IntVect &coords)
{
int d = coords.size();
if (A.get_rows() != d)
{
cerr << "DSVP length error: Coefficient vector has wrong dimension: ";
cerr << A.get_rows() << " vs " << d << endl;
return 1;
}
FloatVect coords_d(d);
for (int i = 0; i < d; i++)
{
coords_d[i] = coords[i].get_d();
}
IntMatrix empty_mat;
MatGSO<Integer, Float> gso(A, empty_mat, empty_mat, GSO_INT_GRAM);
if (!gso.update_gso())
{
cerr << "GSO Failure." << endl;
return 1;
}
Float tmp;
gso.get_r(tmp, d - 1, d - 1);
tmp.pow_si(tmp, -1);
FloatVect alpha(d);
Float mu, alpha2, r_inv;
norm = 0.0;
for (int i = 0; i < d; i++)
{
alpha[i] = coords_d[i];
for (int j = 0; j < i; j++)
{
gso.get_mu(mu, i, j);
alpha[i] -= mu * alpha[j];
}
gso.get_r(r_inv, i, i);
r_inv.pow_si(r_inv, -1);
alpha2.pow_si(alpha[i], 2);
norm += alpha2 * r_inv;
}
return 0;
}
template <class ZT> int test_svp(ZZ_mat<ZT> &A, IntVect &b)
{
IntVect sol_coord; // In the LLL-reduced basis
IntVect sol_coord2; // In the initial basis
IntVect solution;
IntMatrix u;
int status =
lll_reduction(A, u, LLL_DEF_DELTA, LLL_DEF_ETA, LM_WRAPPER, FT_DEFAULT, 0, LLL_DEFAULT);
if (status != RED_SUCCESS)
{
cerr << "LLL reduction failed: " << get_red_status_str(status) << endl;
return status;
}
status = shortest_vector(A, sol_coord, SVPM_PROVED, SVP_DEFAULT);
if (status != RED_SUCCESS)
{
cerr << "Failure: " << get_red_status_str(status) << endl;
return status;
}
vector_matrix_product(sol_coord2, sol_coord, u);
vector_matrix_product(solution, sol_coord, A);
Z_NR<ZT> tmp;
Z_NR<ZT> norm_s;
Z_NR<ZT> norm_b;
for (int i = 0; i < A.get_cols(); i++)
{
tmp.mul(solution[i], solution[i]);
norm_s.add(norm_s, tmp);
tmp.mul(b[i], b[i]);
norm_b.add(norm_b, tmp);
}
if (norm_s != norm_b)
return 1;
return 0;
}
template <class ZT> void zeros_last(ZZ_mat<ZT> &b, ZZ_mat<ZT> &u, ZZ_mat<ZT> &u_inv_t)
{
int i, d = b.get_rows();
for (i = 0; i < d && b[i].is_zero(); i++)
{
}
if (i > 0 && i < d)
{
b.rotate(0, i, d - 1);
if (!u.empty())
u.rotate(0, i, d - 1);
if (!u_inv_t.empty())
u_inv_t.rotate(0, i, d - 1);
}
}
template <class ZT> int lll(Options &o, ZZ_mat<ZT> &b)
{
// Stupid initialization of u and u_inv to be not empty.
ZZ_mat<ZT> u(1, 1), u_inv(1, 1);
const char *format = o.output_format ? o.output_format : "b";
int status, flags = 0;
if (o.verbose)
flags |= LLL_VERBOSE;
if (o.early_red)
flags |= LLL_EARLY_RED;
if (o.siegel)
flags |= LLL_SIEGEL;
if (strchr(format, 'v') != NULL)
{
// LLL-reduction with transform and inverse transform
status = lll_reduction(b, u, u_inv, o.delta, o.eta, o.method, o.float_type, o.precision, flags);
}
else if (strchr(format, 'u') != NULL)
{
// LLL-reduction with transform
status = lll_reduction(b, u, o.delta, o.eta, o.method, o.float_type, o.precision, flags);
}
else
{
status = lll_reduction(b, o.delta, o.eta, o.method, o.float_type, o.precision, flags);
}
for (int i = 0; format[i]; i++)
{
switch (format[i])
{
case 'b':
if (format[i + 1] == 'k')
{
b.print_comma(cout);
i++;
}
else
cout << b << endl;
break;
case 'u':
if (format[i + 1] == 'k')
{
u.print_comma(cout);
i++;
}
else
cout << u << endl;
break;
case 'v':
if (format[i + 1] == 'k')
{
u_inv.print_comma(cout);
i++;
}
else
cout << u_inv << endl;
break;
case 't':
cout << status << endl;
break;
case ' ':
cout << endl;
break;
}
}
if (status != RED_SUCCESS)
{
cerr << "Failure: " << get_red_status_str(status) << endl;
}
return status;
}
template <> int bkz(Options &o, ZZ_mat<mpz_t> &b)
{
CHECK(o.block_size > 0, "Option -b is missing");
vector<Strategy> strategies;
if (!o.bkz_strategy_file.empty())
{
strategies = load_strategies_json(strategy_full_path(o.bkz_strategy_file));
}
BKZParam param(o.block_size, strategies);
// Stupid initialization of u to be not empty.
ZZ_mat<mpz_t> u(1, 1);
const char *format = o.output_format ? o.output_format : "b";
int status;
param.delta = o.delta;
param.flags = o.bkz_flags;
if (o.bkz_flags & BKZ_DUMP_GSO)
param.dump_gso_filename = o.bkz_dump_gso_filename;
if (o.bkz_flags & BKZ_GH_BND)
param.gh_factor = o.bkz_gh_factor;
if (o.bkz_flags & BKZ_MAX_LOOPS)
param.max_loops = o.bkz_max_loops;
if (o.verbose)
param.flags |= BKZ_VERBOSE;
if (o.no_lll)
param.flags |= BKZ_NO_LLL;
status = bkz_reduction(&b, strchr(format, 'u') ? &u : NULL, param, o.float_type, o.precision);
for (int i = 0; format[i]; i++)
{
switch (format[i])
{
case 'b':
if (format[i + 1] == 'k')
{
b.print_comma(cout);
i++;
}
else
cout << b << endl;
break;
case 'u':
if (format[i + 1] == 'k')
{
u.print_comma(cout);
i++;
}
else
cout << u << endl;
break;
case 't':
cout << status << endl;
break;
case ' ':
cout << endl;
break;
}
}
if (status != RED_SUCCESS)
{
cerr << "Failure: " << get_red_status_str(status) << endl;
}
return status;
}
