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gf2matrix.py
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gf2matrix.py
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# gf2matrix.py
#
# Copyright (C) 2017 David Johnston
#
# This program is distributed under the terms of the GNU General Public License.
#
# This file is part of sp800_22_tests.
#
# sp800_22_tests is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# sp800_22_tests is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with sp800_22_tests. If not, see <http://www.gnu.org/licenses/>.
from __future__ import print_function
import copy
MATRIX_FORWARD_ELIMINATION = 0
MATRIX_BACKWARD_ELIMINATION = 1
def print_matrix(matrix):
#print "PRINT MATRIX"
#print "len matrix = ",str(len(matrix))
#for line in matrix:
# print line
for i in range(len(matrix)):
#print "Line %d" % i
line = matrix[i]
#print "Line %d = %s" % (i,str(line))
if i==0:
astr = "["+str(line)+" : "
else:
astr += " "+str(line)+" : "
for ch in line:
astr = astr + str(ch)
if i == (len(matrix)-1):
astr += "]"
else:
astr = astr + "\n"
print(astr)
#print "END PRINT MATRIX"
def row_echelon(M,Q,matrix,blknum):
lm = copy.deepcopy(matrix)
pivotstartrow = 0
pivotstartcol = 0
for i in range(Q):
# find pivotrow
found = False
for k in range(pivotstartrow,Q):
if lm[k][pivotstartcol] == 1:
found = True
pivotrow = k
break
if found:
# Swap with pivot
if pivotrow != pivotstartrow:
lm[pivotrow],lm[pivotstartrow] = lm[pivotstartrow],lm[pivotrow]
# eliminate lower triangle column
for j in range(pivotstartrow+1,Q):
if lm[j][pivotstartcol]==1:
lm[j] = [x ^ y for x,y in zip(lm[pivotstartrow],lm[j])]
pivotstartcol += 1
pivotstartrow += 1
else:
pivotstartcol += 1
return lm
def rank(M,Q,matrix,blknum):
lm = row_echelon(M,Q,matrix,blknum)
rank = 0
for i in range(Q):
nonzero = False
for bit in lm[i]:
if bit == 1:
nonzero = True
if nonzero:
rank += 1
return rank
def computeRank(M, Q, matrix):
m = min(M,Q)
localmatrix = copy.deepcopy(matrix)
# FORWARD APPLICATION OF ELEMENTARY ROW OPERATIONS
for i in range(m-1):
if ( localmatrix[i][i] == 1 ):
localmatrix = perform_elementary_row_operations(MATRIX_FORWARD_ELIMINATION, i, M, Q, localmatrix)
else: # localmatrix[i][i] = 0
row_op,localmatrix = find_unit_element_and_swap(MATRIX_FORWARD_ELIMINATION, i, M, Q, localmatrix)
if row_op == 1:
localmatrix = perform_elementary_row_operations(MATRIX_FORWARD_ELIMINATION, i, M, Q, localmatrix)
# BACKWARD APPLICATION OF ELEMENTARY ROW OPERATIONS
for i in range(m-1,0,-1):
#for ( i=m-1; i>0; i-- ) {
if ( localmatrix[i][i] == 1 ):
localmatrix = perform_elementary_row_operations(MATRIX_BACKWARD_ELIMINATION, i, M, Q, localmatrix)
else: # matrix[i][i] = 0
row_op,localmatrix = find_unit_element_and_swap(MATRIX_BACKWARD_ELIMINATION, i, M, Q, localmatrix)
if row_op == 1:
localmatrix = perform_elementary_row_operations(MATRIX_BACKWARD_ELIMINATION, i, M, Q, localmatrix)
#for aline in localmatrix:
# print " UUU : ",aline
#print
rank = determine_rank(m, M, Q, localmatrix)
return rank
def perform_elementary_row_operations(flag, i, M, Q, A):
j = 0
k = 0
if ( flag == MATRIX_FORWARD_ELIMINATION ):
for j in range(i+1,M):
#for ( j=i+1; j<M; j++ )
if ( A[j][i] == 1 ):
for k in range(i,Q):
#for ( k=i; k<Q; k++ )
A[j][k] = (A[j][k] + A[i][k]) % 2
else:
#for ( j=i-1; j>=0; j-- )
for j in range(i-1,-1,-1):
if ( A[j][i] == 1 ):
for k in range(Q):
#for ( k=0; k<Q; k++ )
A[j][k] = (A[j][k] + A[i][k]) % 2
return A
def find_unit_element_and_swap(flag, i, M, Q, A):
index = 0
row_op = 0
if ( flag == MATRIX_FORWARD_ELIMINATION ):
index = i+1
while ( (index < M) and (A[index][i] == 0) ):
index += 1
if ( index < M ):
row_op = 1
A = swap_rows(i, index, Q, A)
else:
index = i-1
while ( (index >= 0) and (A[index][i] == 0) ):
index = index -1
if ( index >= 0 ):
row_op = 1
A = swap_rows(i, index, Q, A)
return row_op,A
def swap_rows(i, index, Q, A):
A[i],A[index] = A[index],A[i]
#for p in xrange(Q):
# temp = A[i][p]
# A[i][p] = A[index][p]
# A[index][p] = temp
return A
def determine_rank(m, M, Q, A):
i = 0
j = 0
rank = 0
allZeroes = 0
# DETERMINE RANK, THAT IS, COUNT THE NUMBER OF NONZERO ROWS
rank = m
for i in range(M):
#for ( i=0; i<M; i++ ) {
allZeroes = 1
for j in range(Q):
#for ( j=0; j<Q; j++) {
if ( A[i][j] == 1 ):
allZeroes = 0
#break
if ( allZeroes == 1 ):
rank -= 1
return rank
def create_matrix(M, Q):
matrix = list()
for rownum in range(Q):
row = [0 for x in range(M)]
matrix.append(row)
return matrix
def matrix_from_bits(M,Q,bits,blknum):
m = list()
for rownum in range(Q):
row = bits[rownum*M:(rownum+1)*M]
m.append(row)
return m[:]