def Inv_gcd(a, b):
r0, r1, s0, s1 = 1, 0, 0, 1
while b:
qt, rt = division(a, b)
q, a, b = qt, b, rt
r0, r1 = r1, r0 ^ int(mul(hex(q)[2:], hex(r1)[2:], '11B'), 16)
s0, s1 = s1, s0 ^ int(mul(hex(q)[2:], hex(s1)[2:], '11B'), 16)
return s0
def inv(column):
fixedmatrix = bytearray([0x0e, 0x0b, 0x0d, 0x09])
mixcolumnmatrix = bytearray()
for i in range(0, 4):
resultinglist = []
rijndael = gf.makeblist(0x11b)
for j in range(0, 4):
fixedbitlist = gf.makeblist(fixedmatrix[j])
columnvector = gf.makeblist(column[j])
resultingbyte = gf.mul(fixedbitlist, columnvector)
while gf.value(resultingbyte) > 255:
# note the inverted division function!
resultingbyte = gf.div(rijndael, resultingbyte)[1]
resultinglist.append(resultingbyte)
finalvalue = gf.add(resultinglist[0], resultinglist[1])
finalvalue = gf.add(finalvalue, resultinglist[2])
finalvalue = gf.add(finalvalue, resultinglist[3])
mixcolumnmatrix.append(gf.value(finalvalue))
fixedmatrix = gf.circrotateright(fixedmatrix)
return mixcolumnmatrix
def mix(column):
fixedmatrix = bytearray([0x02, 0x03, 0x01, 0x01])
mixcolumnmatrix = bytearray()
for i in range(4):
resultinglist = []
rijndael = gf.makeblist(0x11b)
for j in range(4):
fixedbytelist = gf.makeblist(fixedmatrix[j])
columnvector = gf.makeblist(column[j])
resultingbyte = gf.mul(fixedbytelist, columnvector)
if gf.value(resultingbyte) > 255:
resultingbyte = gf.div(resultingbyte, rijndael)[1]
resultinglist.append(resultingbyte)
finalvalue = gf.add(resultinglist[0], resultinglist[1])
finalvalue = gf.add(finalvalue, resultinglist[2])
finalvalue = gf.add(finalvalue, resultinglist[3])
mixcolumnmatrix.append(gf.value(finalvalue))
fixedmatrix = gf.circrotateright(fixedmatrix)
return mixcolumnmatrix
def recover2d_s0s1(D, failed): n = len(D) - ns j = failed[0] k = failed[1] old_s0 = D[-2] old_s1 = D[-1] new_s0 = calc_s0(D) new_s1 = calc_s1(D) x1 = gf.inv(gf.pow(n - k - 1)) x2 = gf.inv(gf.pow(k - j) ^ 1) Dj = gf.mul((gf.mul(old_s1 ^ new_s1, x1) ^ old_s0 ^ new_s0), x2) Dk = old_s0 ^ new_s0 ^ Dj return Dj, Dk
def recover1d_s1(D, failed): n = len(D) - ns new_s1 = calc_s1(D) old_s1 = D[-1] x = gf.pow(n - failed - 1) x1 = gf.inv(x) return gf.mul(new_s1 ^ old_s1, x1)
def sdc_detect(D): n = len(D) - ns old_s0 = D[-2] old_s1 = D[-1] new_s0 = calc_s0(D) new_s1 = calc_s1(D) if new_s0 == old_s0 and new_s1 == old_s1: return -1 j = n - 1 - gf.log( gf.mul((old_s1 ^ new_s1), gf.inv(old_s0 ^ new_s0)) ) D[j] = old_s0 ^ new_s0 ^ D[j] return j
def maketable():
rcontable = []
rcontable.append([1, 0, 0, 0, 1, 1, 0, 1]) # rcon[0]
rcon = gf.makeblist(0x01)
rijn = gf.makeblist(0x11b)
for i in range(52):
rcontable.append(rcon)
# this is actually a leftwise shift, multiply by 2
rcon = gf.mul(rcon, [0, 0, 0, 0, 0, 0, 1, 0])
if gf.value(rcon) > 255:
# take the remainder from division operation (modulus)
rcon = gf.div(rcon, rijn)[1]
return rcontable
\t\t\t[4] A(x) / B(x)
\t\t\t[5] Change Values
\t\t\t[6] Exit
\t\t--------------------------------
"""
while True:
try:
op = input("\t\t\t\tCHOOSE AN OPERATION: ")
break
except SyntaxError:
print "\n\t\t\t\tPlease input a valid choice.\n"
if op == 1 or op == 2:
gf.printGiven(Ax, Bx, Px)
gf.printPoly(gf.addOrSub(Ax, Bx, op, 1))
elif op == 3:
gf.printGiven(Ax, Bx, Px)
gf.printPoly(gf.mul(Ax, Bx, Px, 1))
elif op == 4:
gf.printGiven(Ax, Bx, Px)
quo, rem = gf.div(Ax, Bx, Px, 1)
gf.printPoly(quo)
print "\t\t\t\tRemainder = ",
gf.printPoly(rem)
elif op == 5:
break
elif op == 6:
print "\n\t\t\t\t\tAu Revoir!\n"
exit()
else:
print "\n\t\t\t\tInvalid choice. Input 1 - 6 only.\n"