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Hack.lu CTF 2017 - McEliece
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''' | |
Attacking McEliece with Generalized Reed-Solomon codes (GRS), method by Sidelnikov & Shestakov. | |
The task is almost the same as The Russian Attack from Sharif CTF: | |
http://ctf.sharif.edu/blog/Write-Ups/SharifCTF-6/Crypto/08.%20The%20Russian%20Attack%20(500%20+%20300%20pts)/ | |
The only change is the field changed from GF(p) to GF(2^8). | |
Here is Sage analogue of the GAP script, because finally Sage supports GRS decoding. | |
''' | |
from sage.all import * | |
ct = load("ciphertext.sobj") | |
pk = load("publickey.sobj") | |
k, n = pk.dimensions() | |
F = ct[0].parent() | |
M = pk.echelon_form() | |
for c01 in F: | |
if c01 == 0: | |
continue | |
alpha = [None] * n | |
# we can set this w.l.o.g | |
alpha[0] = 0 | |
alpha[1] = 1 | |
# First stage: get alpha[k..n-1] | |
good = 1 | |
for j in xrange(k, n): | |
b01 = M[0,j] / M[1,j] | |
if c01 == b01: | |
good = 0 | |
break | |
alpha[j] = c01 / (c01 - b01) | |
if not good: | |
print c01, ":", "FAIL" | |
continue | |
# Second stage: get alpha[2..k-1] | |
for i in xrange(2, k): | |
p = k | |
q = k + 1 | |
while 1: | |
bp = M[0,p] / M[i,p] | |
bq = M[0,q] / M[i,q] | |
A = bp * (alpha[p] - alpha[0]) | |
A /= bq * (alpha[q] - alpha[0]) | |
if A == 1: | |
p += 1 | |
q += 1 | |
if q == n: | |
break | |
continue | |
alpha[i] = (A * alpha[q] - alpha[p]) / (A - 1) | |
break | |
# if guessed completely | |
if alpha.count(None) == 0: | |
print c01, ":", "Got full alpha." | |
C = codes.GeneralizedReedSolomonCode(alpha, k) | |
D = codes.decoders.GRSBerlekampWelchDecoder(C) | |
try: | |
res = pk.solve_left(D.decode_to_code(ct)) | |
print " ", "message vector:", res | |
msg = "".join(map(chr, [v.integer_representation() for v in res])) | |
print " ", "message:", `msg` | |
except: | |
print "no decoding..." |
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