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@hellman hellman/0_mceliece_grs.py
Last active Oct 19, 2017

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Hack.lu CTF 2017 - McEliece
'''
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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