Add files via upload

main
vovuas2003 7 months ago committed by GitHub
commit adfe360621
No known key found for this signature in database
GPG Key ID: B5690EEEBB952194

@ -0,0 +1,60 @@
#break cryptosystem if know a half of private key
import numpy as np
import galois
import pubkey
import privkey
import message
n = 127
k = 32
order = 2 ** 7
GF = galois.GF(order)
def main():
G_ = GF(pubkey.get()) #we need to know a public matrix
P = GF(privkey.get_P()) #and P - only one of two private matrices
S = break_S(P, G_) #to calculate S - the second part of private key
c = GF(message.get())
print(decode(S, P, c)) #and decode the message
def unpad_message(msg):
padding_byte = msg[-1]
for i in range(1, padding_byte + 1):
if msg[-i] != padding_byte:
raise ValueError("Incorrect padding!")
return msg[:-padding_byte]
def my_fix(A):
#make square matrix by deleting right columns
l = len(A)
r = GF.Zeros((l, l))
for i in range(l):
for j in range(l):
r[i][j] = A[i][j]
return r
def decode(S, P, c):
rs = galois.ReedSolomon(n, k, field=GF)
c = c @ np.linalg.inv(P)
c = rs.decode(c)
c = c @ np.linalg.inv(S)
c = [int(i) for i in c]
c = unpad_message(c)
c = bytes(c)
c = c.decode()
return c
def break_S(P, G_):
#G_ = S @ G @ P
rs = galois.ReedSolomon(n, k, field=GF)
G = rs.G
G_ = G_ @ np.linalg.inv(P)
G_ = my_fix(G_)
G = my_fix(G)
S = G_ @ np.linalg.inv(G)
return S
if __name__ == "__main__":
main()

@ -0,0 +1,37 @@
import numpy as np
import galois
import privkey
import message
n = 127
k = 32
order = 2 ** 7
GF = galois.GF(order)
def main():
S = GF(privkey.get_S())
P = GF(privkey.get_P())
c = GF(message.get())
print(decode(S, P, c))
def unpad_message(msg):
padding_byte = msg[-1]
for i in range(1, padding_byte + 1):
if msg[-i] != padding_byte:
raise ValueError("Incorrect padding!")
return msg[:-padding_byte]
def decode(S, P, c):
rs = galois.ReedSolomon(n, k, field=GF)
c = c @ np.linalg.inv(P)
c = rs.decode(c)
c = c @ np.linalg.inv(S)
c = [int(i) for i in c]
c = unpad_message(c)
c = bytes(c)
c = c.decode()
return c
if __name__ == "__main__":
main()

@ -0,0 +1,40 @@
import numpy as np
import galois
import pubkey
n = 127
k = 32
order = 2 ** 7
GF = galois.GF(order)
def main():
G_ = GF(pubkey.get())
print("Message to encode (max len = k-1 = 31):")
message = input()
if len(message) > k-1:
print("Message is too long!")
return
ct = encrypt(G_, message)
ct = list(map(int, ct))
export(ct)
print("Done!")
def pad_message(msg: bytes, pad_size: int) -> list[int]:
padding = pad_size - (len(msg) % pad_size)
return list(msg + padding.to_bytes() * padding)
def encrypt(G_, text):
msg = pad_message(text.encode(), k)
m = GF(msg)
c = m.T @ G_
return c
def export(ct):
output = "ct = [ " + ", ".join([str(int(cell)) for cell in ct]) + " ]"
with open("message.py", "w") as f:
f.write(output)
f.write("\ndef get():\n\treturn ct")
if __name__ == "__main__":
main()

@ -0,0 +1,58 @@
import numpy as np
import galois
import random
n = 127
k = 32
order = 2 ** 7
GF = galois.GF(order)
def main():
S = generate_S()
G = generate_G()
P = generate_P()
G_ = S @ G @ P
export_pubkey(G_)
export_privkey(S, P)
print("Done!")
def generate_S():
S = GF.Random((k, k))
while np.linalg.det(S) == 0:
S = GF.Random((k, k))
return S
def generate_G():
rs = galois.ReedSolomon(n, k, field=GF)
G = rs.G
return G
def generate_P():
r = [i for i in range(n)]
p = []
for i in range(n):
p.append(r.pop(random.randint(0, n - 1 - i)))
P = GF.Zeros((n, n))
for i in range(n):
P[i, p[i]] = 1
return P
def export_pubkey(G_):
rows = [", ".join([str(int(cell)) for cell in row]) for row in G_]
output = "G_ = [ " + ",\n".join([f"[{row}]" for row in rows]) + " ]"
with open("pubkey.py", "w") as f:
f.write(output)
f.write("\ndef get():\n\treturn G_")
def export_privkey(S, P):
rows = [", ".join([str(int(cell)) for cell in row]) for row in S]
output = "S = [ " + ",\n".join([f"[{row}]" for row in rows]) + " ]\n"
rows = [", ".join([str(int(cell)) for cell in row]) for row in P]
output += "P = [ " + ",\n".join([f"[{row}]" for row in rows]) + " ]\n"
with open("privkey.py", "w") as f:
f.write(output)
f.write("\ndef get_S():\n\treturn S")
f.write("\ndef get_P():\n\treturn P")
if __name__ == "__main__":
main()

@ -0,0 +1,13 @@
McEliece cryptosystem implementation
Usage:
0. pip install numpy and galois
1. generate.py - generate and save public and private keys
2. send pubkey.py and encode.py to your friend
3. your friend runs encode.py, write secret string and send message.py to you
4. decode.py - get secret string
Hacker can get your private key if he will know a half of it (and pubkey.py, decode.py and Reed-Solomon algo).
Check break.py to understand how hacker can do this.
todo: check randomization during encode (add vector z, check https://en.wikipedia.org/wiki/McEliece_cryptosystem)
Loading…
Cancel
Save