Quick Math

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WriteUp来源

https://dunsp4rce.github.io/csictf-2020/crypto/2020/07/21/Quick-Math.html

by anishbadhri

题目描述

Ben has encrypted a message with the same value of 'e' for 3 public moduli n1 = 86812553978993 n2 = 81744303091421 n3 = 83695120256591 and got the cipher texts c1 = 8875674977048 c2 = 70744354709710 c3 = 29146719498409 Find the original message. (Wrap it with csictf{})

题目考点

• RSA e过小

解题思路

The given problem is a typical example of hastad attack. Given 3 pairs of n and c with the same value of e=3, the original message can be decoded.

from pwn import remote
from sympy.ntheory.modular import crt
from gmpy2 import iroot
e = 3
N = [86812553978993, 81744303091421, 83695120256591]
C = [8875674977048, 70744354709710, 29146719498409]
resultant, mod = crt(N,C)
value, is_perfect = iroot(resultant,e)
print(bytes.fromhex(str(value)).decode())

Flag

csictf{h45t4d}