Cryptology ePrint Archive: Report 2013/287

The failure of McEliece PKC based on Reed-Muller codes.

I. V. Chizhov and M. A. Borodin

Abstract: This paper describes new algorithm for breaking McEliece cryptosystem, built on Reed-Muller binary code $RM(r, m)$, which receives the private key from the public key. The algorithm has complexity $O(n^d+n^4log_2n)$ bit operations, where $n=2^m, d=\text{GCD}(r,m-1).$ In the case of $\text{GCD}(r,m-1)$ limitation, attack has polynomial complexity. Practical results of implementation show that McEliece cryptosystems, based on the code with length $n=65536$ bits, can be broken in less than 7 hours on a personal computer.

Category / Keywords: public-key cryptography / Reed-Muller binary code, McEliece cryptosystem

Date: received 15 May 2013

Contact author: bor1m at mail ru

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Version: 20130523:162149 (All versions of this report)

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