**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

**Available format(s): **PDF | BibTeX Citation

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

**Short URL: **ia.cr/2013/287

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