Paper 2012/409

MDPC-McEliece: New McEliece Variants from Moderate Density Parity-Check Codes

Rafael Misoczki, Jean-Pierre Tillich, Nicolas Sendrier, and Paulo S. L. M. Barreto

Abstract

In this work, we propose two McEliece cryptosystem variants: one from Moderate Density Parity-Check (MDPC) codes and another from quasi-cyclic MDPC codes. MDPC codes are LDPC codes of higher density than what is usually adopted for telecommunication applications. In general, this leads to a worse error-correction capability. However, in code-based cryptography we are not necessarily interested in correcting many errors, but only a number which ensures an adequate security level, a condition satisfied by MDPC codes. The benefits of their employment are many. Under a reasonable assumption, MDPC codes reduce the key-distinguishing McEliece problem to the problem of decoding linear codes. Since the message-attacks against the McEliece scheme also reduce to this problem, the security of our scheme has the benefit of relying on a single, well studied coding-theory problem. Furthermore, adding a quasi-cyclic structure, our proposal provides extremely compact-keys: for $80$-bits of security, the public-key has only $4801$ bits.

Note: To be in accordance with the submitted version (ISIT).