A Key Recovery Attack on MDPC with CCA Security Using Decoding Errors

Qian Guo; Thomas Johansson; Paul Stankovski

Paper 2016/858

A Key Recovery Attack on MDPC with CCA Security Using Decoding Errors

Qian Guo, Thomas Johansson, and Paul Stankovski

Abstract

Algorithms for secure encryption in a post-quantum world are currently receiving a lot of attention in the research community, including several larger projects and a standardization effort from NIST. One of the most promising algorithms is the code-based scheme called QC-MDPC, which has excellent performance and a small public key size. In this work we present a very efficient key recovery attack on the QC-MDPC scheme using the fact that decryption uses an iterative decoding step and this can fail with some small probability. We identify a dependence between the secret key and the failure in decoding. This can be used to build what we refer to as a distance spectrum for the secret key, which is the set of all distances between any two ones in the secret key. In a reconstruction step we then determine the secret key from the distance spectrum. The attack has been implemented and tested on a proposed instance of QC-MDPC for 80 bit security. It successfully recovers the secret key in minutes. A slightly modified version of the attack can be applied on proposed versions of the QC-MDPC scheme that provides IND-CCA security. The attack is a bit more complex in this case, but still very much below the security level. The reason why we can break schemes with proved CCA security is that the model for these proofs typically does not include the decoding error possibility.

Metadata

Available format(s): PDF
Publication info: Published by the IACR in ASIACRYPT 2016
Keywords: CCA-security key-recovery attack post-quantum cryptography QC-MDPC reaction attack.
Contact author(s): qian guo @ eit lth se
thomas johansson @ eit lth se
paul stankovski @ eit lth se
fywzguoqian @ gmail com
History: 2016-09-08: received
Short URL: https://ia.cr/2016/858
License: CC BY

BibTeX

@misc{cryptoeprint:2016/858,
      author = {Qian Guo and Thomas Johansson and Paul Stankovski},
      title = {A Key Recovery Attack on {MDPC} with {CCA} Security Using Decoding Errors},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/858},
      year = {2016},
      url = {https://eprint.iacr.org/2016/858}
}