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A key recovery attack on MDPC with CCA security using decoding errors

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Author

Summary, in English

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 QCMDPC 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.

Publishing year

2016

Language

English

Pages

789-815

Publication/Series

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volume

10031 LNCS

Document type

Conference paper

Publisher

Springer

Topic

  • Computer Science

Keywords

  • CCA-security
  • Key-recovery attack
  • Post-quantum cryptography
  • QC-MDPC
  • Reaction attack

Conference name

22nd Annual International Conference on the Theory and Applications of Cryptology and Information Security (ASIACRYPT), 2016

Conference date

2016-12-04 - 2016-12-08

Conference place

Hanoi, Viet Nam

Status

Published

ISBN/ISSN/Other

  • ISSN: 03029743
  • ISSN: 16113349
  • ISBN: 9783662538869