A Code-specific Conservative Model for the Failure Rate of Bit-flipping  Decoding of LDPC Codes with Cryptographic Applications

Paolo Santini; Alessandro Barenghi; Gerardo Pelosi; Marco Baldi; Franco Chiaraluce

Paper 2019/1441

A Code-specific Conservative Model for the Failure Rate of Bit-flipping Decoding of LDPC Codes with Cryptographic Applications

Paolo Santini, Alessandro Barenghi, Gerardo Pelosi, Marco Baldi, and Franco Chiaraluce

Abstract

Characterizing the decoding failure rate of iteratively decoded Low- and Moderate-Density Parity Check (LDPC/MDPC) codes is paramount to build cryptosystems based on them, able to achieve indistinguishability under adaptive chosen ciphertext attacks. In this paper, we provide a statistical worst-case analysis of our proposed iterative decoder obtained through a simple modification of the classic in-place bit-flipping decoder. This worst case analysis allows both to derive the worst-case behavior of an LDPC/MDPC code picked among the family with the same length, rate and number of parity checks, and a code-specific bound on the decoding failure rate. The former result allows us to build a code-based cryptosystem enjoying the $\delta$-correctness property required by IND-CCA2 constructions, while the latter result allows us to discard code instances which may have a decoding failure rate significantly different from the average one (i.e., representing weak keys), should they be picked during the key generation procedure.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Bit-flipping decoding cryptography decoding failure rate LDPC codes MDPC codes weak keys
Contact author(s): alessandro barenghi @ polimi it
History: 2019-12-12: received
Short URL: https://ia.cr/2019/1441
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1441,
      author = {Paolo Santini and Alessandro Barenghi and Gerardo Pelosi and Marco Baldi and Franco Chiaraluce},
      title = {A Code-specific Conservative Model for the Failure Rate of Bit-flipping  Decoding of {LDPC} Codes with Cryptographic Applications},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1441},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1441}
}