A Code-specific Conservative Model for the Failure Rate of Bit-flipping Decoding of LDPC Codes with Cryptographic Applications
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 behaviour 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 -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.
Cite
@article{arxiv.1912.05182,
title = {A Code-specific Conservative Model for the Failure Rate of Bit-flipping Decoding of LDPC Codes with Cryptographic Applications},
author = {Paolo Santini and Alessandro Barenghi and Gerardo Pelosi and Marco Baldi and Franco Chiaraluce},
journal= {arXiv preprint arXiv:1912.05182},
year = {2019}
}