## Cryptology ePrint Archive: Report 2019/1441

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

Paolo Santini and Alessandro Barenghi and Gerardo Pelosi and 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.

Category / Keywords: public-key cryptography / Bit-flipping decoding, cryptography, decoding failure rate, LDPC codes, MDPC codes, weak keys

Contact author: alessandro barenghi at polimi it

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/1441

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