Alessandro Barenghi

Paolo Santini, Alessandro Barenghi, Gerardo Pelosi et al.

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 $δ$-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.

Marco Baldi, Alessandro Barenghi, Franco Chiaraluce et al.

In this paper we consider a post-quantum digital signature scheme based on low-density generator matrix codes and propose efficient algorithmic solutions for its implementation. We also review all known attacks against this scheme and derive closed-form estimates of their complexity when running over both classical and quantum computers. Based on these estimates, we propose new parametrization for the considered system to achieve given pre-quantum and post-quantum security levels. Finally, we provide and discuss performance benchmarks obtained through a suitably developed and publicly available reference implementation of the considered system.

Marco Baldi, Alessandro Barenghi, Franco Chiaraluce et al.

This work presents a new code-based key encapsulation mechanism (KEM) called LEDAkem. It is built on the Niederreiter cryptosystem and relies on quasi-cyclic low-density parity-check codes as secret codes, providing high decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known statistical attacks, and takes advantage of a new decoding algorithm that provides faster decoding than the classical bit-flipping decoder commonly adopted in this kind of systems. The main attacks against LEDAkem are investigated, taking into account quantum speedups. Some instances of LEDAkem are designed to achieve different security levels against classical and quantum computers. Some performance figures obtained through an efficient C99 implementation of LEDAkem are provided.