Interleaved Prange: A New Generic Decoder for Interleaved Codes

TL;DR

This paper introduces Interleaved Prange, a novel generic decoding algorithm for interleaved codes, improving decoding efficiency and providing insights into the security of interleaved code-based cryptographic schemes.

Contribution

It presents a new adaptation of Prange's information set decoding for interleaved codes, enhancing decoding performance and analysis.

Findings

Interleaved Prange outperforms simple decoding approaches.

The algorithm's complexity is thoroughly analyzed.

Results support the security assessment of interleaved code cryptosystems.

Abstract

Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem such new settings secure, we first need to understand and analyze the complexity of the underlying problem, in this case the problem of decoding a random interleaved code. A simple approach to decode such codes, would be to randomly choose a vector in the row span of the received matrix and run a classical information set decoding algorithm on this erroneous codeword. In this paper, we propose a new generic decoder for interleaved codes, which is an adaption of the classical idea of information set decoding by Prange and perfectly fits the interleaved setting. We then analyze the cost of the new algorithm and a comparison to the simple approach described above shows the superiority of Interleaved Prange.