Interleaved Prange: A New Generic Decoder for Interleaved Codes

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.