Abstract
The McEliece cryptosystem is a promising candidate for post-quantum public-key encryption. In this work, we propose q-ary codes over Gaussian integers for the McEliece system and a new channel model. With this one Mannheim error channel, errors are limited to weight one. We investigate the channel capacity of this channel and discuss its relation to the McEliece system. The proposed codes are based on a simple product code construction and have a low complexity decoding algorithm. For the one Mannheim error channel, these codes achieve a higher error correction capability than maximum distance separable codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding.
Highlights
We demonstrate that the error correction capability of the proposed q-ary codes with bounded minimum distance decoding can exceed that of maximum distance separable (MDS) codes
A suitable code family is proposed where we demonstrate that the error correction capability of the proposed q-ary codes with bounded minimum distance decoding can exceed that of MDS codes
Such a failure probability is inherent in all McEliece systems that decode beyond the guaranteed error correction capability of the code, for example, systems based on LDPC codes [8,9,10,11]
Summary
We propose a code construction, which achieves a high error correction capability with a very simple decoding strategy This construction is based on product codes. We demonstrate that the error correction capability of the proposed q-ary codes with bounded minimum distance decoding can exceed that of MDS codes. This is possible because we restrict the elements of the error vector to Mannheim weight one. This publication is organized as follows—in Section 2, we introduce the notation and review the basic concept of the McEliece cryptosystem, the information-set decoding attack and of codes over Gaussian integers.
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