Interleaving Loidreau's Rank-Metric Cryptosystem
This work addresses cryptographic security for applications requiring efficient encryption, but it is incremental as it builds on an existing cryptosystem.
The authors tackled the problem of securing Loidreau's rank-metric cryptosystem by proposing an interleaved variant, analyzing attacks, and designing rules to reduce key sizes with example parameters.
We propose and analyze an interleaved variant of Loidreau's rank-metric cryptosystem based on rank multipliers. We analyze and adapt several attacks on the system, propose design rules, and study weak keys. Finding secure instances requires near-MRD rank-metric codes which are not investigated in the literature. Thus, we propose a random code construction that makes use of the fact that short random codes over large fields are MRD with high probability. We derive an upper bound on the decryption failure rate and give example parameters for potential key size reduction.