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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2021

On the security of subspace subcodes of Reed-Solomon codes for public key encryption

Résumé

This article discusses the security of McEliece-like encryption schemes using subspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codes over $\mathbb{F}_{q^m}$ whose entries lie in a fixed collection of $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}$. These codes appear to be a natural generalisation of Goppa and alternant codes and provide a broader flexibility in designing code based encryption schemes. For the security analysis, we introduce a new operation on codes called the twisted product which yields a polynomial time distinguisher on such subspace subcodes as soon as the chosen $\mathbb{F}_q$-subspaces have dimension larger than $m/2$. From this distinguisher, we build an efficient attack which in particular breaks some parameters of a recent proposal due to Khathuria, Rosenthal and Weger.

Dates et versions

hal-02938812 , version 1 (15-09-2020)

Identifiants

Citer

Alain Couvreur, Matthieu Lequesne. On the security of subspace subcodes of Reed-Solomon codes for public key encryption. IEEE Transactions on Information Theory, 2021, 68 (1), pp.632-648. ⟨10.1109/TIT.2021.3120440⟩. ⟨hal-02938812⟩
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