On the security of subspace subcodes of Reed-Solomon codes for public key encryption
release_3clv4io3hveenmn3rebqpiera4
by
Alain Couvreur, Matthieu Lequesne
2020
Abstract
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 𝔽_q^m whose entries lie in a fixed collection of
𝔽_q-subspaces of 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 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.
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