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A New Signature Scheme Based on Punctured Reed--Muller Code With Random Insertion
In this paper, we propose a new signature scheme based on a punctured
Reed--Muller (RM) code with random insertion, which improves the Goppa
code-based signature scheme developed by Courtois, Finiasz, and Sendrier (CFS).
The CFS signature scheme has certain drawbacks in terms of scaling of the
parameters and a lack of existential unforgeability under adaptive chosen
message attacks (EUF-CMA) security proof. Further, the proposed modified RM
code-based signature scheme can use complete decoding, which can be implemented
using a recursive decoding method, and thus syndromes for errors larger than
the error correctability can be decoded for signing, which improves the
probability of successful signing and reduces the signing time. Using the
puncturing and insertion methods, the proposed RM code-based signature scheme
can avoid some known attacks for RM code-based cryptosystems. The parameters of
the proposed signature scheme such as error weight parameter and the
maximum signing trial , can be adjusted in terms of signing time and
security level, and it is also proved that the proposed signature scheme
achieves EUF-CMA security.Comment: 22 pages, 3 figure