How to Achieve a McEliece-Based Digital Signature Scheme
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Reducing Key Length of the McEliece Cryptosystem
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Compact McEliece Keys from Goppa Codes
Selected Areas in Cryptography
Security Bounds for the Design of Code-Based Cryptosystems
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
Parallel-CFS: strengthening the CFS McEliece-based signature scheme
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Smaller decoding exponents: ball-collision decoding
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Algebraic cryptanalysis of mceliece variants with compact keys
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Information-set decoding for linear codes over Fq
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
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At SAC 2009, Misoczki and Barreto proposed a new class of codes, which have parity-check matrices that are quasi-dyadic. A special subclass of these codes were shown to coincide with Goppa codes and those were recommended for cryptosystems based on error-correcting codes. Quasi-dyadic codes have both very compact representations and allow for efficient processing, resulting in fast cryptosystems with small key sizes. In this paper, we generalize these results and introduce quasi-monoidic codes, which retain all desirable properties of quasi-dyadic codes. We show that, as before, a subclass of our codes contains only Goppa codes or, for a slightly bigger subclass, only Generalized Srivastava codes. Unlike before, we also capture codes over fields of odd characteristic. These include wild Goppa codes that were proposed at SAC 2010 by Bernstein, Lange, and Peters for their exceptional error-correction capabilities. We show how to instantiate standard code-based encryption and signature schemes with our codes and give some preliminary parameters.