McEliece Public Key Cryptosystems Using Algebraic-Geometric Codes
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IEEE Transactions on Information Theory
List decoding for binary Goppa codes
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PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
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The original McEliece cryptosystem uses length-n codes over F2 with dimension ≥ n-mt efficiently correcting t errors where 2m ≥ n. This paper presents a generalized cryptosystem that uses length-n codes over small finite fields Fq with dimension ≥ n-m(q-1)t efficiently correcting ⌊qt/2⌋ errors where qm ≥ n. Previously proposed cryptosystems with the same length and dimension corrected only ⌊(q - 1)t/2⌋ errors for q ≥ 3. This paper also presents list-decoding algorithms that efficiently correct even more errors for the same codes over Fq. Finally, this paper shows that the increase from ⌊(q - 1)t/2⌋ errors to more than ⌊qt/2⌋ errors allows considerably smaller keys to achieve the same security level against all known attacks.