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Wild McEliece. (English) Zbl 1290.94041
Biryukov, Alex (ed.) et al., Selected areas in cryptography. 17th international workshop, SAC 2010, Waterloo, Ontario, Canada, August 12–13, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-19573-0/pbk). Lecture Notes in Computer Science 6544, 143-158 (2011).
Summary: The original McEliece cryptosystem uses length-\(n\) codes over \(\mathbb F_2\) with dimension \(\geq n-mt\) efficiently correcting \(t\) errors where \(2^m \geq n\). This paper presents a generalized cryptosystem that uses length-\(n\) codes over small finite fields \(\mathbb F_q\) with dimension \(\geq n-m(q-1)t\) efficiently correcting \(\lfloor{qt/2}\rfloor\) errors where \(q^m \geq n\). Previously proposed cryptosystems with the same length and dimension corrected only \(\lfloor{(q-1)t/2}\rfloor\) errors for \(q\geq 3\). This paper also presents list-decoding algorithms that efficiently correct even more errors for the same codes over \(\mathbb F_q\). Finally, this paper shows that the increase from \(\lfloor{(q-1)t/2}\rfloor\) errors to more than \(\lfloor{qt/2}\rfloor\) errors allows considerably smaller keys to achieve the same security level against all known attacks.
For the entire collection see [Zbl 1208.94008].

MSC:
94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94B35 Decoding
Software:
McEliece; SageMath
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