An observation on the security of McEliece's public-key cryptosystem
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
On the McEliece public-key cryptosystem
CRYPTO '88 Proceedings on Advances in cryptology
New approaches to reduced-complexity decoding
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
The Area-Time Complexity of Binary Multiplication
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Error-Correction Coding for Digital Communications
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Proceedings of the 3rd International Colloquium on Coding Theory and Applications
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CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Failure of the McEliece Public-Key Cryptosystem Under Message-Resend and Related-Message Attack
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Cryptoanalysis of the Original McEliece Cryptosystem
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A Statistical Decoding Algorithm for General Linear Block Codes
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IEEE Transactions on Information Theory
Minimal vectors in linear codes
IEEE Transactions on Information Theory
On the complexity of minimum distance decoding of long linear codes
IEEE Transactions on Information Theory
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Very few public-key cryptosystems are known that can encrypt and decrypt in time b2+o(1) with conjectured security level 2b against conventional computers and quantum computers. The oldest of these systems is the classic McEliece code-based cryptosystem. The best attacks known against this system are generic decoding attacks that treat McEliece's hidden binary Goppa codes as random linear codes. A standard conjecture is that the best possible w-error-decoding attacks against random linear codes of dimension k and length n take time 2(α(R, W)+o(1))n if k/n → R and w/n → W as n → ∞. Before this paper, the best upper bound known on the exponent α(R, W) was the exponent of an attack introduced by Stern in 1989. This paper introduces "ball-collision decoding" and shows that it has a smaller exponent for each (R, W): the speedup from Stern's algorithm to ball-collision decoding is exponential in n.