An observation on the security of McEliece's public-key cryptosystem
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A method for finding codewords of small weight
Proceedings of the 3rd International Colloquium on Coding Theory and Applications
Secure Human Identification Protocols
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Attacking and Defending the McEliece Cryptosystem
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum 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
Smaller decoding exponents: ball-collision decoding
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
New generic algorithms for hard knapsacks
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Cryptography from learning parity with noise
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Decoding random binary linear codes in 2n/20: how 1 + 1 = 0 improves information set decoding
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
An improved threshold ring signature scheme based on error correcting codes
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Improving the performance of the SYND stream cipher
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
A new version of mceliece PKC based on convolutional codes
ICICS'12 Proceedings of the 14th international conference on Information and Communications Security
IND-CCA secure cryptography based on a variant of the LPN problem
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Computational aspects of retrieving a representation of an algebraic geometry code
Journal of Symbolic Computation
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Decoding random linear codes is a fundamental problem in complexity theory and lies at the heart of almost all code-based cryptography. The best attacks on the most prominent code-based cryptosystems such as McEliece directly use decoding algorithms for linear codes. The asymptotically best decoding algorithm for random linear codes of length n was for a long time Stern's variant of information-set decoding running in time $\tilde{\mathcal{O}}\left(2^{0.05563n}\right)$. Recently, Bernstein, Lange and Peters proposed a new technique called Ball-collision decoding which offers a speed-up over Stern's algorithm by improving the running time to $\tilde{\mathcal{O}}\left(2^{0.05558n}\right)$. In this paper, we present a new algorithm for decoding linear codes that is inspired by a representation technique due to Howgrave-Graham and Joux in the context of subset sum algorithms. Our decoding algorithm offers a rigorous complexity analysis for random linear codes and brings the time complexity down to $\tilde{\mathcal{O}}\left(2^{0.05363n}\right)$.