Abstract
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 \(\tilde{\mathcal{O}}\left(2^{0.05363n}\right)\).
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© 2011 International Association for Cryptologic Research
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May, A., Meurer, A., Thomae, E. (2011). Decoding Random Linear Codes in \(\tilde{\mathcal{O}}(2^{0.054n})\) . In: Lee, D.H., Wang, X. (eds) Advances in Cryptology – ASIACRYPT 2011. ASIACRYPT 2011. Lecture Notes in Computer Science, vol 7073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25385-0_6
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