Decoding Random Linear Codes in $\tilde{\mathcal{O}}(2^{0.054n})$ [chapter]

Alexander May, Alexander Meurer, Enrico Thomae
2011 Lecture Notes in Computer Science  
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 timeÕ 2 0.05563n . Recently, Bernstein, Lange and Peters proposed a new
more » ... que called Ball-collision decoding which offers a speed-up over Stern's algorithm by improving the running time toÕ 2 0.05558n . 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 toÕ 2 0.05363n .
doi:10.1007/978-3-642-25385-0_6 fatcat:v646otbbk5dkficfkwrwmmdk5e