Classical and Quantum Algorithms for Generic Syndrome Decoding Problems and Applications to the Lee Metric

The security of code-based cryptography usually relies on the hardness Syndrome Decoding (SD) problem for Hamming weight. best generic algorithms are all improvements an old algorithm by Prange, and they known under name Information Set (ISD) algorithms. This work aims to extend ISD algorithms’ scope changing underlying weight function alphabet size SD. More precisely, we show how use Wagner’s in framework solve SD a wide range functions. We also calculate asymptotic complexities algorithms, both classical quantum case. then apply our results Lee metric, which is currently receiving significant amount attention. By providing parameters decoding seems be hardest, study could have several applications designing cryptosystems their analysis, especially against adversaries.