Efficient List Decoding Applied to $\mathrm{ECC}^2$

Abstract

$\mathrm{ECC}^2$ is an public key encryption system based on elliptic code. It can resist known attacks based on the special structures of algebraic geometric code. However, the computational overhead of decryption of $\mathrm{ECC}^2$ is unsatisfactory, because the list decoding algorithm occupies a major part of the computational overhead of decryption of $\mathrm{ECC}^2$. Therefore, we propose our module basis reduction interpolation of list decoding for elliptic code to speed up the decryption of $\mathrm{ECC}^2$. The algorithm we proposed is based on the theory of Gr$\ddot{\mathrm{o}}$bner basis of modules. By implementing our proposed algorithm combined with $\mathrm{ECC}^2$, it shows that the proposed algorithm performs better than the list decoding algorithms used in $\mathrm{ECC}^2$.

Supported by Guangdong Major Project of Basic and Applied Basic Research (2019B030302008) and the National Natural Science Foundation of China (No. 61972429).