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).
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Guan, P., Wan, Y., Zhang, Z., Zhang, F. (2022). Efficient List Decoding Applied to \(\mathrm{ECC}^2\). In: Shen, H., et al. Parallel and Distributed Computing, Applications and Technologies. PDCAT 2021. Lecture Notes in Computer Science(), vol 13148. Springer, Cham. https://doi.org/10.1007/978-3-030-96772-7_52
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