Survey on Applications of List Decoding to Cryptography

Abstract

Since the conception of list decoding is proposed in the 1950s, list decoding not only is applied to communication and coding theory, but also plays a significant role in computational complexity and cryptography. In recent years, with the rapid development of quantum computing, the traditional cryptographic schemes based on factorization and other difficult problems are greatly threatened. The code-based cryptosystems, whose security relies on the NP-hard problems in coding theory, are attracting more and more attention as a candidate of the post-quantum cryptography, and so does the list decoding algorithm. This paper systematically reviews the applications of list decoding to cryptography, including early applications in proving that any one-way function has hard-core bits, designing traitor tracing schemes, designing public key schemes using polynomial reconstruction as cryptographic primitives, improving the traditional code-based cryptosystems and solving Discrete Logarithm Problems (DLP), and recent applications to designing secure communication interactive protocols, solving the elliptic curve discrete logarithm problem, and designs new cryptographic schemes based on error correction codes. Finally, the new research issues of the algorithm improvement of list decoding, its application to the design of cryptographic protocol and cryptoanalysis, and the exploration of new application scenarios are discussed.