Quantum algorithms for typical hard problems: a perspective of cryptanalysis
Jingwen Suo, Licheng Wang, Sijia Yang, Wenjie Zheng, Jiankang Zhang
Abstract
Abstract In typical well-known cryptosystem, the hardness of classical problems plays a fundamental role in ensuring its security. While, with the booming of quantum computation, some classical hard problems tend to be vulnerable when confronted with the already-known quantum attacks, as a result, it is necessary to develop the post-quantum cryptosystem to resist the quantum attacks. With the purpose to bridge the two disciplines, it is significant to summarize known quantum algorithms and their threats toward these cryptographic intractable problems from a perspective of cryptanalysis. In this paper, we discussed the designing methodology, algorithm framework and latest progress of the mathematic hard problems on which the typical cryptosystems depend, including integer factorization problem, discrete logarithmic problem and its variants, lattice problem, dihedral hidden subgroup problems and extrapolated dihedral coset problem. It illustrated the reason why some cryptosystems such as RSA and ECC are not resistant to quantum attacks, yet some of them like lattice cryptosystems remain intact facing quantum attacks.