Quantum algorithms for typical hard problems: a perspective of cryptanalysis
Quantum algorithms for typical hard problems: a perspective of cryptanalysis
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 alreadyknown 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.
Cryptanalysis, Dihedral hidden subgroup problem, Lattice problem, Quantum algorithms
1-26
Suo, Jingwen
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Wang, Licheng
79adf188-69a8-45b1-a8bb-eeccb1cf5491
Yang, Sijia
1cef61a2-f709-4732-b8c1-45ac9564b802
Zheng, Wenjie
3b29dabc-f300-44a4-b4a3-e2ee79a05fb8
Zhang, Jiankang
6add829f-d955-40ca-8214-27a039defc8a
1 June 2020
Suo, Jingwen
d2336840-1ea6-4059-bd84-260f12ecf829
Wang, Licheng
79adf188-69a8-45b1-a8bb-eeccb1cf5491
Yang, Sijia
1cef61a2-f709-4732-b8c1-45ac9564b802
Zheng, Wenjie
3b29dabc-f300-44a4-b4a3-e2ee79a05fb8
Zhang, Jiankang
6add829f-d955-40ca-8214-27a039defc8a
Suo, Jingwen, Wang, Licheng, Yang, Sijia, Zheng, Wenjie and Zhang, Jiankang
(2020)
Quantum algorithms for typical hard problems: a perspective of cryptanalysis.
Quantum Information Processing, 19 (6), , [178].
(doi:10.1007/s11128-020-02673-x).
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 alreadyknown 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.
Text
Quantumalgorithmsfortypicalhardproblemsa perspective of cryptanalysis
- Accepted Manuscript
More information
Accepted/In Press date: 7 April 2020
e-pub ahead of print date: 30 April 2020
Published date: 1 June 2020
Additional Information:
Funding Information:
This work was supported by the National Key Research and Development Program of China (2018YFE0126000), the National Natural Science Foundation of China (NSFC) (No. 61972050), the Shandong provincial Key R&D Program of China (Grant No. 2018CXGC0701) and the 111 Project (No. B08004).
Publisher Copyright:
© 2020, The Author(s).
Keywords:
Cryptanalysis, Dihedral hidden subgroup problem, Lattice problem, Quantum algorithms
Identifiers
Local EPrints ID: 440720
URI: http://eprints.soton.ac.uk/id/eprint/440720
ISSN: 1570-0755
PURE UUID: 9a907309-c1cf-4ab4-b647-60961ad576bf
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Date deposited: 14 May 2020 16:31
Last modified: 17 Mar 2024 05:33
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Contributors
Author:
Jingwen Suo
Author:
Licheng Wang
Author:
Sijia Yang
Author:
Wenjie Zheng
Author:
Jiankang Zhang
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