Abstract
Advances in quantum computation threaten to break public key cryptosystems that are based on the difficulty of factorization or the difficulty of discrete logariths, although, no quantum algorithms have been found to be able to solve certain mathematical problems on non-commutative algebraic structures up to now. The proposed new quasi-inverse based cryptography scheme is vulnerable to a linear algebra attack based on the probable occurrence of weak keys in the generation process. In this paper, we illustrate that two of the quasi-inverse based cryptography are vulnerable to a structural attack and that it only requires polynomial time to obtain the equivalent keys for some given public keys. In addition, we conduct a detailed analysis on attack methods and provide some improved suggestions on these two schemes.
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Foundation item: Supported by the National Natural Science Foundation of China ( 61303212, 61170080, 61202386), the State Key Program of National Natural Science of China( 61332019, U1135004), the Major Research Plan of the National Natural Science Foundation of China (91018008), Major State Basic Research Development Program of China (973 Program) (2014CB340600), the Natural Science Foundation of Hubei Province ( 2011CDB453, 2014CFB440)
Biography: LIU Jinhui, female, Ph.D. candidate, research direction: cryptography.
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Liu, J., Zhang, H. & Jia, J. Cryptanalysis of schemes based on pseudoinverse matrix. Wuhan Univ. J. Nat. Sci. 21, 209–213 (2016). https://doi.org/10.1007/s11859-016-1161-x
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DOI: https://doi.org/10.1007/s11859-016-1161-x
Key words
- cryptography
- post-quantum computational cryptography
- key exchange protocol
- cryptanalysis
- matrix decomposition