LIU Jinhui, ZHANG Huanguo, JIA Jianwei. Cryptanalysis of Schemes Based on Polynomial Symmetrical Decomposition[J]. Chinese Journal of Electronics, 2017, 26(6): 1139-1146. doi: 10.1049/cje.2017.05.005
Citation: LIU Jinhui, ZHANG Huanguo, JIA Jianwei. Cryptanalysis of Schemes Based on Polynomial Symmetrical Decomposition[J]. Chinese Journal of Electronics, 2017, 26(6): 1139-1146. doi: 10.1049/cje.2017.05.005

Cryptanalysis of Schemes Based on Polynomial Symmetrical Decomposition

doi: 10.1049/cje.2017.05.005
Funds:  This work is supported by the National Natural Science Foundation of China (No.61303212, No.61170080, No.61202386), the State Key Program of National Natural Science of China(No.61332019, No.U1135004), the Major Research Plan of the National Natural Science Foundation of China (No.91018008), the National Basic Research Program of China (973 Program) (No.2014CB340600), and the Hubei Natural Science Foundation of China (No.2011CDB453, No.2014CFB440).
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  • Corresponding author: ZHANG Huanguo (corresponding author) was born in Hebei Province, China, in 1945. He graduated from Xidian University in 1970 with a B.E. degree. He is now a professor and Ph.D. supervisor at the School of Computer, Wuhan University.(Email:liss@whu.edu.cn)
  • Received Date: 2015-10-22
  • Rev Recd Date: 2016-05-11
  • Publish Date: 2017-11-10
  • Advances in quantum computation threaten to break public key cryptosystems such as RSA, ECC, and ElGamal that are based on the difficulty of factorization or taking a discrete logarithm, although up to now, no quantum algorithms have been found that are able to solve certain mathematical problems on non-commutative algebraic structures. Against this background, some novel public key cryptography based on Polynomial symmetrical decomposition (PSD) problem have been proposed. We find that these schemes are not secure. We present that they are vulnerable to structural attack, linearization equations attack, overdefined systems of multivariate polynomial equations attack and that, they only require polynomial time complexity to retrieve the same secret key for some given public keys respectively. We also propose an improvement to enhance public key cryptography based on PSD problem. In addition, we discuss possible lines of future work.
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