One-Way Function Construction Based on the MQ Problem and Logic Function

Abstract:

Multivariate quadratic based public-key cryptography called MQ problem which based on calculation of a secure cryptography of multivariate equations and MQ cryptography security is based on the difficulty of the solution of multivariate equations. But computer and mathematician scientists put a lot of effort and a long time to research MQ cryptography and they have proved that MQ cryptography is NP complete problem. Therefore, before the P problem Equal to the NP problem we do not figure out selected multivariate equations by random in polynomial time. So we can use this feature to construct the relative safety method of the public key encryption. A new type of public-key cryptosystem has been brought up in this paper that one-way shell core function which has such advantages as more security and flexibility, and provides a more inclusive public-key cryptosystem.

• Periodical: Applied Mechanics and Materials (Volumes 220-223)
• Pages: 2360-2363
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.220-223.2360
• Online since: November 2012
• Authors: Yan Jun Sun, Chang Ming Liu, Hai Yu Li, Zhe Yuan
• Keywords: Key Exchange, Multivariate Quadratic, One-Way Shell Core function

References

[1] PEI Shi-hui,Zhao Hong-wei,Zhao Yong-zhe.Public Key Cryptography Based on Ergodic Matrices over Finite Field.Wuhan University Journal of Natural Sciences,2006,11(6):1525-1528.

DOI: 10.1007/bf02831812

[2] Zhao Yongzhe, Wang Liou. Information-Exchange Using the Ergodic Matrices in GF(2). Applied Cryptography and Network Security Technical Track Proceedings, 2nd International Conference ACNS 2004, 2004: 388-397.

[3] Aviad Kipnis, Adi Shamir. Cryptanalysis of the HFE Public Key Cryptosystem. Proceedings of Crypto'99, 1999: 166-175.

DOI: 10.1007/3-540-48405-1_2

[4] Adi Shamir, Jacques Patarin. Efficient Algorithms for solving Overdefined Systems of Multivariate Polynomial Equations. Springer, 2000: 392-407.

DOI: 10.1007/3-540-45539-6_27

[5] Nicolas Courtois. The security of Hidden Field Equations (HFE)[C]. Cryptographers' Track RSA Conference 2001, 2001: 266-281.

DOI: 10.1007/3-540-45353-9_20

[6] M C Wunderlich, J.L. Selfridge. A design for a number theory package with an optimized trial division routine[J]. Communications of ACM, 1974, 17(5): 272–276.

DOI: 10.1145/360980.361001

[7] Nicolas T Courtois, Alexander Klimov, Jacques Patarin, Adi Shamir. Efficient algorithms for solving overdefined systems of multivariate polynomial equations [J]. EUROCRYPT 2000 proceedings of the 19th international annual conference on the theory and application of cryptographic techniques, 2000: 392–407.

DOI: 10.1007/3-540-45539-6_27