Cryptanalysis of variants of UOV

Authors:
Yuh-Hua Hu;Chun-Yen Chou;Lih-Chung Wang;Feipei Lai
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan;Department of Mathematical Education, National Hualien University of Education, Hualien, Taiwan;Department of Applied Mathematics, National Donghwa University, Hualien, Taiwan;Departments of Electrical Engineering & of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan
Venue:
ISC'06 Proceedings of the 9th international conference on Information Security
Year:
2006

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Abstract

The Unbalanced Oil and Vinegar scheme (UOV) is a signature scheme based on multivariate quadratic equations. It has o oil variables and v vinegar variables. UOV has m equations and n variables, where m = o and n = v + o. In this paper, we define the weak key of UOV and study how to find the weak key from the public key. Second, we study the security when m o. And our result shows that the security strengths of the current version of TTS, TRMS, Rainbow and MFE are 259 ~267.6 3DES operations.