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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Generating Parameters for Algebraic Torus-Based Cryptosystems
verfasst von : Tomoko Yonemura, Yoshikazu Hanatani, Taichi Isogai, Kenji Ohkuma, Hirofumi Muratani
Erschienen in: Cryptology and Network Security
Verlag: Springer Berlin Heidelberg
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Algebraic torus-based cryptosystems are public key cryptosystems based on the discrete logarithm problem, and have compact expressions compared with those of finite field-based cryptosystems. In this paper, we propose parameter selection criteria for the algebraic torus-based cryptosystems from the viewpoints of security and efficiency. The criteria include the following conditions: consistent resistance to attacks on algebraic tori and their embedding fields, and a large degree of freedom to select parameters suitable for each implementation. An extension degree and a characteristic size of a finite field on which the algebraic tori are defined are adjustable. We also provide examples of parameters satisfying the criteria.