Abstract
Jacobian varieties of hyperelliptic curves have been recently used in cryptosystems. However, lacking of efficient point-counting algorithms for such varieties over finite fields makes the design of secure cryptosystems very difficult. This paper presents efficient algorithms to calculate the CM type and ideal factorization of Frobenius endomorphisms of Jacobian varieties over finite fields F p in polynomial time of log p. Then we show how to construct secure hyperelliptic curves of small genera over large prime fields F p in polynomial time of log p.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35515-3_53
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© 2000 IFIP International Federation for Information Processing
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Chao, J., Matsuo, K., Tsujii, S. (2000). Fast Construction of Secure Discrete Logarithm Problems over Jacobian Varieties. In: Qing, S., Eloff, J.H.P. (eds) Information Security for Global Information Infrastructures. SEC 2000. IFIP — The International Federation for Information Processing, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35515-3_25
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DOI: https://doi.org/10.1007/978-0-387-35515-3_25
Publisher Name: Springer, Boston, MA
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