کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
401275 | 675321 | 2012 | 33 صفحه PDF | دانلود رایگان |
For counting points of Jacobians of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof’s genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-of-the-art security level of approximately 21282128 and desirable speed properties. This curve and its quadratic twist have a Jacobian group whose order is 16 times a prime.
► We give a detailed point-counting algorithm for genus 2 curves over a prime field.
► We conduct a large-scale computation, using more than 1000,000 CPU hours.
► We obtain a doubly-secure curve with 128 bit security.
► This curve has small coefficients for the Kummer pseudo-group law.
Journal: Journal of Symbolic Computation - Volume 47, Issue 4, April 2012, Pages 368–400