Constructing Abelian Varieties for Pairing-Based Cryptography
نویسنده
چکیده
Constructing Abelian Varieties for Pairing-Based Cryptography
منابع مشابه
Trilinear maps for cryptography
We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is based on a discrete logarithm problem on the quotient of certain modules defined through the N\'{e}ron-Severi groups. The discrete logarithm problem is reduci...
متن کاملA Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
We give an algorithm that produces families of Weil numbers for ordinary abelian varieties over finite fields with prescribed embedding degree. The algorithm uses the ideas of Freeman, Stevenhagen, and Streng to generalize the Brezing-Weng construction of pairing-friendly elliptic curves. We discuss how CM methods can be used to construct these varieties, and we use our algorithm to give exampl...
متن کاملEfficient pairing computation on supersingular Abelian varieties
We present a general technique for the efficient computation of pairings on supersingular Abelian varieties. This formulation, which we call the eta pairing, generalises results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic three. We then show how our general technique leads to a new algorithm which is about twice as fast as the Duursma-Lee...
متن کاملConstructing Pairing-Friendly Genus 2 Curves with Split Jacobian
Genus 2 curves with simple but not absolutely simple jacobians can be used to construct pairing-based cryptosystems more efficient than for a generic genus 2 curve. We show that there is a full analogy between methods for constructing ordinary pairing-friendly elliptic curves and simple abelian varieties, which are iogenous over some extension to a product of elliptic curves. We extend the noti...
متن کاملIsogeny graphs of ordinary abelian varieties
Fix a prime number . Graphs of isogenies of degree a power of are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse graphs of so-called l-isogenies, resolving that, in arbitrary dimension, their structure is similar, but not identical, to the “volcanoes” occurri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008