The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Examples of genus two CM curves defined over the rationals
Mathematics of Computation
Constructing hyperelliptic curves of genus 2 suitable for cryptography
Mathematics of Computation
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Abelian varieties with prescribed embedding degree
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
The 2-adic CM method for genus 2 curves with application to cryptography
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
Constructing pairing-friendly genus 2 curves with ordinary Jacobians
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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We present two contributions in this paper. First, we give a quantitative analysis of the scarcity of pairing-friendly genus 2 curves. This result is an improvement relative to prior work which estimated the density of pairing-friendly genus 2 curves heuristically. Second, we present a method for generating pairing-friendly parameters for which $${\rho\approx 8}$$ , where 驴 is a measure of efficiency in pairing-based cryptography. This method works by solving a system of equations given in terms of coefficients of the Frobenius element. The algorithm is easy to understand and implement.