36 citations · 55 across the 11 of their papers we have counts for
14 papers
Schertz style class invariants for higher degree CM fields
Andreas Enge, Marco Streng
Special values of Siegel modular functions for generate class fields of CM fields. They also yield abelian varieties with a known endomorphism ring…
Short addition sequences for theta functions
Andreas Enge, William Hart, Fredrik Johansson
The main step in numerical evaluation of classical Sl2 (Z) modular forms and elliptic functions is to compute the sum of the first N nonzero terms in the sparse q-series belonging…
Implementing cryptographic pairings at standard security levels
Andreas Enge, Jérôme Milan
This study reports on an implementation of cryptographic pairings in a general purpose computer algebra system. For security levels equivalent to the different AES flavours, we exh…
Computing class polynomials for abelian surfaces
Andreas Enge, Emmanuel Thomé
We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing…
Singular values of multiple eta-quotients for ramified primes
Andreas Enge, Reinhard Schertz
We determine the conditions under which singular values of multiple -quotients of square-free level, not necessarily prime to~6, yield class invariants, that is, algebraic numbe…
Bilinear pairings on elliptic curves
Andreas Enge
We give an elementary and self-contained introduction to pairings on elliptic curves over finite fields. For the first time in the literature, the three different definitions of th…