Primality testing and Abelian varieties over finite fields

DOI10.1007/BFb0090185zbMath0744.11065OpenAlexW1534126003MaRDI QIDQ1189509

Leonard M. Adleman, Ming-Deh A. Huang

Publication date: 18 September 1992

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0090185

zbMATH Keywords

algorithm elliptic curve abelian varieties of dimension 2 Jacobian varieties over finite fields random polynomial time primality test

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Number-theoretic algorithms; complexity (11Y16) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Finite ground fields in algebraic geometry (14G15) Varieties over finite and local fields (11G25) Primality (11Y11)

Related Items (19)

Diffie-Hellman Oracles ⋮ Fast generation of prime numbers and secure public-key cryptographic parameters. ⋮ A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point ⋮ Sharpening ``Primes is in P for a large family of numbers ⋮ It is easy to determine whether a given integer is prime ⋮ Computing the Mordell-Weil Rank of Jacobians of Curves of Genus Two ⋮ Interactions of computational complexity theory and mathematics ⋮ Some results on pseudosquares ⋮ A Subexponential Algorithm for Discrete Logarithms Over all Finite Fields ⋮ Principally Polarized Ordinary Abelian Varieties Over Finite Fields ⋮ Kronecker's and Newton's approaches to solving: a first comparison ⋮ Counting points on curves and Abelian varieties over finite fields ⋮ The computational complexity of recognizing permutation functions ⋮ Abelian Surfaces over Finite Fields as Jacobians ⋮ On counting and generating curves over small finite fields ⋮ Book Review: Inevitable randomness in discrete mathematics ⋮ Proving primality in essentially quartic random time ⋮ Integers and polynomials: comparing the close cousins \(\mathbb Z\) and \(\mathbb F_q[x\)] ⋮ Computational complexity of uniform quantum circuit families and quantum Turing machines

This page was built for publication: Primality testing and Abelian varieties over finite fields