Genus 2 point counting over prime fields
From MaRDI portal
Publication:412199
DOI10.1016/j.jsc.2011.09.003zbMath1267.11127OpenAlexW2129089669MaRDI QIDQ412199
Publication date: 4 May 2012
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jsc.2011.09.003
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Applications to coding theory and cryptography of arithmetic geometry (14G50)
Related Items (28)
Fast cryptography in genus 2 ⋮ Implementation of point-counting algorithms on genus 2 hyperelliptic curves based on the birthday paradox ⋮ Jacobian coordinates on genus 2 curves ⋮ Improved complexity bounds for counting points on hyperelliptic curves ⋮ Counting points on genus-3 hyperelliptic curves with explicit real multiplication ⋮ Computing zeta functions of cyclic covers in large characteristic ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers ⋮ Four\(\mathbb {Q}\)NEON: faster elliptic curve scalar multiplications on ARM processors ⋮ Unnamed Item ⋮ Counting points on hyperelliptic curves in average polynomial time ⋮ ON THE DISTRIBUTION OF ORDERS OF FROBENIUS ACTION ON ^-TORSION OF ABELIAN SURFACES ⋮ Trisection for genus 2 curves in odd characteristic ⋮ Counting points on hyperelliptic curves of type \(y^2=x^{2g+1}+ax^{g+1}+bx\) ⋮ Computing in degree \(2^k\)-extensions of finite fields of odd characteristic ⋮ Symbolic Trisection Polynomials for Genus 2 Curves in Odd Characteristic ⋮ Bisection and squares in genus 2 ⋮ Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus ⋮ Kummer for genus one over prime-order fields ⋮ The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields ⋮ Curves, Jacobians, and cryptography ⋮ Efficient arithmetic in (pseudo-)Mersenne prime order fields ⋮ Counting points on hyperelliptic curves of genus 2 with real models ⋮ Taking roots over high extensions of finite fields ⋮ Computing zeta functions of algebraic curves using Harvey's trace formula ⋮ Constructing abelian surfaces for cryptography via Rosenhain invariants ⋮ Hyper-and-elliptic-curve cryptography ⋮ Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solving zero-dimensional systems through the rational univariate representation
- Counting points on curves over finite fields
- Formulae for arithmetic on genus 2 hyperelliptic curves
- A new polynomial factorization algorithm and its implementation
- Computing Frobenius maps and factoring polynomials
- Polynomial evaluation and interpolation on special sets of points
- Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic
- Fast computation of special resultants
- Change of order for bivariate triangular sets
- A generic approach to searching for Jacobians
- Modular Polynomials for Genus 2
- A Hyperelliptic Smoothness Test, II
- Evaluating Polynomials at Fixed Sets of Points
- Fast Algorithms for Manipulating Formal Power Series
- On the analogue of the division polynomials for hyperelliptic curves.
- Sharp estimates for triangular sets
- Deformation theory and the computation of zeta functions
- Modular equations for hyperelliptic curves
- Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
- Advances in Cryptology - EUROCRYPT 2004
- Handbook of Elliptic and Hyperelliptic Curve Cryptography
- Kedlaya's Algorithm in Larger Characteristic
- Fast genus 2 arithmetic based on Theta functions
- Algorithmic Number Theory
- Public Key Cryptography - PKC 2006
- Fast construction of irreducible polynomials over finite fields
- Fast construction of irreducible polynomials over finite fields
- Counting points on curves and Abelian varieties over finite fields
This page was built for publication: Genus 2 point counting over prime fields
