Factoring integers and oracles for elliptic and hyperelliptic curves

DOI10.4064/bc126-2MaRDI QIDQ6196944

Robert Dryło

Publication date: 15 March 2024

Published in: Banach Center Publications (Search for Journal in Brave)

zbMATH Keywords

hyperelliptic curveelliptic curveInteger factorizationKummer hypersurface

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20) Factorization (11Y05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Factoring integers with elliptic curves
• Hyperelliptic cryptosystems
• Factoring \(n\) and the number of points of Kummer hypersurfaces \(\bmod n\)
• On oracle factoring of integers
• Mathematics of Public Key Cryptography
• Factorization with genus 2 curves
• The Arithmetic of Elliptic Curves
• Computing in the Jacobian of a Hyperelliptic Curve
• Factoring with Cyclotomic Polynomials
• A p + 1 Method of Factoring
• A method for obtaining digital signatures and public-key cryptosystems
• Equivalence of counting the number of points on elliptic curve over the ring Zn and factoring n
• Public-Key Cryptosystems Based on Composite Degree Residuosity Classes
• Jacobians of Hyperelliptic Curves over ℤn and Factorization of n
• Integer factoring problem and elliptic curves over the ring $\mathbb Z_n$
• Algebraic aspects of cryptography. With an appendix on hyperelliptic curves by Alfred J. Menezes, Yi-Hong Wu, and Robert J. Zuccherato
• Computing the order of points on an elliptic curve modulo \(N\) is as difficult as factoring \(N\)

This page was built for publication: Factoring integers and oracles for elliptic and hyperelliptic curves