Computing the order of points on an elliptic curve modulo \(N\) is as difficult as factoring \(N\)

DOI10.1016/S0893-9659(00)00159-2zbMath0979.94036WikidataQ126586847 ScholiaQ126586847MaRDI QIDQ5938924

Paz Morillo, Sebastià Martín, Jorge Luis Villar

Publication date: 7 August 2001

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

elliptic curvescostly computational problemsfactorization of integerspublic-key cryptography

Mathematics Subject Classification ID

Cryptography (94A60) Elliptic curves over global fields (11G05) Applications to coding theory and cryptography of arithmetic geometry (14G50) Factorization (11Y05)

Related Items (4)

Factoring integers and oracles for elliptic and hyperelliptic curves ⋮ Factorization, malleability and equivalent problems ⋮ Smooth factors of integers and elliptic curve based factoring with an oracle ⋮ On oracle factoring of integers

Uses Software

• ECPP

Cites Work

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• Factoring integers with elliptic curves
• Elliptic Curves and Primality Proving
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• 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

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