The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences

DOI10.1007/978-3-642-04159-4_20zbMath1256.94055arXiv0803.0728OpenAlexW2167334956MaRDI QIDQ3644209

Katherine E. Stange, Kristin E. Lauter

Publication date: 3 November 2009

Published in: Selected Areas in Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0728

Mathematics Subject Classification ID

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17)

Related Items (4)

ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS ⋮ Perfect powers generated by the twisted Fermat cubic ⋮ On symmetries of elliptic nets and valuations of net polynomials ⋮ The elliptic curve Diffie-Hellman problem and an equivalent hard problem for elliptic divisibility sequences

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic nets and elliptic curves
• Periodicity mod \(q\) of elliptic sequences and \(S\)-integral points on elliptic curves
• \(p\)-adic properties of division polynomials and elliptic divisibility sequences
• An efficient algorithm for deciding quadratic residuosity in finite fields \(GF(p^ m)\)
• Common divisors of elliptic divisibility sequences over function fields
• Primitive divisors of elliptic divisibility sequences
• An improved algorithm for computing logarithms over<tex>GF(p)</tex>and its cryptographic significance (Corresp.)
• A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
• Reducing elliptic curve logarithms to logarithms in a finite field
• The Tate Pairing Via Elliptic Nets
• Memoir on Elliptic Divisibility Sequences

This page was built for publication: The Elliptic Curve Discrete Logarithm Problem and Equivalent Hard Problems for Elliptic Divisibility Sequences