On index calculus algorithms for subfield curves

DOI10.1007/978-3-030-81652-0_5zbMath1485.94086OpenAlexW3183990474MaRDI QIDQ832332

Simon-Philipp Merz, Robert Granger, Steven D. Galbraith, Christophe Petit

Publication date: 25 March 2022

Full work available at URL: http://pure-oai.bham.ac.uk/ws/files/104974339/On_Index_Calculus_Algorithms_for_Subfield_Curves.pdf

zbMATH Keywords

Koblitz curveselliptic curve discrete logarithm problem

Mathematics Subject Classification ID

Cryptography (94A60) Applications to coding theory and cryptography of arithmetic geometry (14G50) Elliptic curves over local fields (11G07)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Using symmetries in the index calculus for elliptic curves discrete logarithm
• Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem
• Index calculus in the trace zero variety
• Recent progress on the elliptic curve discrete logarithm problem
• Parallel collision search with cryptanalytic applications
• Elliptic curve cryptosystems over small fields of odd characteristic
• A new efficient algorithm for computing Gröbner bases \((F_4)\)
• Efficient computation of zero-dimensional Gröbner bases by change of ordering
• Kangaroos, monopoly and discrete logarithms
• Elliptic curve discrete logarithm problem over small degree extension fields
• Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields
• On the discrete logarithm problem in elliptic curves
• Improvement of Faugère et al.’s Method to Solve ECDLP
• Last Fall Degree, HFE, and Weil Descent Attacks on ECDLP
• Galois invariant smoothness basis
• The Function Field Sieve in the Medium Prime Case
• The Probability of Relatively Prime Polynomials
• Solving sparse linear equations over finite fields
• Elliptic Curve Cryptosystems
• An improved algorithm for computing logarithms over<tex>GF(p)</tex>and its cryptographic significance (Corresp.)
• On Polynomial Systems Arising from a Weil Descent

This page was built for publication: On index calculus algorithms for subfield curves