The Function Field Sieve in the Medium Prime Case

DOI10.1007/11761679_16zbMath1140.94349OpenAlexW1565956864MaRDI QIDQ3593100

Antoine Joux, Reynald Lercier

Publication date: 24 September 2007

Published in: Advances in Cryptology - EUROCRYPT 2006 (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/11761679_16

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16)

Related Items (17)

Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields ⋮ On index calculus algorithms for subfield curves ⋮ New discrete logarithm computation for the medium prime case using the function field sieve ⋮ Index calculus in the trace zero variety ⋮ A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm ⋮ Technical history of discrete logarithms in small characteristic finite fields. The road from subexponential to quasi-polynomial complexity ⋮ Elliptic periods and primality proving ⋮ Updating key size estimations for pairings ⋮ Indiscreet logarithms in finite fields of small characteristic ⋮ Weakness of \(\mathbb{F}_{3^{6 \cdot 1429}}\) and \(\mathbb{F}_{2^{4 \cdot 3041}}\) for discrete logarithm cryptography ⋮ Applications to cryptography of twisting commutative algebraic groups ⋮ Refined analysis to the extended tower number field sieve ⋮ On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field ⋮ Using abelian varieties to improve pairing-based cryptography ⋮ Selecting polynomials for the Function Field Sieve ⋮ Asymptotic complexities of discrete logarithm algorithms in pairing-relevant finite fields ⋮ Traps to the BGJT-algorithm for discrete logarithms

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