Function field sieve method for discrete logarithms over finite fields
From MaRDI portal
Publication:1854276
DOI10.1006/inco.1998.2761zbMath1006.11078OpenAlexW2056307179MaRDI QIDQ1854276
Leonard M. Adleman, Ming-Deh A. Huang
Publication date: 14 January 2003
Published in: Information and Computation (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/0b7040804793ad8c91b71fbbfcfb35d238d15fe6
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Data encryption (aspects in computer science) (68P25) Number-theoretic algorithms; complexity (11Y16)
Related Items (17)
New discrete logarithm computation for the medium prime case using the function field sieve ⋮ The generalized Weil pairing and the discrete logarithm problem on elliptic curves ⋮ Generating sets for the multiplicative groups of algebras over finite fields and expander graphs ⋮ A General Polynomial Selection Method and New Asymptotic Complexities for the Tower Number Field Sieve Algorithm ⋮ Solving discrete logarithms on a 170-bit MNT curve by pairing reduction ⋮ An \(L(1/3)\) discrete logarithm algorithm for low degree curves ⋮ Technical history of discrete logarithms in small characteristic finite fields. The road from subexponential to quasi-polynomial complexity ⋮ On the signature calculus for finite fields of order square of prime numbers ⋮ Faster individual discrete logarithms in finite fields of composite extension degree ⋮ Use of SIMD-based data parallelism to speed up sieving in integer-factoring algorithms ⋮ Updating key size estimations for pairings ⋮ The Function Field Sieve in the Medium Prime Case ⋮ 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 ⋮ Faster initial splitting for small characteristic composite extension degree fields ⋮ Refined analysis to the extended tower number field sieve ⋮ Selecting polynomials for the Function Field Sieve
Cites Work
- Algebraic function fields and codes
- The development of the number field sieve
- On a problem of Oppenheim concerning Factorisatio Numerorum
- Discrete logarithms in \(\mathrm{GF}(p)\)
- A Subexponential Algorithm for Discrete Logarithms Over all Finite Fields
- Fast evaluation of logarithms in fields of characteristic two
- A public key cryptosystem and a signature scheme based on discrete logarithms
- A method for obtaining digital signatures and public-key cryptosystems
- Monte Carlo Methods for Index Computation (mod p)
- Discrete logarithms and local units
- Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Function field sieve method for discrete logarithms over finite fields
