Algorithmica
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
A pipeline architecture for factoring large integers with the quadratic sieve algorithm
SIAM Journal on Computing - Special issue on cryptography
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
Mathematics of Computation
Algorithmic number theory
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Euclid's algorithm and the lanczos method over finite fields
Mathematics of Computation
An algorithm for evaluation of discrete logarithms in some nonprime finite fields
Mathematics of Computation
Function field sieve method for discrete logarithms over finite fields
Information and Computation
Computing discrete logarithms in real quadratic congruence function fields of large genus
Mathematics of Computation
Applying sieving to the computation of quadratic class groups
Mathematics of Computation
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Using number fields to compute logarithms in finite fields
Mathematics of Computation
Analysis of the Xedni Calculus Attack
Designs, Codes and Cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Some Parallel Algorithms for Integer Factorisation
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Massively Parallel Computation of Discrete Logarithms
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
The Solution of McCurley's Discrete Log Challenge
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
An Analytic Approach to Smooth Polynominals over Finite Fields
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
The Security of Individual RSA Bits
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The Security of Individual RSA Bits
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Computational aspects of discrete logarithms
Computational aspects of discrete logarithms
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
A block Lanczos algorithm for finding dependencies over GF(2)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Signature Schemes Based on 3rd Order Shift Registers
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Secure PC-Franking for Everyone
EC-WEB '00 Proceedings of the First International Conference on Electronic Commerce and Web Technologies
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
Speeding up Exponentiation using an Untrusted Computational Resource
Designs, Codes and Cryptography
Special polynomial families for generating more suitable pairing-friendly elliptic curves
EHAC'06 Proceedings of the 5th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications
Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
ACM Transactions on Mathematical Software (TOMS)
Solving discrete logarithms from partial knowledge of the key
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
A new method of building more non-supersingular elliptic curves
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
Hard instances of the constrained discrete logarithm problem
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
A new baby-step giant-step algorithm and some applications to cryptanalysis
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
An algorithm to solve the discrete logarithm problem with the number field sieve
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Efficient primitives from exponentiation in Zp
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
On the efficient implementation of pairing-based protocols
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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The first practicalpublic key cryptosystem to be published, the Diffie–Hellmankey exchange algorithm, was based on the assumption that discretelogarithms are hard to compute. This intractability hypothesisis also the foundation for the presumed security of a varietyof other public key schemes. While there have been substantialadvances in discrete log algorithms in the last two decades,in general the discrete log still appears to be hard, especiallyfor some groups, such as those from elliptic curves. Unfortunatelyno proofs of hardness are available in this area, so it is necessaryto rely on experience and intuition in judging what parametersto use for cryptosystems. This paper presents a brief surveyof the current state of the art in discrete logs.