How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Status report on factoring (at the Sandia National Labs)
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
A high security log-in procedure
Communications of the ACM
Cryptography, a Primer
Shift Register Sequences
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Evaluating logarithms in GF(2n)
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
An efficient signature scheme based on quadratic equations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
How discreet is the discrete log?
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Secrecy, authentication, and public key systems.
Secrecy, authentication, and public key systems.
An Efficient Parallel Algorithm for the Solution of Large Sparse Linear Matrix Equations
IEEE Transactions on Computers
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Analysis of the Berlekamp-Massey linear feedback shift-register synthesis algorithm
IBM Journal of Research and Development
A polynomial form for logarithms modulo a prime (Corresp.)
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
A subexponential-time algorithm for computing discrete logarithms over
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Computing logarithms in GF(2n)
Proceedings of CRYPTO 84 on Advances in cryptology
A public-key cryptosystem based on shift register sequences
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
VLSI implementation of public-key encryption algorithms
Proceedings on Advances in cryptology---CRYPTO '86
Applications of combinatorial designs in computer science
ACM Computing Surveys (CSUR)
A perfect zero-knowledge proof for a problem equivalent to discrete logarithm
CRYPTO '88 Proceedings on Advances in cryptology
Intractable problems in number theory (invited talk)
CRYPTO '88 Proceedings on Advances in cryptology
A family of Jacobians suitable for discrete log cryptosystems
CRYPTO '88 Proceedings on Advances in cryptology
Diffie-Hellman is as strong as discrete log for certain primes
CRYPTO '88 Proceedings on Advances in cryptology
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
CRYPTO '89 Proceedings on Advances in cryptology
Computing the number of points of elliptic curves over finite fields
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Computing Frobenius maps and factoring polynomials
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Conditionally secure secret sharing schemes with disenrollment capability
CCS '94 Proceedings of the 2nd ACM Conference on Computer and communications security
Key management for encrypted broadcast
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Key management for encrypted broadcast
ACM Transactions on Information and System Security (TISSEC)
IEEE Transactions on Computers
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
A verifiable secret shuffle and its application to e-voting
CCS '01 Proceedings of the 8th ACM conference on Computer and Communications Security
Polynomials over finite fields free from large and small degree irreducible factors
Journal of Algorithms - Analysis of algorithms
Designs, Codes and Cryptography
A Rigorous Proof of the Waterloo Algorithm for the Discrete Logarithm Problem
Designs, Codes and Cryptography
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
IEEE Transactions on Computers
IEEE Transactions on Computers
A New LFSR with D and T Flip-Flops as an Effective Test Pattern Generator for VLSI Circuits
EDCC-3 Proceedings of the Third European Dependable Computing Conference on Dependable Computing
New Public-Key Cryptosystem Using Divisor Class Groups
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Some Parallel Algorithms for Integer Factorisation
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Recent Progress and Prospects for Integer Factorisation Algorithms
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
A Chosen Text Attack on the RSA Cryptosystem and Some Discrete Logarithm Schemes
CRYPTO '85 Advances in Cryptology
Computation of Discrete Logarithms in Prime Fields (Extended Abstract)
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for the Construction of Hyperelliptic Cryptosystems
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Shared Generation of Authenticators and Signatures (Extended Abstract)
CRYPTO '91 Proceedings of the 11th 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
A Subexponential Algorithm for Discrete Logarithms over All Finite Fields
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
NFS with Four Large Primes: An Explosive Experiment
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Computation of Discrete Logarithms in F2607
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Redundant Representation of Finite Fields
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Computer algebra handbook
A reliable block Lanczos algorithm over small finite fields
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Software implementation of Tate pairing over GF(2m)
Proceedings of the conference on Design, automation and test in Europe: Designers' forum
Transformations of two cryptographic problems in terms of matrices
ACM SIGSAM Bulletin
Secure authenticated group key agreement protocol in the MANET environment
Information Security Tech. Report
On the Equivalence of Generic Group Models
ProvSec '08 Proceedings of the 2nd International Conference on Provable Security
New cryptosystems design based on hybrid-mode problems
Computers and Electrical Engineering
IEEE Transactions on Wireless Communications
Discrete logarithm based protocols
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems with very small key lengths
EUROCRYPT'92 Proceedings of the 11th 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
Relationships among the computational powers of breaking discrete log cryptosystems
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on class semigroups of imaginary quadratic non-maximal orders
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Elgamal public key cryptosystem and signature scheme in GU(m,p,n)
Proceedings of the 3rd international conference on Security of information and networks
Parallelization of the Lanczos algorithm on multi-core platforms
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
Using wiedemann's algorithm to compute the immunity against algebraic and fast algebraic attacks
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
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
The function field sieve in the medium prime case
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Correspondences on hyperelliptic curves and applications to the discrete logarithm
SIIS'11 Proceedings of the 2011 international conference on Security and Intelligent Information Systems
Fast point quadrupling on elliptic curves
Proceedings of the Third Symposium on Information and Communication Technology
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Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u 驴 GF(q) is that integer k, 1 驴 k 驴 q-1, for which u = gk. The well-known problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its applicability in cryptography. Several cryptographic systems would become insecure if an efficient discrete logarithm algorithm were discovered. This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2n). It appears that in order to be safe from attacks using these algorithms, the value of n for which GF(2n) is used in a cryptosystem has to be very large and carefully chosen. Due in large part to recent discoveries, discrete logarithms in fields GF(2n) are much easier to compute than in fields GF(p) with p prime. Hence the fields GF(2n) ought to be avoided in all cryptographic applications. On the other hand, the fields GF(p) with p prime appear to offer relatively high levels of security.