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Abstract: The presumed difficulty of computing discrete logarithms in finite fields is the basis of several popular public key cryptosystems. The secure identification option of the Sun Network File System, for example, uses discrete logarithms in a field GF (p) with p a prime of 192 bits. This paper describes an implementation of a discrete logarithm algorithm which shows that primes of under 200 bits, such as that in the Sun system, are very insecure. Some enhancements to this system are suggested. 1. ... (Update)
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BibTeX entry: (Update)
B. A. LaMacchia, A. M. Odlyzko, Computation of discrete logarithms in prime fields, Designs, Codes and Cryptography 1 (1991) 47--62. http://citeseer.ist.psu.edu/lamacchia91computation.html More
@article{ lamacchia91computation,
author = "B. A. LaMacchia and A. M. Odlyzko",
title = "Computation of Discrete Logarithms in Prime Fields",
journal = "Lecture Notes in Computer Science",
volume = "537",
pages = "616--618",
year = "1991",
url = "citeseer.ist.psu.edu/lamacchia91computation.html" }
Citations (may not include all citations):2003 The Art of Computer Programming (context) - Knuth - 1981
601 A public key cryptosystem and a signature scheme based on di.. (context) - ElGamal - 1985
450 Using encryption for authentication in large networks of com.. (context) - Needham, Schroeder - 1978
428 IEEE Transactions on Information Theory (context) - Diffie, Hellman et al. - 1976
411 How to prove yourself: practical solution to identification .. - Fiat, Shamir - 1987
257 Elliptic curve cryptosystems (context) - Koblitz - 1987
176 Timestamps in Key Distribution Protocols (context) - Denning, Sacco - 1981
135 Modular multiplication without trial division (context) - Montgomery - 1985
134 Reducing elliptic curve logarithms to logarithms in a finite.. (context) - Menezes, Vanstone et al.
122 A practical zero-knowledge protocol fitted to security micro.. (context) - Guillou, Quisquater - 1988
112 Efficient identification and signatures for smart cards (context) - Schnorr - 1990
50 The number field sieve - Lenstra, Lenstra et al. - 1990
47 Discrete logarithms in finite fields and their cryptographic.. - Odlyzko - 1985
43 Factoring with two large primes (context) - Lenstra, Manasse
40 Implementing the Rivest Shamir and Adleman public key encryp.. (context) - Barrett - 1987
35 Discrete logarithms in GF (context) - Coppersmith, Odlyzko et al. - 1986
35 The discrete logarithm problem (context) - McCurley - 1990
34 using the number field sieve (context) - Gordon, in
34 An interactive identification scheme based on discrete logar.. (context) - Brickell, McCurley
28 Solving large sparse linear systems over finite fields - LaMacchia, Odlyzko
24 A survey of hardware implementations of RSA (context) - Brickell - 1990
15 An improvement of the Fiat-Shamir identification and signatu.. (context) - Micali, Shamir - 1989
11 Factoring numbers using singular integers (context) - Adleman
11 Key distribution systems based on identification information (context) - Okamoto - 1988
11 Key distribution system based on identification information (context) - Okamoto, Tanaka - 1989
10 Modifications to the number field sieve (context) - Coppersmith
10 Secure networking in the Sun environment - Taylor, Goldberg - 1986
10 A subexponential-time algorithm for computing discrete logar.. (context) - ElGamal - 1985
9 Fast evaluation of discrete logarithms in fields of characte.. (context) - Coppersmith - 1984
8 How to keep authenticity alive in a computer network (context) - Bauspiess, Knobloch
8 Advances in Cryptology: Proceedings of Crypto (context) - Miller, elliptic et al. - 1986
8 Factoring with cubic integers (context) - Pollard - 1988
6 Efficient zero-knowledge identification scheme for smart car.. (context) - Beth - 1988
5 Computing logarithms in fields of characteristic two (context) - Blake, Fuji-Hara et al. - 1984
3 Zero-knowledge authentication scheme with secrete key exchan.. (context) - Brandt, Damgard et al. - 1989
3 Advances in Cryptology: Proceedings of Crypto (context) - Koyama, Ohta et al. - 1988
2 An ID-based cryptosystem based on the discrete logarithm pro.. (context) - Tsujii, Itoh - 1989
2 Lecture Notes in Computer Science (context) - Bos, Coster et al. - 1990
2 Advances in Cryptology: Proceedings of Eurocrypt (context) - Lenstra, Manasse et al.
1 Diffie-Hellman and ElGamal protocols with one single authent.. (context) - Gunther
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.research.att.com/~bal/):
Solving Large Sparse Linear Systems Over Finite Fields - LaMacchia, Odlyzko (1991) (Correct)
Improved Low-Density Subset Sum Algorithms - Coster, Joux, LaMacchia.. (1991) (Correct)
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