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Abstract: The first practical public key cryptosystem to be published, the Diffie-Hellman key exchange algorithm, was based on the assumption that discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the presumed security of a variety of other public key schemes. While there have been substantial advances in discrete log algorithms in the last two decades, in general the discrete log still appears to be hard, especially for some groups, such as those from... (Update)
Context of citations to this paper: More
...(number eld sieves) have been steadily improving 11 over the years and so it s harder to gauge how large p should be for long term security. In [48], Odlyzko proposes using a 9 the subgroup generated by g p 1 2 is fg p 1 2 = p 1; g p 1 2 ) 2 = 1g. 10 Assuming that the...
.... Surveys of many e#cient algorithms (including heuristic ones) for computing the discrete logarithm can be found in [1, 10, 11, 13, 17, 18, 20, 21, 23]. Some algebraic and number theoretic characteristics of the discrete logarithm, including the degree of its polynomial...
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BibTeX entry: (Update)
A. M. Odlyzko. Discrete logarithms: The past and the future. Designs, Codes, and Cryptography, 19:129-145, 2000. http://citeseer.ist.psu.edu/odlyzko99discrete.html More
@article{ odlyzko00discrete,
author = "Andrew Odlyzko",
title = "Discrete Logarithms: The Past and the Future",
journal = "Designs, Codes, and Cryptography",
volume = "19",
number = "2--3",
pages = "129--145",
year = "2000",
url = "citeseer.ist.psu.edu/odlyzko99discrete.html" }
Citations (may not include all citations):1065 Handbook of Applied Cryptography (context) - Menezes, Van Oorschot et al. - 1996 ACM
704 Applied Cryptography (context) - Schneier - 1995 ACM
635 New directions in cryptography - Diffie, Hellman - 1976
601 A public key cryptosystem and a signature scheme based on di.. (context) - ElGamal - 1985 ACM DBLP
164 Polynomial-time algorithms for prime factorization and discr.. - Shor - 1997 ACM DBLP
147 Efficient signature generation by smart cards (context) - Schnorr - 1991 DBLP
124 Lower bounds for discrete logarithms and related problems - Shoup - 1997 DBLP
116 Algorithmic Number Theory (context) - Bach, Shallit - 1996 ACM
72 The Development of the Number Field Sieve (context) - Lenstra, Lenstra et al. - 1993
62 Solving sparse linear equations over finite fields (context) - Wiedemann - 1986 ACM
58 Monte Carlo methods for index computations mod p (context) - Pollard - 1978
55 Hardness of computing the most significant bits of secret ke.. (context) - Boneh, Venkatesan - 1996
47 Discrete logarithms in finite fields and their cryptographic.. - Odlyzko - 1985 ACM DBLP
43 Analysis of Coppersmith's block Wiedemann algorithm for the .. (context) - Kaltofen - 1995 ACM DBLP
40 Computation of discrete logarithms in prime fields - LaMacchia, Odlyzko - 1991 ACM DBLP
35 Discrete logarithms in GF (context) - Coppersmith, Odlyzko et al. - 1986
34 using the number field sieve (context) - Gordon, in - 1993
34 Solving homogeneous linear equations over GF (context) - Coppersmith - 1994
28 Fast evaluation of logarithms in fields of characteristic tw.. (context) - Coppersmith - 1984
28 Solving large sparse linear systems over finite fields - LaMacchia, Odlyzko - 1991 ACM DBLP
27 Speeding up Pollard's rho method for computing discrete loga.. - Teske - 1998 ACM DBLP
27 A block Lanczos algorithm for finding dependencies over GF (context) - Montgomery - 1995
25 Further analysis of Coppersmith's block Wiedemann algorithm .. (context) - Villard
24 Parallel collision search with cryptanalytic applications (context) - Van Oorschot, Wiener - 1999 DBLP
23 the complexity of matrix group problems (context) - Babai, Szemeredi - 1984
22 Solving linear equations over GF (context) - Coppersmith - 1993
21 Computational aspects of discrete logarithms (context) - Lambert - 1996 ACM
19 A pipeline architecture for factoring large integers with th.. (context) - Pomerance, Smith et al. - 1988 ACM DBLP
16 Integers without large prime factors (context) - Hildebrand, Tenenbaum - 1993
16 Discrete logarithms and local units (context) - Schirokauer - 1993
15 Computing discrete logarithms in high-genus hyperelliptic Ja.. - Enge ACM
14 Lower bounds on generic algorithms in groups - Maurer, Wolf - 1998 DBLP
14 The security of individual RSA bits (context) - Hastad, Naslund - 1998 ACM DBLP
13 Massively parallel computation of discrete logarithms - Gordon, McCurley - 1992 ACM DBLP
11 Analysis of the Xedni calculus attack - Jacobson, Koblitz et al. ACM DBLP
10 Computing discrete logarithms in real quadratic congruence f.. - Muller, Stein et al. - 1999 ACM
10 Factoring large numbers with the TWINKLE device (context) - Shamir
9 Monopoly and discrete logarithms (context) - Pollard
9 The solution of McCurley's discrete log challenge (context) - Weber, Denny - 1998 ACM DBLP
8 Euclid's algorithm and the Lanczos method over finite fields - Teitelbaum - 1998 ACM
8 Security of discrete log cryptosystems in the random oracle .. - Schnorr, Jakobsson
7 Applying sieving to the computation of quadratic class group.. - Jacobson - 1999 ACM
7 The state of elliptic curve cryptography (context) - Koblitz, Menezes et al. ACM DBLP
7 The technical newsletter of RSA Laboratories (context) - Odlyzko, of et al. - 1995
7 sparse matrices over finite fields via created catastrophes (context) - Pomerance, Smith et al. - 1992
6 Time-memory-processor trade-offs (context) - Amirazizi, Hellman - 1988
5 Discrete logarithms: The effectiveness of the index calculus.. - Schirokauer, Weber et al. - 1996 DBLP
5 Function field sieve method for discrete logarithms over fin.. (context) - Adleman, Huang
5 An algorithm for evaluation of discrete logarithms in some n.. (context) - Semaev - 1998 ACM
4 Asymptotic formulae for the counting function of smooth poly.. (context) - Soundararajan
4 Using number fields to compute logarithms in finite fields (context) - Schirokauer - 1999 ACM
4 Factorization of RSA-140 using the number field sieve - Cavallar, Kioen et al. ACM DBLP
4 Attacking elliptic curve cryptosystems using the parallel Po.. (context) - Escot, Sager et al. - 1998
4 the complexity of a deterministic algorithm for a discrete l.. (context) - Nechaev - 1994
4 Computing discrete logarithms with quadratic number rings (context) - Weber - 1998 DBLP
3 An analytic approach to smooth polynomials over finite field.. (context) - Panario, Gourdon et al. - 1998
3 in Cryptography and Computational Number Theory (context) - McCurley, logarithm et al. - 1990
2 On smooth ideals in number fields - Buchmann, Hollinger - 1996
2 The index calculus method using non-smooth polynomials (context) - Garefalakis, Panario ACM
1 Details and current status available at hhttp://www (context) - Security, challenge
1 in Algorithmic Number Theory: First Intern (context) - Adleman, field et al. - 1994
1 The largest computer on Earth (context) - net
1 Applications and Algorithms (context) - Odlyzko, logarithms et al. - 1994
1 An algorithm for discrete logarithms over an arbitrary finit.. (context) - Semaev - 1995
1 manuscript in preparation (context) - Schirokauer
1 Special prime numbers and discrete logs in prime finite fiel.. (context) - Semaev
1 See hhttp://setiathome (context) - home, project
1 available at hhttp://www (context) - number, list
1 Details and current status available at hhttp://www (context) - curve
1 Polynomials over finite fields free from large and small deg.. (context) - Garefalakis, Panario ACM DBLP
1 in Advances in Cryptology - ASIACRYPT (context) - Silverman, Suzuki et al. - 1998
1 Several reports on GCHQ's secret discovery of non-secret (context) - reports, secret et al.
1 software for massive distributed computations (context) - com
1 Some parallel algorithms for integer factorization (context) - Brent - 1999
1 512--525 (context) - Manstavicius, elements et al. - 1992
1 quant-phi (context) - e-print, hhttp et al.
1 The discrete logarithm problem (context) - Lebedev
1 Integer factoring (context) - Lenstra ACM DBLP
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