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Abstract: The difficulty of computing discrete logarithms known to be "short" is examined, motivated by recent practical interest in using Diffie-Hellman key agreement with short exponents (e.g. over Zp with 160-bit exponents and 1024-bit primes p). A new divide-and-conquer algorithm for discrete logarithms is presented, combining Pollard's lambda method with a partial Pohlig-Hellman decomposition. For random DiffieHellman primes p, examination reveals this partial decomposition itself allows... (Update)
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...Z p , and elements g x 2 Z p and g y 2 Z p , find g xy 2 Z p . These two problems hold their properties in a prime order subgroup[30, 28]. We assume that all numerical operations of the protocol are on the cyclic group where it is hard to solve these problems. We consider the...
...the order of J K L . 3. 3 Attacks Based on Composite Order Subgroups The attacker can exploit subgroups that do not have large prime order [51]. This is best illustrated by an example. Suppose Alice and Bob choose a prime M U R , where q is prime, and a generator of order...
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BibTeX entry: (Update)
P. vanOorschot, M. Wiener, "On Diffie-Hellman Key Agreement with Short Exponents", Proceedings of Eurocrypt '96, Springer-Verlag LNCS, May 1996. http://citeseer.ist.psu.edu/article/vanoorschot96diffiehellman.html More
@article{ vanoorschot96diffiehellman,
author = "Paul C. van Oorschot and Michael J. Wiener",
title = "On {Diffie-Hellman} Key Agreement with Short Exponents",
journal = "Lecture Notes in Computer Science",
volume = "1070",
pages = "332--??",
year = "1996",
url = "citeseer.ist.psu.edu/article/vanoorschot96diffiehellman.html" }
Citations (may not include all citations):2003 The Art of Computer Programming (context) - Knuth - 1981
2003 The Art of Computer Programming (context) - Knuth - 1973
1529 A method for obtaining digital signatures and public key cry.. - Rivest, Shamir et al. - 1978
635 New directions in cryptography - Diffie, Hellman - 1976 ACM
168 An improved algorithm for computing logarithms over GF (p) a.. (context) - Pohlig, Hellman - 1978
147 Efficient signature generation by smart cards (context) - Schnorr - 1991 DBLP
74 The Photuris session key management protocol (context) - Karn, Simpson - 1995
59 Cryptanalysis of short RSA secret exponents (context) - Wiener - 1990 ACM
58 Monte Carlo methods for index computation (mod p (context) - Pollard - 1978
40 Computation of discrete logarithms in prime fields - LaMacchia, Odlyzko - 1991 ACM DBLP
35 The discrete logarithm problem (context) - McCurley - 1990
32 Factoring by electronic mail (context) - Lenstra, Manasse ACM DBLP
29 Towards the equivalence of breaking the Diffie-Hellman proto.. - Maurer
24 Fast Generation of Prime Numbers and Secure Public-Key Crypt.. - Maurer - 1995 DBLP
23 On using RSA with low exponent in a public-key network (context) - Hastad
21 Comparison of three modular reduction functions - Bosselaers, Govaerts et al. ACM DBLP
17 Parallel collision search with application to hash functions.. (context) - van Oorschot, Wiener - 1994 ACM DBLP
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7 Simple Key Management for Internet Protocols (SKIP (context) - Aziz - 1995
4 A note on discrete logarithms with special structure (context) - Heiman
3 National Technical Information Service (context) - of, Digital et al. - 1994
2 Discrete-log with compressible exponents - Yacobi ACM DBLP
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