A non-uniform birthday problem with applications to discrete logarithms

Discrete Applied Mathematics

Volumn 160, Issue 10-11, 2012, Pages 1547-1560

  Galbraith, Steven D ^a   Holmes, Mark ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Birthday paradox; Discrete logarithm problem; Probabilistic analysis of randomised algorithms

Indexed keywords

ANALYSIS OF ALGORITHMS; BIRTHDAY PARADOX; DISCRETE LOGARITHM PROBLEMS; DISCRETE LOGARITHMS; GENERALISATION; RANDOMISED ALGORITHMS;

COMBINATORIAL MATHEMATICS; MATHEMATICAL TECHNIQUES;

SPHERES;

EID: 84859927504     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2012.02.019     Document Type: Article

References (17)

1. R. Arratia, L. Goldstein, and L. Gordon Two moments suffice for poisson approximations: the Chen-Stein method Ann. Probab. 17 1 1989 9 25
2. R. Arratia, L. Goldstein, and L. Gordon Poisson approximation and the Chen-Stein method Statist. Sci. 5 4 1990 403 424
3. M. Camarri, and J. Pitman Limit distributions and random trees derived from the birthday problem with unequal probabilities Electron. J. Probab. 5 2 2000 1 18
4. S. Chatterjee, P. Diaconis, and E. Meckes Exchangeable pairs and Poisson approximation Electron. Encyclopedia Probab. 2004
5. L.H.Y. Chen Poisson approximation for dependent trials Ann. Probab. 3 3 1975 534 545
6. A. DasGupta The matching, birthday and the strong birthday problem: a contemporary review J. Statist. Plann. Inference 130 2005 377 389
7. P. Flajolet, D. Gardy, and L. Thimonier Birthday paradox, coupon collectors, caching algorithms and self-organizing search Discrete Appl. Math. 39 3 1992 207 229
8. S.D. Galbraith, J.M. Pollard, R.S. Ruprai, The discrete logarithm problem in an interval, Math. Comput. (in press).
9. S.D. Galbraith, and R.S. Ruprai An improvement to the Gaudry-Schost algorithm for multidimensional discrete logarithm problems M. Parker, Twelfth IMA International Conference on Cryptography and Coding LNCS vol. 5921 2009 Springer Cirencester 368 382
10. S.D. Galbraith, and R.S. Ruprai Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval P.Q. Nguyen, D. Pointcheval, PKC 2010 LNCS vol. 6056 2010 Springer 368 383
11. P. Gaudry, and E. Schost A low-memory parallel version of Matsuo, Chao and Tsujii's algorithm D.A. Buell, ANTS VI LNCS vol. 3076 2004 Springer 208 222
12. G.R. Grimmett, and D.R. Stirzaker Probability and Random Processes second Ed. 1992 Oxford University Press
13. K. Nishimura, and M. Sibuya Occupancy with two types of balls Ann. Inst. Statist. Math. 40 1 1988 77 91
14. K. Nishimura, and M. Sibuya Probability to meet in the middle J. Cryptology 2 1 1990 13 22 (Pubitemid 20686013)
15. J.M. Pollard Monte Carlo methods for index computation (mod p) Math. Comput. 32 143 1978 918 924
16. J.M. Pollard Kangaroos, monopoly and discrete logarithms J. Cryptology 13 4 2000 437 447
17. B.I. Selivanov On waiting time in the scheme of random allocation of coloured particles Discrete Math. Appl. 5 1 1995 73 82