The DOI matches its Crossref record; 39 of the 42 references it cites were found in a registry or an index.
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“For y $ ←Y , the probability of y to be a j-node, denoted by q (a N ) : Z ≥0 → [0, 1], is q (a N ) ( j) ≈ 1 e a • a j j! . (5 ) For x $ ←X , the probability of f (x) to be a j-node, denoted by r (a N ) : N → [0, 1], is r (a N ) ( j) ≈ j • q (a N ) ( j). (6 )”
From Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2 (2018) · cites this paper as [29]
Citations
Cites
The Art of Computer Programming: Volume 3: Sorting and Searching
Knuth, D. E. (1973) · Cited by 3,955
The Art of Computer Programming. Volume 2: Seminumerical Algorithms.
Taussky, O., & Knuth, D. E. (1970) · American Mathematical Monthly · doi:10.2307/2317055 · Cited by 3,863
Asymptotics and Special Functions
Olver, F. W. J. (1997) · A K Peters/CRC Press eBooks · doi:10.1201/9781439864548 · Cited by 3,368
Titchmarsh, E. C. (1932) · BURJC Digital (King Juan Carlos University) · Cited by 2,290
Stanley, R. P. (1986) · Springer eBooks · doi:10.1007/978-1-4615-9763-6 · Cited by 1,796
Asymptotic methods in analysis
de Bruijn, N. G. (1958) · International Linear Collider · Cited by 1,332
Pemantle, R., Wilson, M. C., & Melczer, S. (2024) · Cambridge University Press eBooks · doi:10.1017/9781108874144.003 · Cited by 939
Singularity Analysis of Generating Functions
Flajolet, P., & Odlyzko, A. M. (1990) · SIAM Journal on Discrete Mathematics · doi:10.1137/0403019 · Cited by 786
Self-citationThe Art of Computer Programming, Volume 3, Sorting and Searching
Wilkes, M. (1974) · The Computer Journal · doi:10.1093/comjnl/17.4.324 · Cited by 731
A monte carlo method for factorization
Pollard, J. M. (1975) · BIT Numerical Mathematics · doi:10.1007/bf01933667 · Cited by 403
On the Altitude of Nodes in Random Trees
Meir, A., & Moon, J. W. (1978) · Canadian Journal of Mathematics · doi:10.4153/cjm-1978-085-0 · Cited by 362
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Cohen, G., Mora, T., & Moreno, Ó. (1993) · Lecture notes in computer science · doi:10.1007/3-540-56686-4 · Cited by 295
Proceedings of the Steklov Institute of Mathematics
(2013) · Proceedings of the Steklov Institute of Mathematics · doi:10.1134/11501.1531-8605 · Cited by 251
Ordered Cycle Lengths in a Random Permutation
Shepp, L. A., & Lloyd, S. P. (1966) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1966-0195117-8 · Cited by 245
The average height of binary trees and other simple trees
Flajolet, P., & Odlyzko, A. M. (1982) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(82)90004-6 · Cited by 239
Self-citationProbability Distributions Related to Random Mappings
Harris, B. (1960) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177705677 · Cited by 224
Rényi, A., & Szekeres, G. (1967) · Journal of the Australian Mathematical Society · doi:10.1017/s1446788700004432 · Cited by 118
Gaussian limiting distributions for the number of components in combinatorial structures
Flajolet, P., & Soria, M. (1990) · Journal of Combinatorial Theory Series A · doi:10.1016/0097-3165(90)90056-3 · Cited by 107
Self-citationFactorization of the Eighth Fermat Number
Brent, R. P., & Pollard, J. M. (1981) · Mathematics of Computation · doi:10.1090/s0025-5718-1981-0606520-5 · Cited by 97
The first cycles in an evolving graph
Flajolet, P., Knuth, D. E., & Pittel, B. G. (1989) · Discrete Mathematics · doi:10.1016/0012-365x(89)90087-3 · Cited by 93
Self-citationHow easy is collision search. New results and applications to DES
Quisquater, J.-J., & Delescaille, J. (2007) · Springer eBooks · doi:10.1007/0-387-34805-0_38 · Cited by 75
Random mappings with constraints on coalescence and number of origins
Arney, J., & Bender, E. (1982) · Pacific Journal of Mathematics · doi:10.2140/pjm.1982.103.269 · Cited by 69
Julia sets and bifurcation diagrams for exponential maps
Devaney, R. L. (1984) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1984-15253-4 · Cited by 58
Periodic oscillations of coefficients of power series that satisfy functional equations
Odlyzko, A. M. (1982) · Advances in Mathematics · doi:10.1016/0001-8708(82)90005-6 · Cited by 58
Self-citationLimit Distributions of Certain Characteristics of Random Mappings
Stepanov, V. E. (1969) · Theory of Probability and Its Applications · doi:10.1137/1114078 · Cited by 54
La série génératrice exponentielle dans les problèmes d'énumération
Foata, D. C. (1974) · Les Presses de l'Université de Montréal eBooks · Cited by 46
Toward a theory of Pollard's rho method
Bach, E. (1991) · Information and Computation · doi:10.1016/0890-5401(91)90001-i · Cited by 45
Goulden, I. P., & Jackson, D. M. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 43
The Asymptotic Distribution of Maximum Tree Size in a Random Forest
Pavlov, Y. L. (1978) · Theory of Probability and Its Applications · doi:10.1137/1122061 · Cited by 39
Lambda-Upsilon-Omega: An assistant algorithms analyzer
Flajolet, P., Salvy, B., & Zimmermann, P. (1989) · Lecture notes in computer science · doi:10.1007/3-540-51083-4_60 · Cited by 22
Self-citationRandom Mappings with Bounded Height
Sachkov, V. N. (1973) · Theory of Probability and Its Applications · doi:10.1137/1118009 · Cited by 21
Cycle Length in a Random Function
Purdom, P. W., & Williams, J. H. (1968) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1968-0228032-3 · Cited by 20
On the Distribution of the Number of Vertices in Strata of a Random Mapping
Proskurin, G. V. (1974) · Theory of Probability and Its Applications · doi:10.1137/1118106 · Cited by 16
Limit theorem concerning random mapping patterns
Mutafchiev, L. R. (1988) · COMBINATORICA · doi:10.1007/bf02189091 · Cited by 13
Lambda-Upsilon-Omega the 1989 cookbook
Flajolet, P., Zimmermann, P., & Salvy, B. (1989) · Cited by 13
Self-citationDevaney, R. L. (1989) · Banach Center Publications · doi:10.4064/-23-1-221-228 · Cited by 12
Quisquater, J.-J., & Delescaille, J.-P. (1988) · Lecture notes in computer science · doi:10.1007/3-540-48184-2_23 · Cited by 11
Components and Cycles of a Random Function
DeLaurentis, J. M. (1988) · Lecture notes in computer science · doi:10.1007/3-540-48184-2_21 · Cited by 8
Fonctions generatrices et asymptotique automatique
Salvy, B. (1989) · OpenGrey (Institut de l'Information Scientifique et Technique) · Cited by 2
Research works printed but not linked: 9
- A. Z. Broder. Weighted random mappings; properties and applications. Technical Report STAN-CS-85-1054, Computer Science Dept., Stanford University, 1985. (Author’s PhD Thesis).
- B.W. Char, K.O. Geddes, G.H. Gonnet, M.B. Monagan, and S.M. Watt. MAPLE: Reference Manual. University of Waterloo, 1988. 5th edition.
- M. A. Evgrafov. Analytic Functions. Dover, New York, 1966.
- J. Jaworski. Random Mappings. PhD thesis, A. Mickiewicz University, 1985. (In Polish).
- V. F. Kolchin. Random Mappings. Optimization Software Inc., New York, 1986. Translated from Slučajnye Otobraženija, Nauka, Moscow, 1984.
- L. R. Mutafčiev. On some stochastic problems of discrete mathematics. In Mathematics and Education in Mathematics (Sunny Beach), pages 57–80, Bulgarian Academy of Sciences, Sophia, Bulgaria, 1984.
- A. I. Pavlov. On an equation in a symmetric semigroup. Proceedings of the Steklov Institute of Mathematics, 177(4):121–128, 1988. (Issue on Probabilistic Problems of Discrete Mathematics).
- Yu. L. Pavlov. On random mappings with constraints on the number of cycles. Proceedings of the Steklov Institute of Mathematics, 177(4):131–143, 1988. (Issue on Probabilistic Problems of Discrete Mathematics).
- M. Soria. Méthodes d’analyse pour les constructions combinatories et les algorithmes. Doctorat ès sciences, Université de Paris-Sud, Orsay, 1989.
Cited by
Sorted by citations
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
Guide to Elliptic Curve Cryptography
Hankerson, D., Menezes, A., & Vanstone, S. A. (2004) · Springer eBooks · doi:10.1007/b97644 · Cited by 3,102
Combinatorial Stochastic Processes
Pitman, J., & Picard, J. (2006) · Springer eBooks · doi:10.1007/b11601500 · Cited by 988
Singularity Analysis of Generating Functions
Flajolet, P., & Odlyzko, A. M. (1990) · SIAM Journal on Discrete Mathematics · doi:10.1137/0403019 · Cited by 786
Self-citationKey establishment in large dynamic groups using one-way function trees
Sherman, A. T., & McGrew, D. A. (2003) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2003.1199073 · Cited by 707
Metadata
- Authors
- Flajolet, P., & Odlyzko, A. M.
- Affiliations
- Institut national de recherche en sciences et technologies du numérique (FR)
- AT&T (United States) (US)
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer Berlin Heidelberg
- Published
- 2007-11-15
- Pages
- 329-354
- OpenAlex
- W2226303357
- Cited by
- 274
- References
- 42
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 5 · 2023: 7 · 2022: 6 · 2021: 6 · 2020: 9 · 2019: 15 · 2018: 12 · 2017: 11 · 2016: 15 · 2015: 15 · 2014: 17 · 2013: 11 · 2012: 13
- FWCI
- 12.13
- Type
- conference paper
- Language
- en
- Open access
- green
- inria.hal.science
- Licence
- other-oa
- Locations
- Springer eBooks (publishedVersion)
- HAL (submittedVersion, other-oa)
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Theoretical Computer Science › Algorithms and Data Compression
- Keywords
- random maps, finite sets, generating functions, singularity analysis, characteristic parameters, symbolic computation, random number generation, algorithm analysis
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