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
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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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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