Extensions of the birthday surprise

Klamkin, Murray S.; Newman, Donald J.

doi:10.1016/s0021-9800(67)80075-9

Cited by 67 publications

(40 citation statements)

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“…Interestingly, there is a much earlier work by Klamkin and Newman [KN67] which considers a similar problem. We interpret and extend their work in terms of a concrete hash function in Section 4.2.…”

Section: Expected Number Of Trials To Obtain An R-collisionmentioning

confidence: 99%

“…In an earlier work, Klamkin and Newman [KN67] consider the following problem: given m equally likely alternatives, repeatedly choose the alternatives one by one with replacements until one item occurs r times. They study the expected number of trials for this event to occur and show that as m goes to infinity the expected number of trials is approximately rΓ(1 + 1/r)m (r−1)/r , where Γ denotes the usual Gamma function defined by…”

Section: $(R)mentioning

confidence: 99%

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On Quantifying the Resistance of Concrete Hash Functions to Generic Multicollision Attacks

Ramanna

Sarkar

2011

IEEE Trans. Inform. Theory

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Bellare and Kohno (2004) introduced the notion of balance to quantify the resistance of a hash function h to a generic collision attack. Motivated by their work, we consider the problem of quantifying the resistance of h to a generic multi-collision attack. To this end, we introduce the notion of r-balance µ r (h) of h and obtain bounds on the success probability of finding an r-collision in terms of µ r (h). These bounds show that for a hash function with m image points, if the number of trials q is Θ rm ( r−1 r )µr(h) , then it is possible to find r-collisions with a significant probability of success. The behaviour of random functions and the expected number of trials to obtain an r-collision is studied. These results extend and complete the earlier results obtained by Bellare and Kohno (2004) for collisions (i.e., r = 2). Going beyond their work, we provide a new design criteria to provide quantifiable resistance to generic multicollision attacks. Further, we make a detailed probabilistic investigation of the variation of r-balance over the set of all functions and obtain support for the view that most functions have r-balance close to one.

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Section: Expected Number Of Trials To Obtain An R-collisionmentioning

confidence: 99%

Section: $(R)mentioning

confidence: 99%

On Quantifying the Resistance of Concrete Hash Functions to Generic Multicollision Attacks

Ramanna

Sarkar

2011

IEEE Trans. Inform. Theory

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“…In the compact scenario, the random selection strategy performs very poorly -this strategy is precisely characterized by the well known Coupon Collector's problem [14]. When exactly Ò symbols are present in the system, random selection requires Ç´ÐÓ Òµ symbols on average to recover each useful symbol, so this strategy is not suitable for sending all of a large set of symbols.…”

Section: Discussionmentioning

confidence: 99%

Informed content delivery across adaptive overlay networks

ByersJohn

ConsidineJeffrey

MitzenmacherMichael

et al. 2002

SIGCOMM Comput. Commun. Rev.

147

196

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Overlay networks have emerged as a powerful and highly flexible method for delivering content. We study how to optimize throughput of large, multipoint transfers across richly connected overlay networks, focusing on the question of what to put in each transmitted packet. We first make the case for transmitting encoded content in this scenario, arguing for the digital fountain approach which enables end-hosts to efficiently restitute the original content of size Ò from a subset of any Ò symbols from a large universe of encoded symbols. Such an approach affords reliability and a substantial degree of application-level flexibility, as it seamlessly tolerates packet loss, connection migration, and parallel transfers. However, since the sets of symbols acquired by peers are likely to overlap substantially, care must be taken to enable them to collaborate effectively. We provide a collection of useful algorithmic tools for efficient estimation, summarization, and approximate reconciliation of sets of symbols between pairs of collaborating peers, all of which keep messaging complexity and computation to a minimum. Through simulations and experiments on a prototype implementation, we demonstrate the performance benefits of our informed content delivery mechanisms and how they complement existing overlay network architectures.

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“…An alternative exact and asymptotic result for a general case, for the expected number of repetitions necessary for one of the alternatives to occur a certain number of times, was given by Klamkin and Newman [17]. Thus, we get…”

Section: Moments and Generating Functionsmentioning

confidence: 91%

“…The distribution (1.1) and diverse extensions have been intensively studied (see, e.g., [1,3,4,5,7,8,10,11,12,13,17,20,21,22,23,24,25,26,27]). …”

Section: S T (X) = X T (X) Tmentioning

confidence: 99%

On the birthday problem: some generalizations and applications

Rathie

Zörnig

2003

International Journal of Mathematics and Mathematical Sciences

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We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functions U(−; −; −) which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.

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Extensions of the birthday surprise

Cited by 67 publications

References 1 publication

On Quantifying the Resistance of Concrete Hash Functions to Generic Multicollision Attacks

On Quantifying the Resistance of Concrete Hash Functions to Generic Multicollision Attacks

Informed content delivery across adaptive overlay networks

On the birthday problem: some generalizations and applications

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