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Singularity Analysis of Generating Functions
This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic
Solving low density subset sum problems
  • J. Lagarias, A. Odlyzko
  • Computer Science, Mathematics
    24th Annual Symposium on Foundations of Computer…
  • 1983
This method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below dc (n), as n → ∞.
On the distribution of spacings between zeros of the zeta function
Etude numerique de la distribution des espacements des zeros de la fonction zeta de Riemann. Observation de certains phenomenes inatendus
String Overlaps, Pattern Matching, and Nontransitive Games
Asymptotic enumeration methods
12 Large singularities of analytic functions 113 12.1 The saddle point 13 Multivariate generating functions 128 14 Mellin and other integral transforms 134 15 Functional equations, recurrences, and
Random Mapping Statistics
A general framework in which the analysis of about twenty characteristic parameters of random mappings is carried out is introduced, and an open problem of Knuth is solved, namely that of finding the expected diameter of a random mapping.
Paris metro pricing for the internet
PMP (Paris Metro Pricing) is the simplest differentiated services solution, designed to accommodate user preferences at the cost of sacrificing some of the utilization efficiency of the network.
Algebraic properties of cellular automata
Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata, and the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities.
Discrete Logarithms in Finite Fields and Their Cryptographic Significance
  • A. Odlyzko
  • Computer Science, Mathematics
  • 1 December 1985
This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2n), finding that in order to be safe from attacks using these algorithms, the value of n for which GF( 2n) is used in a cryptosystem has to be very large and carefully chosen.
A bound for the least prime ideal in the Chebotarev Density Theorem
as x --, oc. In [7] two versions of the Chebotarev density theorem were proved, one unconditional and the other on the assumption of the Generalized Riemann Hypothesis (GRH), each of which expressed