Andrew M. Odlyzko

Learn More
  • R Feynman, Quan, +23 authors U Vazi-Rani
  • 1994
A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consideration. Several researchers, starting with David Deutsch,(More)
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 expansion for the Taylor coefficients ofthe function. This approach is based on contour integration using Cauchy’s formula and Hankel-like contours. It constitutes an(More)
The subset sum problem is to decide whether or not the 0-l integer programming problem <italic>&Sgr;<supscrpt>n</supscrpt><subscrpt>i=l</subscrpt> a<subscrpt>i</subscrpt>x<subscrpt>i</subscrpt></italic> = <italic>M</italic>, <italic>&forall;I</italic>, <italic>x<subscrpt>I</subscrpt></italic> = 0 or 1, has a solution, where the(More)
Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u ∈ GF(q) is that integer k, 1 ≤ k ≤ q − 1, for which u = g k . The well-known problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its applicability in cryptography. Several cryptographic systems(More)
The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short non-zero vectors in special lattices. The Lagarias-Odlyzko(More)