Much asymptotic analysis has been devoted to factoring algorithms. We present a practical analysis of the complexity of the elliptic curve algorithm, suggesting optimal parameter selection and run-time guidelines. The parameter selection is aided by a novel use of Bayesian statistical decision techniques as applied to random algorithms. We discuss how frequently the elliptic curve algorithm succeeds in practice and compare it with the quadratic sieve algorithm.
This journal, begun in 1943 as Mathematical Tables and Other Aids to Computation, publishes original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes. It is devoted to advances in numerical analysis, the application of computational methods, high speed calculating, and other aids to computation.
Founded in 1888, to further mathematical research and scholarship, the 30,000-member American Mathematical Society provides programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and everyday life. The headquarters of the AMS are in Providence, Rhode Island. The Society also maintains a government relations office in Washington, D.C., the Mathematical Reviews editorial office in Ann Arbor, Michigan, and a warehouse and distribution facility in Pawtucket, Rhode Island. The Society has approximately 240 employees.
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Mathematics of Computation
© 1993 American Mathematical Society
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