Computational Number Theory and Computational Algebraic Geometry

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9412383 Huang This research will further explore the rich and potentially fruitful interplay between number theory and algebraic geometry to investigate computational problems in number theory, with emphasis on: discrete logarithms over various groups, which is a fundamental problem of cryptographic significance; polynomial congruences modulo primes, including the univariate and multivariate cases; and finding small nonresidues in finite fields; develop efficient algorithms for computing with curves over finite fields, with emphasis on fundamental arithmetical problems on curves which are important for applications in computational number theory, cryptography and coding theory; apply the results obtained to public-key cryptography, coding theory, and other areas as well. ***