Computational Number Theory and Computational Algebraic Geometry

9412383 Huang这项研究将进一步探索数论和代数几何之间丰富而富有成果的相互作用， 研究数论中的计算问题，重点是：各种群上的离散群，这是密码学意义上的基本问题;多项式同余模素数，包括单变量和多变量情况; 和寻找有限域中的小非剩余; 发展有效的算法计算曲线在有限领域，重点是基本算术问题的曲线，这是重要的应用程序在计算数论，密码学和编码理论; 将所得结果应用于公钥密码学、编码理论和其他领域。 ***

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. ***