Algorithms in number theory and cryptography

点击翻译按钮获取中文摘要

In the past few decades, cryptography, the study of data security, has emerged as an important concern in our society. As information becomes increasingly accessible through the Internet, the need to protect and authenticate data is more imperative than ever. The security of many methods in modern public-key cryptography relies on the supposed difficulty of certain computational problems in mathematics and, in particular, number theory. These schemes are set up in such a way that presumably the only way for an attacker to break the given system is to solve an instance of one such problem. Currently, only three number-theoretic problems are widely accepted as foundations for secure public-key protocols. Furthermore, these three problems have strong theoretical relationships. In many cases, being able to solve one efficiently implies the ability to solve the other two efficiently as well. In other words, one dramatic mathematical discovery could render many current public-key cryptographic techniques insecure.