RSA加密体制的密钥生成技术的研究

RSA是一种非对称加密算法,在公钥加密标准和电子商业中被广泛应用.RSA的可靠性基于大整数的分解难度.事实证明,因子分解的难度随着密钥长度的增加而增加.本文讨论密钥长度为1000位以上密钥生成技术,这种技术主要涉及通过素性检测生成一个大素数.运用Rabin-Miller算法检测素数,并在成功生成两个大素数之后,运用欧几里德算法在默认公钥的前提下求得私钥,然后就可运用公钥和私钥进行加密与解密了.

The Analysis of Key Generating in RSA

In cryptography, RSA is an algorithm for public key encryption. RSA is widely used in electronic commerce protocols, and is believed to be secure given sufficiently long keys. It was proved that the longer the length of the key, the harder it is to be factored. In the text, we will discuss the realization of the key generation, when the user need a key length of more than 1024 bits. In this procedure, we need two large prime numbers. So we must first generate two odd integers and then test the primality of these two odd integers. As an example, one of the more efficient and popular algorithm, the Miller-Rabin algorithm, is described in this text. After generating two prime integers successfully, we can use Euclid algorithm to calculate the public-key and the private-key easily. In the end, the user can use the public key to encrypt and the private-key to decrypt.