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RSA的安全性是依据大整数分解的困难性而设计的。RSA公开密钥加密体制中n为2个大素数的乘积,即针对n=pq（p,q为大素数）的大整数分解,这里介绍了RSA算法的扩展算法的加密和解密原理,即针对n=p1,p2,…,pr（p1,p2,…,pr为大素数）的大整数分解。通过扩展素因子的个数达到RSA算法的安全性。比较RSA算法,扩展的RSA算法不仅可用于数据加密解密,也可用于数字签名。利用扩展的RSA算法实现数字签名也具有较高的安全性和可靠性。“,”The security of RSA is designed on the basis of the difficulty of large integer decomposition.In the RSA public key encryption system the public key n is the product of two large prime number,aiming at the large integer n decomposition of the form n=pq（in which p,q as large prime number）.The paper describes the encryption and decryption theory of extending RSA algorithm,aiming at the large integer n decomposition to the form n=p1,p2,…,pr（in which p1,p2,…,pr as large prime number）.The addition of prime number could enhance the security of RSA algorithm.Compared to RSA algorithm,the extending RSA algorithm could be applied to both digital encryption/decryption and digital signature.Digital signature algorithm based on extending RSA algorithm is also of high security and reliability.