有限域上RSA-ELGamal加密及数字签名方案  

RSA-ELGamal encryption and digital signature scheme over finite fields

作　　者：杨倩倩 范自强 YANG Qianqian;FAN Ziqiang(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232000,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232000

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第1期39-44,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：安徽理工大学2022年研究生创新基金立项建设项目(2022CX2134)。

摘　　要：基于增强的RSA和ELGamal加密算法,提出了有限域上多项式的RSA-ELGamal加密方案.新的加密方案基于大整数分解问题(IFP)和难解的离散对数问题(DLP)的结合,使其安全性高于单个使用有限域上多项式形式的RSA加密算法和ELGamal加密体制.新提出的加密方案可对多个明文进行加密,在对明文加密时通过引入RSA的公钥对明文进行隐藏,加密效率高,安全性强.在新加密方案基础上引入单向哈希函数,并提出相应的数字签名方案,签名方案利用多个接收者分别验证和加密消息,进一步增强签名被攻击的概率.加密方案和数字签名的安全性主要基于大整数的分解和离散对数求解的双重困难问题,使得签名具有不可攻击性,提高此类签名方案的安全性.A RSA-ELGamal encryption scheme for polynomials over finite fields was proposed based on enhanced RSA and ELGamal encryption algorithms.The new encryption scheme was based on the combination of large integer factorization problem(IFP)and difficult to solve discrete logarithm problem(DLP),making its security higher than that of a single RSA encryption algorithm and ELGamal encryption system using polynomial form over finite fields.The newly proposed encryption scheme can encrypt multiple plaintexts.When encrypting plaintexts,RSA′s public key was introduced to hide them,resulting in high encryption efficiency and strong security.On the basis of the new encryption scheme,a one-way hash function was introduced,and a corresponding digital signature scheme was proposed.The signature scheme utilizes multiple receivers to verify and encrypt messages separately,further enhancing the probability of signature attacks.The security of encryption schemes and digital signatures were mainly based on the dual difficulty problem of factoring large integers and solving discrete logarithms,which were made signatures invincible and improved the security of such signature schemes.

关 键 词：RSA ELGAMAL 数字签名 有限域 IFP DLP 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]