基于增强的RSA和ELGamal加密算法的新签名方案

A New Signature Scheme Based on Enhanced RSA and ELGamal Encryption Algorithms

摘要: 密码学解决了安全通信的必要条件，如隐私、机密性、密钥交换、身份验证和不可否认性。邵祖华提出基于因式分解和离散对数的两个数字签名，由于在两个签名协议中引入多个指数密运算，导致计算量大。Malhotra M提出一种基于增强的RSA和ELGamal的新加密方案，相比现有的加密方案效率更高。在他们的基础上本文提出了一种基于增强的RSA和ELGamal密码系统相结合的算法，增强的RSA密码体制基于整数分解问题(IFP)，而ELGamal密码体制依赖于离散对数问题(DLP)。该模型基于IFP与DLP的结合，在解决两个著名难题的困难的基础上，为非对称密码系统提供了很好的计算速度，与ELGamal和现有的RSA-ELGamal混合系统相比，该算法具有更高的吞吐量和更短的加密时间，分析了新加密算法的高安全性。在该模型的基础上引入单向哈希函数，提出了相应的数字签名方案。这个签名方案的安全性不仅基于因数分解和离散对数的困难性，还有求逆函数的困难性，其安全性高于基本的ELGamal数字签名方案。

Abstract: Cryptography solves the necessary conditions for secure communication, such as privacy, confiden-tiality, key exchange, authentication and non repudiation. Shao Zuhua proposed two digital signa-tures based on factorization and discrete logarithm. Because of the introduction of multiple expo-nential secret operations in the two signature protocols, the computation is large. Malhotram pro-posed a new encryption scheme based on enhanced RSA and ElGamal, which is more efficient than the existing encryption schemes. On their basis, this paper proposed an algorithm based on the combination of enhanced RSA and ElGamal cryptosystems. The enhanced RSA cryptosystem is based on Integer factorization problem (IFP), while ElGamal cryptosystem relies on discrete loga-rithm problem (DLP). This model is based on the combination of IFP and DLP. On the basis of solving the difficulties of two famous problems, it provides a very good computing speed for asymmetric cryptographic systems. Compared with ElGamal and existing RSA ElGamal hybrid systems, this al-gorithm has higher throughput and shorter encryption time. The high security of the new encryp-tion algorithm is analyzed. Based on this model, a one-way hash function is introduced and a corre-sponding digital signature scheme is proposed. The security of this signature scheme is not only based on the difficulty of factorization and discrete logarithm, but also on the difficulty of finding the inverse function. Its security is higher than that of the basic ElGamal digital signature scheme.