The Study Of The REESSE1+Public Key Encryption Scheme Based On IBE

REESSE1+, as a public key cryptosystem, has opened up new directions forpublic key cryptography, and may be the alternative in quantum computationalera.The system presents three mathematical problems, it is a public key cryptosystembased on multi-problem and may become one of the alternative encryption scheme forquantum computer age. The three problems are: Multivariate Permutation Problem,Anomalous Subset Product Problem, and Transcendental Logarithm Problem.Identity-based encryption Encryptionis a new direction of development of thepublic-key cryptosystem, the design ideaof which was first put forward by the Israelicryptographer Adi Shamir.Compared with the certificate-based cryptography, IBE willbe the user’s identity as a public key, do not need to keep each user’s public keycertificate, thus avoiding the use of certificates from storage and managementoverhead.It simplifies the key management process of the certificate-basedcryptography.Firstly, the structure principle, thecharacteristic and the framework of IBE arestudied clearly.Then, the key generation algorithm, the encryption algorithms and thedecryption algorithm in REESSE1+are introducedin detail.Finally,IBE andREESSE1+based on multi-problemare combined to creat an IBE scheme based onmulti-problem.The scheme applies the idea of IBE to REESSE1+, so the schemeimproves REESSE1+, andpromotesits popularization and application.The new program consists of five parts: the system initialization, the user identitymapping, the private key generation, the encryption, the decryption. These five partsare described in detail and research, and then we construct a complete identity-basedREESSE1+public key encryption scheme. By the reduction method, we analyses thecomplexity of the scheme is at least equivalent to DLP in the same prime domain.From the security and time complexity of the scheme, the advantage of the program isconcluded.In the user identity mapping, the user’s ID is mapped as a public keysequencemeeting the requirement of REESSE1+.In the private key generation, the keygeneration algorithm of REESSE1+is improved based on IBE basic principle, andtheprivate key is calculatedfromthepublic key through the private key generationalgorithm. These two parts are completed by the private key generator.PKG encryptesinformation using the user’s identityand its security depends on the MPP problem. Inthe encryption and the decryption, both sides of communication use REESSE1+encryption and decryption algorithm to encrypt and decrypt messages, so a newencryption scheme based IBE is constructed. The new scheme provides the newresearch direction for the construction of IBE, also proposesa new application spaceof the REESSE1+public key cryptosystem.