Fully homomorphic encryption(FHE) is the cryptosystem which supports both addition and multiplication. The existence of the cryptosystems which have efficiency and fully homomorphism would bring great practical implications in the outsourcing of private computations, for instance, in the context of cloud computing. But FHE scheme which runs fast for practical use is not proposed until now because the scheme requires huge complexity. This book, therefore, provides the new fully homomorphic encryption scheme without "bootstrapping" which runs fast for practical use. The system runs on octonion...

Gentrys bootstrapping technique is still the only known method for obtaining fully homomorphic encryption. I propose a new fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The security of the proposed fully homomorphic encryption scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption...

Since Diffie and Hellman proposed the concept of the public key cryptosystem (PKC), key agreement protocol (KAP) and digital signature scheme (DSS) in 1976, various PKC, KAP and DSS were proposed.The signcryption which is a new public-key technology that combines signing and encrypting a message, that is, DSS+PKC or DSS+KAP in a single step was proposed by Y. Zheng in 1997. The signcryption is particularly useful in cloud computing for ensuring confidential, authenticated transmissions. I propose the new method for performing the function of both KAP and DSS simultaneously (signcryption) on...