Analysis And Design Of Algebraic Homomorphism Encryption Scheme

In recent years, cloud computing is a high profile hot spot in the field of informa-ion communication. Ciphertext retrieval and processing is one of key techniques in he field of cloud computing security. In virtue of homomorphic encryption scheme s endowed with extensibility, since homomorphic encryption techniques can well solve the above problems, therefore the research of homomorphism of various sense of cryptography encryption is concentrated encryption algorithm analysis and how to design of the homomorphism is a long stated open problem. How to find an effi-cient and provably secure algebraically homomorphism scheme. One that supports both addition and multiplication operations. That is, algebraically homomorphic encryption scheme. Which has some useful properties:the plaintext space can be extended adaptively without the need for reencryption and it operates over aritrary infinite fields as well. According to the parameter selection, it’s error——correcting capability is determined by a certain amount of error information transmitted from ciphertext. It is one of the important theory significance and the application value of the research topic.To studies of algebraically homomorphism scheme, The following is the results obtained in this work:1. Analyses are conducted on the two algebraically homomorphism schemes based on coding theory, Kiayias-Yung scheme and Frederik-Ahmad scheme. Spe-cific analysis of two schemes of the correctness, algebraically homomorphism, the efficiency of encryption and decryption, although the Frederik-Ahmad scheme full use of the RS code decoding principle, which decode has the very strong error cor-recting capability, but its decoding algorithm is more complicated. And the key and the length of ciphertext is too large to cause the efficiency of the scheme with low efficiency.2. This paper use safety cipher technology to design a new algebraically homo-morphism schemes based on BCH coding theory, compared with the Frederik-Ahmad scheme, the new scheme based on the correctness, algebraically homomorphism, be-cause of the encoding and decoding of codewords from the different field, decod-ing BCH code easier than RS code in time-domain. Therefore, the new encryption and decryption scheme with greatly efficiency.