Fully Homomorphic Encryption

Abstract In 1978, Rivest et al. (1978) proposed the concepts of data bank and fully homomorphic encryption. Some individuals organizations encrypt original store them in for privacy protection. Data is also called cloud. Therefore, cloud stores a large amount data, which obviously huge wealth. How to use these effectively? First all, we must solve problem calculation encrypted problem. Rivest, Adleman Dertouzos conjecture that if all encryption, is, addition multiplication ciphertext are corresponding plaintext, then can be effectively computed by elementary without changing structure plaintext (under condition homomorphism). The RAD has been more than 30 years, but no one could this since cryptographic encryption system too complicated. 2009, C. Gentry, computer scholar at Stanford University, first scheme Gentry (2009b) based on ideal lattice, he won 2022 highest award theoretical science—the Godel Award. Based Gentry’s work, second third schemes LWE distribution trapdoor matrix technology have proposed; see Brakerski Vaikuntanathan (2011a), (2011b), (2012), (2014), (2015) (2013) 2013. main purpose chapter systematically analyze discuss above three techniques, order understand latest research trends post-quantum cryptography.