On The Homomorphic Computation Of Cryptographic Algorithms

Fully homomorphic encryption allows arbitrary computation on encrypted data without decryption, after decryption, the resulting ciphertext just corresponds to some specific manipulation of plaintext. This homogeneity makes it possible that one can computes encrypted data in the untrusted terminal encryption, which fundamentally solved the confidentiality problems that the data and operation entrust third party. Furthermore, the fully homomorphic encryption technique also has important applications in ciphertext index, electronic voting, multiparty computation.Since the first fully homomorphic encryption scheme was constructed by Craig Gentry in 2009, the FHE scheme has been developped and optimized continuously, resulting many FHE schemes based on different security hypotheses. But its huge key size and computation complexity makes it very difficult in the practical applications.By introducing hybrid encryption scheme, we can improve the efficiency of FHE. hybrid encryption scheme combines general cryptosystem(symmetric cryptography and public key cryptography) and the homomorphic cryptosystem, the initial information is encrypted with general cryptosystem while the decryption and evaluation are accomplished by homomorphic cryptosystem, this reduce the storage expense of ciphertext and the communications.This thesis studies the consumption of the homomorphic circuits when evaluate the decryptions of the general cryptosystems, which help us to find a better cryptosystem for hybrid encryption. The main work is as follows:Firstly, we briefly introduced the research background, present the situation and the research trend for the fully homomorphic encryption.Secondly, we detailedly analyzed all kinds of fully homomorphic encryption schemes and their key techniques. It can be classified into two:the fully homomorphic encryption of Gentry’s blueprint and the fully homomorphic encryption based on LWE problem. Corresponding to Gentry09, DGHV, BV11, BGV modular switch scheme, Bra12 scale-invariant scheme, GSW13 approximate eigenvector method.Finally, we introduced the hybrid encryption technique. Summarized the homomorphiccomputation of some cryptographic algorithms, such as the symmetry cryptography AES, hash function SHA-256 and the public key cryptography Elgamal. In order to find a better cryptographic scheme for hybrid encryption, we work on the homomorphic computation of other symmetry cryptographies. In particularly, we give a detailedly analysis on the homomorphic computation of CLAFIA cryptography and KASUMI cryptography, we obtained the consumption of homomorphic circuits in different kinds of encoding and encapsulation. In addition, under the bit encoding and bits encapsulation, we simply analyzed the homomorphic computation on 12 kinds of symmetric cryptographic algorithms such as DES, and put the consumption of homomorphic circuits together into the table.