Research Of Homomorphic Encryption Technology And Application

Homomorphic encryption, proposed by Rivest et al. in the70s of the last century, is a class with the special nature of the encryption algorithm. Compared with the general encryption algorithm, homomorphic encryption can implement not only the basic cryptographic operations, but also specific types of computations on ciphertexts, which means the results of calculating before decrypting is same as decrypting before calculating. This property is of great significance for the protection of information security:with homomorphic encryption technology,we can calculate multiple ciphertexts and then decrypt rather than decrypting each ciphertext at first, which spends the high price of computation; homomorphic encryption technology allows the party without secret key to calculate ciphertexts, do not have to send all the ciphertexts to key party, thus, it can not only reduce the cost of communication, but also transfer computing tasks, which can balance the computational cost of all parties; in homomorphic encryption technology, the decrypting party can only get the final results instead of every ciphertext message, this would improve the security of the information greatly. Because of the advantages of homomorphic encryption in computational complexity, communication complexity and security, a growing number of scholars involve in the study of its theory and applications.The frequent network activity expose growing number of information security problems, which exacerbate the demand of SMC(Secure Multi-Party Computation). Homomorphic encryption, as one of the core technology of the SMC, its superiority that compared with the general algorithm contribute to the design of efficient, secure computing protocols. But the defects of homomorphic encryption system still limit the scope of its application. Therefore, research on the theory and applications of homomorphic encryption is of great significance. In this paper, the main work of the homomorphic encryption as follows:First of all, introduce several typical homomorphic encryption schemes, including partially homomorphic encryption schemes and fully homomorphic encryption schemes. We point out characteristics of each scheme and the application achievements relying on those characteristics in the security field. Based on these work, we summarize the existing problems of homomorphic encryption cryptosystems, and propose further ideas.Next, introduce the "many-to-one" homomorphic encryption scheme. The present homomorphic encryption schemes are mostly in the form of "one-to-one", means one party encrypts and the other decrypts in public key cryptosystem. With the changing of network scenarios, this form of cryptography has been unable to satisfy the demand of multi-party.In the field of wireless LAN,3G networks and limited network, the "one-to-many"’,"many-to-one" and’"many-to-many" interactive forms ask the diversity of cryptography forms. In order to improve the practicality, we combine the concept homomorphic encryption with the cryptography form of "multi-party encryption, one party decryption" to propose the "many-to-one" homomorphic encryption scheme. Firstly, We propose a practical application scenarios in "many-to-one" cryptography form and then define the model of the "many-to-one" homomorphic encryption scheme; Secondly, build our scheme on the basis of Dijk et al.’s integer homomorphic scheme and prove the correctness, homomorphism and security of the "many-to-one" homomorphic encryption scheme under the model definition; At last, by analysis of our scheme, we show that the "many-to-one " homomorphic encryption scheme can not only achieve many-to-one form, but also has a homogeneity between the ciphertexts with different keys, which avoids appearing the case of the multiple keys. According to the way of scheme building, I extend and make a "many-to-one" homomorphic encryption scheme in multi-level, which achieves the homomorphism of high permission ciphertext to low permission ciphertext and extends the range of practicality.Finally, introduce secure multi-party multiplication protocol based on homomorphic encryption technology. With the strict analysis of the characteristics of homomorphic encryption, we realize that the reasonable using of this technology can reduce the computational complexity and communication complexity of multi-party computation. Secure multi-party multiplication is a special problem of secure multi-party computation, which can be used by multi-party to share the multiplication result. For the problems of high cost of communication and large amount of data which are caused by frequently using the secure two-party multiplication protocol in the present protocols, a serial secure multi-party multiplication protocol in the complex communication environment and a parallel secure multi-party multiplication protocol in the ideal communication environment are presented in this paper with the help of the semi-honest model. At last, correctness and security of those protocols are analyzed. Compared with the present protocols, the analysis shows that the proposed protocols have advantages in the communication cost and the execution efficiency. Compared with the existing multiplicative protocol of multi-party, two protocols in this paper combine the specific network environment, and enhance the practicality of the protocol. In addition, as a basic Multi-party Computation protocol, this protocol provides a new way for the study of other multi-party computation protocols using homomorphic encryption technology.