Research On Verifiable Outsourced Computation And Linear Codes Based On A Generic Construction

Cryptography and coding theory play an important role in information security and other fields, and thus they have always been an interesting subject of study. In this paper, we will study two problems. One is to construct verifiable outsourced computation scheme based on some cryptographic algorithms in cloud computing,and the other is to study linear codes based on a generic construction and consider their applications in cryptography and other fields. The main results of this paper are as follows:1. We study the construction of verifiable outsourced computation for arbitrary functions. Based on ensuring the privacy of input and output data, we improve previous verifiable outsourced computation schemes for arbitrary functions by using hybrid encryption based on fully homomorphic encryption(FHE), which can efficiently reduce the client’s computation cost. Moreover, our scheme can greatly reduce online communication cost. Finally, we prove the security and the efficiency of our scheme.2. We study the privacy-preserving face recognition protocol. In previous work of privacy preserving face recognition, in order to protect individuals’ privacy, face recognition is performed over encrypted face images. However, these results increase the computation cost of the client and the face database owners, which may enable face recognition not to be executed. Consequently, it would be desirable to reduce computation cost over sensitive biometric data in such environments. In this paper, we propose a privacy-preserving face recognition protocol with outsourced computation by using hybrid encryption based on fully homomorphic encryption(FHE). The proposed protocol can efficiently protect individuals’ privacy and substantially improve the previous works in terms of the online computation cost by outsourcing large computation task to a cloud server who has large computing power.3. Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes,association schemes, strongly regular graphs and other fields. Based on a generic construction, many linear codes with few weights and good error correcting capability have been produced with this generic approach. Firstly, the relationships among some classes of linear codes obtained with this approach are established, so that the parameters of some classes of linear codes can be derived from those of other classes with known parameters. Secondly, a class of linear codes with a few weights over the finite field GF(p) are presented and their weight distributions are also determined, where p is a prime. Some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear codes. In addition, this codes can be applied in secret sharing schemes.4. As applications of binary codes, we study their applications in codebooks.A generic construction of codebooks based on binary codes is introduced. With this generic construction, a few previous constructions of optimal codebooks are extended,and a new class of codebooks almost meeting the Levenshtein bound is presented by using semibent functions. Many codebooks meeting or amost meeting the Levenshtein bound from binary codes are obtained in this paper. In addition, three bounds on the parameters of binary codes are derived.