Distributed Oblivious Function Evaluation and Its Applications

This paper is about distributed oblivious function evaluation (DOFE). In this setting one party (Alice) has a functionf(x), and the other party (Bob) with an input α wants to learnf(α) in an oblivious way with the help of a set of servers. What Alice should do is to share her secret functionf(x) among the servers. Bob obtains what he should get by interacting with the servers. This paper proposes the model and security requirements for DOFE and analyzes three distributed oblivious polynomial evaluation protocols presented in the paper. Keywords oblivious function evaluation - oblivious polynomial evaluation - secure multiparty computation - distributed - information security The research is supported by the National Basic Research 973 Program of China under Grant No. 1999035802 and the National Natural Science Foundation of China under Grant No.60273029.Hong-Da Li was born in 1960. He received the Ph.D. degree from Northwestern Polytechnical University in 2001. His current research interests are cryptology and cryptographic protocol.Xiong Yang received the B.S. degree in mathematics from Yan'an University, China, in 1984. He is an associate professor in College of Economy and Trade at South China University of Tropical Agriculture. His research interest is information security.Deng-Guo Feng was born in 1963. He is now a Ph.D. supervisor. His research interests focus on information security.Bao Li was born in 1965. He received the Ph.D. degree in cryptography in 1995 from Xidian University. His research interests include cryptographic protocols and public key cryptosystems.

Oblivious Polynomial Evaluation

The problem of two-party oblivious polynomial evaluation (OPE) is studied, where one party (Alice) has a polynomial P(x) and the other party (Bob) with an input x wants to learn P(x) in such an oblivious way that Bob obtains P(x) without learning any additional information about P except what is implied by P(x) and Alice does not know Bob's input x. The former OPE protocols are based on an intractability assumption except for OT protocols. In fact, evaluating P(x) is equivalent to computing the product of the coefficient vectors (a(0),...,a(n)) and (1,...,x(n)). Using this idea, an efficient scale product protocol of two vectors is proposed first and then two OPE protocols are presented which do not need any other cryptographic assumption except for OT protocol. Compared with the existing OPE protocol, another characteristic of the proposed protocols is the degree of the polynomial is private. Another OPE protocol works in case of existence of untrusted third party. Keywords oblivious polynomial evaluation, oblivious transfer, secure multi-party computation, information.

不经意多项式求值

多方安全计算(MPC)最早由Yao提出，由于很多的密码学问题都可用多方安全计算模型来描述，因此它在现代密码学中占有很重要的地位。许多密码学家对此进行了广泛、深入的研究，并得到了一般的结论：在一定的密码学假设下，任意的一个用布尔电路表示的函数都可有效计算。

分布式不经意函数求值及其应用

双方的不经意函数求值(OFE，Oblivious Function Evaluation)是多方安全计算的一种特殊情况：两个参与方，Alice和Bob，分别拥有函数f(x)和数α，他们想以不经意的方式计算f(α)，使Bob在不泄露α的情况下得到函数值f(α)，而且除f(α)外，他没有得到关于f(α)的其他信息。