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A two-round honest-verifier zero-knowledge protocol

Science China(information Sciences) 2010年第5期53卷 954-963页

作者： liu hanwu 1,2.& lin dongdai 1 1 the state key laboratory of information security,{2., Chinese Academy of Sciences,{3., China 2.Graduate University of the Chinese Academy of Sciences, beijing 100049, China 1. The state key {2. of {3. {3. Institute of Software Chinese Academy of Sciences Beijing 100190 China2. Graduate University of the Chinese Academy of Sciences Beijing 100049 China

Since the concept of zero-knowledge protocols was introduced, it has attracted a lot of attention and in turn showed significant effect on the development of cryptography, complexity theory and other areas. The round complexity of a zero-knowledge protocol is a very important efficiency consideration, and it is required to be as small as possible. Generally, it is desirable to have zero-knowledge protocols with constant numbers of rounds. Goldreich and Oren proved that only languages in BPP have one-round and two-round zero-knowledge protocols. Moreover, they also showed that only languages in BPP have one-round honest-verifier zero-knowledge protocols. The notion of honest-verifier zero-knowledge protocols is highly non-trivial and fascinating itself, and has many other uses. Thus, the problem as to whether there exist two-round honest-verifier zero-knowledge protocols becomes an important open problem. In this paper, we introduce a new simulation technique and present a two-round honest-verifier zero-knowledge protocol for any language in N P under a standard complexity assumption based on this technique.

关键词： proof system argument system zero-knowledge witness indistinguishability black-box one-way permutation commitment scheme zap

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On designated-weight Boolean functions with highest algebraic immunity

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Science China Mathematics 2010年第11期53卷 2847-2854页

作者： liu MeiCheng1,3. DU YuSong2. PEI DingYi2.& {2. dongdai1 1The state key {2. of {3. security, institute of software of Chinese Academy of Sciences, beijing 100190, China 2.ollege of Mathematics and {3. Sciences, Guangzhou University, Guangzhou 510006, China 3.raduate University of Chinese Academy of Sciences, {12. 100049, China 1. The state key {2. of {3. {3. Institute of Software of Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100049 China2. College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China

Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions. In this paper, we study ∑d-1 i=0 (ni)-weight Boolean functions with algebraic immunity achiev-ing the minimum of d and n - d + 1, which is highest for the functions. We present a simpler sufficient and necessary condition for these functions to achieve highest algebraic immunity. In addition, we prove that their algebraic degrees are not less than the maximum of d and n - d + 1, and for d = n1 +2.their nonlinearities equalthe minimum of ∑d-1 i=0 (ni) and ∑ d-1 i=0 (ni). Lastly, we identify two classes of such functions, one having algebraic degree of n or n-1.

关键词： cryptography Boolean function algebraic immunity algebraic degree nonlinearity

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