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在加密函数存在的假设下,我们证明了NP中的全部语言都拥有零知识证明,就是说能证明一个CNF公式是可满足的而不泄露该公式的任何其它特性,特别是,不产生满足的賦值,也不产生更弱的一些特性,比如是否存在一个满足的賦值,其中x1=真,或者是否存在一个满足的赋值,其中x_1=x_3等。上述结果使我们能够证明密码协议领域(两方及多方)里的两个基本定理。这两个定理提供自动且有效的变换,当给定一个在极弱敌情下无误的协议时,输出一个在极强敌情下也无误的协议。这样,这两个定理指明了发展两方及多方密码协议的一些强有力的方法。
Under the assumption of the existence of an encryption function, we prove that all languages in the NP possess zero-knowledge proof, that is, to prove that a CNF formula is satisfiable without revealing any other property of the formula, in particular, not satisfying Assignments also do not produce weaker features such as whether there is a satisfying assignment, where x1 = true, or whether there is a satisfying assignment, where x_1 = x_3, and so on. The above result enables us to prove the two basic theorems in the field of cryptographic protocols (both parties and parties). These two theorems provide an automatic and efficient transformation that, when given an unmistakable agreement under very weak rivalries, outputs an agreement that is also error-free in very strong circumstances. Thus, these two theorems point out some powerful ways to develop a two-party and multi-party cryptographic protocol.