The concept of zero-knowledge has been extensively used in the design of cryptographic protocols since being introduced. The round complexity of zero- knowledge protocols is a very important e±ciency con- sideration, and in general it is desirable to have zero- knowledge protocols with constant numbers of rounds. In this paper, we suggest a novel method to use the program of the veri¯er and use the method to construct some con- stant round honest-veri¯er zero-knowledge protocols. The notion of honest-veri¯er zero-knowledge protocols is highly non-trivial and fascinating itself. It also has many other uses.
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