Efficient 4-round zero-knowledge proof system for NP

A 4-round zero-knowledge interactive proof system for NP (Non-deterministic Polynomial) is presented when assuming the existence of one-way permutations and collision-free hash functions. This construction is more efficient than the original construction of 5-round zero-knowledge proof system for NP. The critical tools used in this paper are: zap, hash-based commitment scheme and non-interactive zero-knowledge.