چكيده به لاتين
Proof of zero knowledge is one of the important features of public-key cryptosystems and its meaning is to access confidential information, such as private key and message text by holding public-key and encrypted text. In a zero-proof knowledge system, the proof-taker seeks to convince another person, the prover, that has secret information without disclosing any knowledge of it. Completeness, soundness and zero knowledge are important features of zero knowledge proof systems. indent In this dissertation, first we review the public-key and lattice systems and its applications, then we introduce zero knowledge proof systems, then we examine the practical realization of these systems in algorithms called zero knowledge proof protocols. indent Finally, we present applications of these systems in cryptography such as authentication systems, identity-based digital signature systems, and identity-based key distribution systems.