Using a zero-knowledge proof, she can demonstrate that sufficient taxes were paid without disclosing her sales prices or earnings to a third party.

A zero-knowledge proof allows them both to learn who is wealthier (and thus who should pay the restaurant tab) without revealing how much either is worth.

Our construction does not use the expensive tools like homomorphic encryption and zero-knowledge proof.

Most of these constructions use general zero-knowledge proofs for fully malicious multi-party computation (MPC) protocols.

If we repeat the zero-knowledge proof for t times, the probability is reduced to at most 1/[2.

Nevertheless, in this paper we give an alternative zero-knowledge proof, which is significantly simpler.

com/2014/11/27/zero-knowledge-proofs-illustrated-primer/)

zero-knowledge proofs , which allows people to verify and complete transactions without needing to see the other party's data or even their identity.

If both of them hold, the verifier checks whether the

zero-knowledge proof is valid as follows.

Recently, Manuel Blum of the University of California at Berkeley showed how to give an efficient

zero-knowledge proof for any mathematical theorem.

Then, It will give a new set of practical primitives (signatures, Public-key encryption, Pseudorandom functions, Etc) and suitable methods to combine them with efficient

zero-knowledge proofs.

Key areas covered "Cryptography" include: Fundamentals of Encryption, Public Key Encryption, Symmetric Key Encryption, Hashing Methods, Key Exchange Methods, Digital Certificates and Authentication, Tunneling, Crypto Cracking, Light-weight Cryptography, Blockchain, and

Zero-knowledge Proofs.

In another variation, Manuel Blum of the University of California at Berkeley and MIT's Silvio Micali recently found a way to make

zero-knowledge proofs noninteractive.