1. ZK Protocol Based on Sequential Squaring Consider a two-pass protocol with ZK based on the difficulty of the factorization problem, for which the proof of zero knowledge leakage is relatively straightforward. The prover’s public key is a natural number n, the product of two large prime numbers r and q, which constitute his private secret. The…

Cyclic groups of prime order can be represented by the multiplicative groups of finite fields GF(2^s) of binary polynomials for certain values of the degree s. The order of the multiplicative group of such fields equals

Robust and user-friendly strict authentication protocols for remote users can be built on the basis of open key agreement schemes. Consider an implementation using the Diffie-Hellman scheme, in which the system parameters are a large prime number p and a primitive element α modulo p. …

1. Using the ElGamal Public Key Encryption Algorithm Let’s examine the implementation of a zero-knowledge secret disclosure protocol based on the ElGamal public key encryption algorithm. In this algorithm, the public key is of the form

1. Protocols Based on Public Key Encryption Algorithms Zero-knowledge protocols can be implemented using well-known public key encryption algorithms. These protocols employ a secret key. The individual who correctly performs the encryption process will find that the decrypted message only confirms the knowledge of the secret key associated with the public key. However, an adversary could potentially choose…

A notable advantage of the multi-round Fiat-Shamir protocol is its relatively low computational complexity — each participant in the protocol performs no more than 2z modular multiplications, where z is the predetermined number of rounds. However, a significant drawback of all multi-round protocols is the need for a very large…

Multi-round protocols with zero-knowledge proof involve repeated execution of three standard steps: 1. The prover generates a one-time random secret key and calculates a corresponding one-time public key, often termed as a commitment, which is then transmitted to the verifier. 2. The verifier generates a binary request (r = 0 or r = 1) with equal probability (0.5) and sends this bit…

Zero-knowledge protocols represent a fascinating class within cryptographic techniques. These protocols have been designated as ‘zero-knowledge’ because they enable a particular interaction: during their execution, one party (the prover) can convincingly demonstrate to another (the verifier) the possession of specific secret knowledge without actually revealing the secret itself. More precisely…

1. Введение 1.1 Краткое описание полного гомоморфного шифрования Полное гомоморфное шифрование (Fully Homomorphic Encryption, FHE) является революционным достижением в области криптографии, позволяя проводить вычисления непосредственно над зашифрованными данными без необходимости их предварительного расшифрования. Этот принцип позволяет обеспечить безопасность данных в процессе их обработки, что открывает широкие возможности для безопасного облачного вычисления, приватных информационных систем и защиты персональных данных.