Finite Field Discrete Logarithmic Quantum Solving Circuit Optimization Construction Method

Abstract

The present invention relates to a finite-field discrete logarithm quantum solution circuit optimization construction method, comprising: constructing an addition carry gate circuit for finite-field discrete logarithms, so as to realize equivalent conversion of multiplication cyclic group generators; setting the addition carry gate Auxiliary bits, and realize recursively performing the operation of the addition carry gate through the addition quantum circuit; use the addition carry gate circuit to perform the comparison operation, and judge the carry information when the quantum register and the constant are added, so as to realize the optimization of the modulo N addition quantum circuit; through the modulo N The addition operation realizes the multiplication operation, and constructs the modular N multiplication quantum circuit; realizes the modular exponentiation operation through the modular N multiplication operation, and constructs the modular exponentiation quantum circuit; combines the modular exponentiation quantum circuit and the existing quantum Fourier transform quantum circuit, constructs and realizes the finite field A quantum algorithm circuit for solving discrete logarithms. The invention realizes the modular addition process through the logic quantum circuit, reduces the calculation amount and complexity of the logarithm solution, reduces the calculation load of software and hardware, and has strong application prospects.

Description

technical field

[0001] The invention belongs to the technical field of quantum computing and cryptography, and in particular relates to a method for optimizing the construction of a finite-field discrete logarithm quantum solution circuit. Background technique

[0002] For any prime p, there exists a multiplicative cyclic group G modulo p. Suppose the generator of the cyclic group is g, then the cyclic group can be expressed as {g, g 2 ,..., g p-1}. Any element x=g in a given group r ∈ G, the problem of exponentiation r is the discrete logarithm problem (Discrete Logarithm Problem, DLP). DLP is the first hard problem to be used to design public-key cryptographic protocols. In 1976, the DLP-based key exchange protocol proposed by Diffie and Hellman became the beginning of research on public key cryptographic protocols. In 1985, ElGamal proposed a cryptographic algorithm and digital signature protocol based on DLP. Nowadays, DLP is widely used to design cryptographic sc...

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