Finite field discrete logarithm quantum solving line optimization construction method

Abstract

The invention relates to a finite field discrete logarithm quantum solving line optimization construction method, which comprises the following steps of: constructing an addition carry gate line for afinite field discrete logarithm so as to realize equivalent conversion of a multiplication cyclic group generation element; setting an addition carry gate auxiliary bit, and recursively executing theoperation of an addition carry gate through an addition quantum circuit; carrying out comparison operation by utilizing an addition carry gate circuit, and judging carry information when the quantumregister and the constant are added so as to realize modular N addition quantum circuit optimization; achieving multiplication operation through modular N addition operation, and constructing a modular N multiplication quantum circuit; achieving modular exponentiation operation through modular N multiplication operation, and constructing a modular exponentiation quantum circuit; combining a modular exponentiation quantum circuit and an existing quantum Fourier transform quantum circuit to construct a quantum algorithm circuit for solving discrete logarithms in a finite field. According to themethod, the modular addition process is realized through the logic quantum circuit, the logarithm solving calculation amount and complexity are reduced, the software and hardware operation load is reduced, and the method has a relatively strong application prospect.

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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Problems solved by technology

There is currently no work on circuit design for quantum algorithms for solving the discrete logarithm problem over finite fields

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