Finite Field Discrete Logarithmic Quantum Solving Circuit Optimization Construction Method

A construction method, discrete logarithm technology, applied in the field of quantum computing and cryptography, to achieve strong application prospects, reduce operating load, reduce the amount of calculation and computational complexity

Active Publication Date: 2021-12-17
PLA STRATEGIC SUPPORT FORCE INFORMATION ENG UNIV PLA SSF IEU
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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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  • Finite Field Discrete Logarithmic Quantum Solving Circuit Optimization Construction Method
  • Finite Field Discrete Logarithmic Quantum Solving Circuit Optimization Construction Method
  • Finite Field Discrete Logarithmic Quantum Solving Circuit Optimization Construction Method

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Embodiment Construction

[0037] In order to make the purpose, technical solution and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and technical solutions.

[0038] For the current problem of solving polynomial bounded discrete logarithms, in the embodiments of the present invention, see figure 1 As shown, a finite-field discrete logarithmic solution circuit optimization construction method is provided, which includes the following content:

[0039] S101) Constructing an addition carry gate circuit for finite field discrete logarithms, so as to realize equivalent conversion of multiplication cyclic group generators;

[0040] S102) Set the auxiliary bit of the addition carry gate, and implement the operation of the addition carry gate recursively through the addition quantum circuit;

[0041] S103) use the addition carry gate circuit to perform a comparison operation, and ...

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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...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/08H04L9/30
CPCH04L9/0852H04L9/3013
Inventor 张凯马智
Owner PLA STRATEGIC SUPPORT FORCE INFORMATION ENG UNIV PLA SSF IEU
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