Quantum AES Inverse Circuit Using Segmented Finite Fields
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Solution Overview
Problem
Existing multiplicative inverse calculation methods in finite fields for AES cryptography in quantum computer environments are inefficient due to high time and space complexity, and the use of inefficient finite fields and single-type circuits during quantum circuit transformation processes.
Innovation Solution
An apparatus and method for calculating a multiplicative inverse in a quantum computer environment by dividing an input degree-8 finite field into two degree-4 finite fields, using three degree-2 multipliers configured for optimal circuit depth and qubit consumption, to perform multiplicative inverse calculations efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing field towering technique is used for multiplicative inverse calculation in quantum computer environment, then the calculation can be performed, but time complexity (T-depth) and space complexity (qubit consumption) are high
Solution Approach 1:
The patent divides the degree-8 finite field GF(2^8) into two degree-4 finite fields GF(2^4), and further divides each degree-4 field into two degree-2 finite fields GF(2^2). This hierarchical segmentation allows multiplicative inverse calculations to be performed on smaller fields and combined through field towering, reducing the overall circuit depth and qubit consumption compared to direct calculation in the full degree-8 field.
2Productivity
If existing field towering technique is used for multiplicative inverse calculation in quantum computer environment, then the calculation can be performed, but qubit consumption is high
Solution Approach 1:
The patent divides the degree-8 finite field GF(2^8) into two degree-4 finite fields GF(2^4), and further divides each degree-4 field into two degree-2 finite fields GF(2^2). This hierarchical segmentation allows multiplicative inverse calculations to be performed on smaller fields and combined through field towering, reducing the overall circuit depth and qubit consumption compared to direct calculation in the full degree-8 field.
3Ease of manufacture
If single-type circuit is used for operations in lower finite fields during quantum circuit transformation, then circuit design is simplified, but calculation efficiency is reduced
Solution Approach 1:
The patent employs different types of quantum circuits optimized for specific finite field operations: degree-2 multiplier circuits for multiplication in GF(2^2), degree-4 multiplier circuits for multiplication in GF(2^4), and degree-4 multiplicative inverse calculation circuits for inverse calculation in GF(2^4). This localized optimization of circuit types for each specific operation and field size improves calculation efficiency while maintaining manageable design complexity through modularity.
Data Source
AI summary
Disclosed herein are an apparatus and method for calculating a multiplicative inverse. The apparatus for calculating a multiplicative inverse includes a data input unit for receiving input data, a multiplicative inverse calculation unit for dividing an input degree-8 finite field corresponding to the input data into two first degree-4 finite fields so as to perform Advanced Encryption Standard (AES) encryption on the input data, and for performing a multiplicative inverse calculation on the first degree-4 finite fields in consideration of a circuit depth value (T-Depth) and qubit consumption of quantum gates in a quantum circuit, and a data output unit for outputting result data obtained by performing the multiplicative inverse calculation.