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Resource Constraint Estimation of In-Quantum Implementated Mini-AES

Syed Shahmir, Ghulam Murtaza, Ala-Al-Fuqaha, Saif Al-Kuwari, Tasawar Abbas

Abstract

The advancement in quantum technology has brought the implementation of Grover's Search attack on cybersecurity algorithms much closer to reality. For such tasks, the Hilbert space has to be designed to make the relation between the input and output of these cryptographic algorithms in quantum circuits. Also, these algorithms are tested on current quantum simulators such as Qiskit, where memory constraints and limited processing power are hurdles. Here, we present an easy-to-implement method using a conventional arithmetic number field approach which can be applied to quantum circuits by CNOT and Toffoli gates, while focusing on resource constraints. Also, we give a Python code that can generate a Qiskit code for the quantum implementation of similar cryptographic S-boxes using the CNOT and 3-Tofflie gates by using simple logic presented in this paper.

Resource Constraint Estimation of In-Quantum Implementated Mini-AES

Abstract

The advancement in quantum technology has brought the implementation of Grover's Search attack on cybersecurity algorithms much closer to reality. For such tasks, the Hilbert space has to be designed to make the relation between the input and output of these cryptographic algorithms in quantum circuits. Also, these algorithms are tested on current quantum simulators such as Qiskit, where memory constraints and limited processing power are hurdles. Here, we present an easy-to-implement method using a conventional arithmetic number field approach which can be applied to quantum circuits by CNOT and Toffoli gates, while focusing on resource constraints. Also, we give a Python code that can generate a Qiskit code for the quantum implementation of similar cryptographic S-boxes using the CNOT and 3-Tofflie gates by using simple logic presented in this paper.

Paper Structure

This paper contains 13 sections, 6 equations, 4 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contribution
  4. Organization
  5. Preliminaries
  6. Mini-AES
  7. Nibble Sub ($\gamma$)
  8. Mix-Column ($\theta$)
  9. Shift-Row ($\pi$) and Key-Addition
  10. Circuit Design
  11. Circuit Implementation
  12. Results
  13. Conclusion

Figures (4)

  • Figure 1: Flow chart representation of Mini-AES.
  • Figure 2: Nonlinear substitutions in Mini-AES implementations phan_mini_2002.
  • Figure 3: Schematics of the Quantum circuit of the Mini-AES S-box (Nibble-Sub) using Toffoli and CNOT gates derived from ANF expressions.
  • Figure 4: Quantum circuit diagrams for mix-column operation, where the multiplier gates i.e. (a) 3 multiplier, (b) 2 multiplier are constructed using composite logic, and used in (c) the mix-column operation utilizing these multipliers and their inverse. Which are the same operations applied in reverse order.