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A practical-quantum differential attack on block ciphers

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Abstract

Differential attack is a basic cryptanalysis method for block ciphers that exploits the high probability relations between the input and output differences. The existing work in quantum differential cryptanalysis of block ciphers is focused on resource estimation to recover the last round subkeys on the basis of relations constructed using classical methods. To find such relations using quantum computing, we propose a method to search the high probability differential and impossible differential characteristics. The method explores all possible input and output difference pairs using superposition of qubits. The proposed method is used to design the quantum circuit to search the differential characteristics for a toy cipher smallGIFT. We execute the quantum circuit on a quantum simulator to get differential and impossible characteristics. These characteristics are validated with the characteristics obtained using branch-and-bound based method. The differential characteristic is used to mount quantum key recovery attack using Grover’s search. We provide the estimation of quantum resources to search the differential characteristics of lightweight block cipher GIFT-64 on a quantum computer.

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Notes

  1. Python implementation at https://github.com/tarunyadav/QuantumDifferentialAttack

  2. Source code available at https://github.com/tarunyadav/QuantumDifferentialAttack

  3. https://qiskit.org/

  4. Grover’s Oracle and Diffusion source code taken from [20]

  5. Source code available at https://github.com/tarunyadav/QuantumDifferentialAttack

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Authors and Affiliations

  1. Scientific Analysis Group, DRDO, Metcalfe House Complex, 110 054, Delhi, India

    Tarun Yadav, Manoj Kumar, Amit Kumar & S K Pal

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  1. Tarun Yadav
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  2. Manoj Kumar
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  3. Amit Kumar
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  4. S K Pal
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Correspondence to Tarun Yadav.

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Appendix

Appendix

1.1 A Quantum Circuit of Differential Characteristics Search for 3 rounds of smallGIFT

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Practical-Quantum Differential Characteristics Search for 3-round smallGIFT (Round 1)

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Practical-Quantum Differential Characteristics Search for 3-round smallGIFT (Round 2)

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Practical-Quantum Differential Characteristics Search for 3-round smallGIFT (Round 3)

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Fig. 19
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Practical-Quantum Differential Characteristics Search for 3-round smallGIFT (Measurement)

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Yadav, T., Kumar, M., Kumar, A. et al. A practical-quantum differential attack on block ciphers. Cryptogr. Commun. (2023). https://doi.org/10.1007/s12095-023-00650-6

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