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Quantum Algorithm for the Invariant Estimate of the Closeness of Classical Ciphers to the One-Time Pad

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An invariant measure of the closeness of a block cipher to the perfect (ideal) cipher of the one-time pad has been proposed. The measure is the same for any implementation of the one-time pad. A quantum algorithm based on the determination of the eigenvalue (phase) of the quantum state has been proposed to estimate the closeness of the block cipher to ideal in terms of the proposed measure with high probability and accuracy.

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Fig. 1.

Notes

  1. Additional “garbage” qubits, which are initially in the 0 state and after the calculation of the function return to the initial 0 state, are required for an unitary implementation of the encryption function (for details of the general method of cleaning of garbage qubits, see [32]). These auxiliary qubits are omitted below for brevity. The number of auxiliary qubits depends on the used encryption function. Various estimates for some ciphers show that the number of auxiliary qubits in a single quantum encryption scheme is polynomial in the length of the key n [12]. If the message is longer than the key, the message is encrypted by blocks. In this case, the number of applications of quantum schemes is equal to the number of blocks Nc, whereas the number of auxiliary qubits does not increase with the number of blocks, i.e., the length of the message, because auxiliary qubits “vanish” after each application and are used repeatedly.

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ACKNOWLEDGMENTS

I am grateful to I.M. Arbekov, V.A. Kiryukhin, S.P. Kulik, and A.V. Urivskii for numerous discussions and to colleagues from Infoteks and the Academy of Cryptography of the Russian Federation for discussions and support.

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  1. Academy of Cryptography of the Russian Federation, 121552, Moscow, Russia

    S. N. Molotkov

  2. Osipyan Institute of Solid State Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow region, Russia

    S. N. Molotkov

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Translated by R. Tyapaev

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Molotkov, S.N. Quantum Algorithm for the Invariant Estimate of the Closeness of Classical Ciphers to the One-Time Pad. Jetp Lett. 117, 75–82 (2023). https://doi.org/10.1134/S0021364022602846

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