Paper 2024/1836 Original: eprint.iacr.org/2024/1836 ↗

Symmetric Encryption on a Quantum Computer

Abstract

Classical symmetric encryption algorithms use $N$ bits of a shared secret key to transmit $N$ bits of a message over a one-way channel in an information theoretically secure manner. This paper proposes a hybrid quantum-classical symmetric cryptosystem that uses a quantum computer to generate the secret key. The algorithm leverages quantum circuits to encrypt a message using a one-time pad-type technique whilst requiring a shorter classical key. We show that for an $N$-qubit circuit, the maximum number of bits needed to specify a quantum circuit grows as $N^{3/2}$ while the maximum number of bits that the quantum circuit can encode grows as $N^2$. We do not utilise the full expressive capability of the quantum circuits as we focus on second order Pauli expectation values only. The potential exists to encode an exponential number of bits using higher orders of Pauli expectation values. Moreover, using a parameterised quantum circuit (PQC), we could further augment the amount of securely shared information by introducing a secret key dependence on some of the PQC parameters. The algorithm may be suitable for an early fault-tolerant quantum computer implementation as some degree of noise can be tolerated. Simulation results are presented along with experimental results on the 84-qubit Rigetti Ankaa-2 quantum computer.