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Optimized reversible quantum circuits for F_(2^8) multiplication

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Imaña Pascual, José Luis (2021) Optimized reversible quantum circuits for F_(2^8) multiplication. Quantum information processing, 20 (1). ISSN 1570-0755

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Official URL: http://dx.doi.org/10.1007/s11128-020-02937-6




Abstract

Quantum computers represent a serious threat to the safety of modern encryption standards. Within symmetric cryptography, Advanced Encryption Standard (AES) is believed to be quantum resistant if the key sizes are large enough. Arithmetic operations in AES are performed over the binary field F_(2^m) generated by an irreducible pentanomial of degree m=8 using polynomial basis (PB) representation. Multiplication over F_(2^m) is the most complex and important arithmetic operation, so efficient implementations are highly desired. A number of quantum circuits realizing F_(2^m) multiplication have been proposed, where the number of qubits, the number of quantum gates and the depth of the circuit are mainly considered as optimization objectives. In this work, optimized reversible quantum circuits for F_(2^8) multiplication using PB generated by two irreducible pentanomials are presented. The proposed reversible multipliers require the minimum number of qubits and CNOT gates, and the minimum depth among similar F_(2^8) multipliers found in the literature.


Item Type:Article
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©2021 Springer
This work has been supported by the Spanish MINECO and CM under grants S2018/TCS-4423 and RTI2018-093684-B-I00.

Uncontrolled Keywords:Quantum computing; Reversible circuit; Optimization; Finite field arithmetic; Multiplier; Cryptography
Subjects:Sciences > Computer science > Artificial intelligence
ID Code:64046
Deposited On:18 Feb 2021 16:54
Last Modified:19 Feb 2021 08:57

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