Geodesic
Optimization of $S$-boxes GOST R 34.12-2015 > quantum circuits without ancilla qubits
Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 2, pp. 43-52 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the ways to implement $S$-boxes by quantum circuits with a minimal number of logical qubits and logical quantum gates without using ancilla qubits. New quantum circuits that implement the $S$-boxes of the GOST R 34.12-2015 “Magma” on 4 logical qubits are constructed. It means that for substitutions $s \in S(V_n)$ with a large number of cycles there exist quantum circuits on $n$ logical qubits that implement the substitution $s$ with fewer logical quantum gates compared with substitutions $g \in S(V_n)$ with a small number of cycles. 
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     title = {Optimization of $S$-boxes {GOST} {R} {34.12-2015~<<Magma>>} quantum circuits without ancilla qubits},
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D. V. Denisenko; M. V. Nikitenkova. Optimization of $S$-boxes GOST R 34.12-2015 <> quantum circuits without ancilla qubits. Matematičeskie voprosy kriptografii, Tome 11 (2020) no. 2, pp. 43-52. http://geodesic.mathdoc.fr/item/MVK_2020_11_2_a3/

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