In this article we present a procedure that allows to synthesize optimal circuit representing any reversible function within reasonable size limits. The procedure allows to choose either the NCT or the MCT gate set and specify any number of ancillary qubits to be used in the circuit. We will explore efficacy of this procedure by synthesizing various sources of nonlinearity used in contemporary symmetric ciphers and draw conclusions about properties of those transformations in quantum setting. In particular we will try to synthesize optimal circuit representing ASCON cipher SBOX which recently won NIST competition for Lightweight Cryptography standard.

This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: s ^α L _α and 1/s ^α C _α, (0 α 1) were obtained using the Laplace transform based on the expansion of the factor sign to an infinite fraction with varying degrees of accuracy – the continued fraction expansion method (CFE). Then circuit synthesis methods were applied. As a result, equivalent circuit diagrams of fractional order elements were obtained. The obtained equivalent schemes consist both of classical RLC elements, as well as active elements built based on operational amplifiers. Numerical experiments were conducted for the constructed models, presenting responses to selected input signals.