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Zjednodušení kvantových obvodů pro modulární umocňování
 Fišer, Petr ; Ivánek, Jiří (advisor) ; Nentvich, Libor (referee)
This thesis is based on top of the previous thesis "Security of modern encryption protocols" where we introduced a new paradigm for constructing quantum circuits. We have built circuits for modular arithmetic (addition, multiplication and exponentiation) in order to break El-Gamal asymmetric cryptosystem. Current thesis reviews all proposed circuits and discusses possibilities of their further optimization in goal of lowering the number of used qbits at least by an order of magnitude. It also shows that this is not possible due to existence of COPY gates which make the design inherently unoptimizable. Getting rid of COPY gates is, however, not possible without substantial rewrite of the whole paradigm. The overall estimate of number of qbits used in circuits thus remains O(log(m)log^2(N)) where m is a processed number and N is a modulus. The thesis also proposes optimization of the modular multiplication circuit that, if issues with COPY gates are resolved, allows us to lower the number of used qbits by about O(log(m)) at the price of a longer execution time.
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