Security Issues in QCA Circuit Design - Power Analysis Attacks - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 198

where Γ − are the values of the Hamiltonian before and after the

transition, k is the Boltzmann constant and T is the temperature. Once the
pre-transition and post-transition Hamiltonians are known, the upper bound of
power dissipation for a QCA cell can be calculated. The power model is derived
by including the effects of dissipative coupling to a heat bath.
The power dissipation model for each QCA cell is similar, therefore the total
power for one clock cycle can be computed by summing up the power consumed
by each cell. The cells interact via the electronic kink energy between them.
Power can be computed by tracking the polarisation of the cells before and
after the switching of the input cells, where next-near-neighbour coupling is
ignored since the interaction between cells falls off by the fifth power of the
distance [ 22 ]. Using the values of cell polarisation and clock energy, the total
power consumption in a QCA circuit for the transition from a current input to
the next input can be calculated.
To perform a power analysis attack of a QCA circuit, a power tool for large
circuits is required. Based on the upper bound power model discussed earlier,
a power tool called QCAPro was developed [ 33 ]. QCAPro also offers a quick
design check to verify the correct polarisation of a design. The input required
for the QCAPro tool is the layout file generated by QCADesigner [ 36 ] which is a
widely used design and simulation tool for QCA. The current version of QCAPro
[ 33 ] only provides the average, maximum and minimum power consumption of
a QCA circuit during the input switching. For this research, it was necessary
to modify the tool to compute and provide the power consumption in one clock
cycle according to every input change.

Γ + and

2.2 Power Consumption in a Cell

The power dissipated in each cell is a function of the rate of change of the
clock and the tunneling energy. The adiabaticity of the system is directly pro-
portional to the amount of clock smoothing which can be implemented by a
Gaussian function [ 30 ]. Clock signals with smoothing factors 0.6, 1.2, 1.8, 2.4
and 3.0, which correspond to the clock smoothing of 3 . 98 10 − 4 ,1 . 58 10 − 3 , × ×

10 − 1 ,areshowninFig. 3 . The actual power
dissipated using the quantum model for various values of these parameters was
calculated and compared with the upper bound power, which is shown in Fig. 4 .
The results show that the upper bounds do indeed hold and are reached when
the clock smoothing is zero, i.e., non-adiabatic switching. Therefore, it confirms
the validity of the upper bound power assumption in this research. Note that, as
can be seen from Fig. 4 , for a smoother clock, for higher tunneling energies, less
power is dissipated, while for a less smooth clock, for higher tunneling energies,
more power is dissipated.
The power consumption of a QCA cell is computed under a non-adiabatic
clock. Two cases are shown in Fig. 5 , including cell's polarisation keeps unchanged
as 1 and changes from

10 − 3 ,2 . 51 10 − 2 and 1 . 0

6 . 31 × × ×

1 to 1. There are three parts to the power consumption
of a cell whenever the Hamiltonian changes, as shown in Fig. 5 (b). The first part
occurs when the clock goes from low to high ( γ L to γ H ) to depolarise a cell.

−