Nanoscience and Nanotechnology. 2011; 1(2): 58-63
DOI: 10.5923/j.nn.20110102.11
A5/1 Implementation in Quantum Cellular Automata
Mohammad Amin Amiri
1,*
, Sattar Mirzakuchaki
2
, Mojdeh Mahdavi
1
1
Department of Electronics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
2
E. E. Department, Iran University of Science and Technology, Tehran, Iran
Abstract Quantum Cellular Automata (QCA) is an emerging technology at the nanotechnology level. The cryptogra-
phy is an interesting application of QCA technology which has not been much mentioned yet. Utilizing the QCA technol-
ogy, we have implemented the A5/1 stream cipher which was the original encryption algorithm for GSM. The implementa-
tion of this cryptographic algorithm is accomplished by means of the implementation of its main modules. The main prop-
erties of the implemented modules such as latency, area and complexity are discussed in this paper.
Keywords Quantum Cellular Automata, A5/1, Cryptography, Implementation
1. Introduction
The microelectronics industry has improved the integra-
tion, the power consumption, and the speed of integrated
circuits during past several decades by means of reducing
the feature size of transistors. But it seems that even by de-
creasing the transistor sizes, some problems such as power
consumption cannot be ignored. Using the QCA technology
for realizing logic circuits is one of the approaches which in
addition to decreasing the size of logic circuits and increas-
ing the clock frequency of these circuits, reduces the power
consumption of these circuits. QCA which was first intro-
duced by Lent et al. [1] represents an emerging technology
at the nanotechnology level. QCA cells have quantum dots,
in which the position of electrons will determine the binary
levels of 0 and 1.
A5/1 was the original encryption algorithm for GSM.
This algorithm was developed in 1987. The approximate
design of A5/1 was leaked in 1994, and the exact design of
this algorithm was reverse engineered from an actual GSM
phone by Bericeno in 1999 [2].
In Quantum Cellular Automata, a cell contains four
quantum dots, as schematically shown in Fig. 1. The quan-
tum dots are shown as the open circles which represent the
confining electronic potential. Each cell is occupied by two
electrons which are schematically shown as the solid dots.
In a cell, the electrons are allowed to jump between the in-
dividual quantum dots by the mechanism of quantum me-
chanical tunneling but they are not allowed to tunnel be-
tween cells. The barriers between cells are assumed suffi-
cient to completely suppress intercellular tunneling. If
they're left alone, they will meet the configuration corre-
* Corresponding author:
amiri@ee.iust.ac.ir (Mohammad Amin Amiri)
Published online at http://journal.sapub.org/nn
Copyright © 2011 Scientific & Academic Publishing. All Rights Reserved
sponding to the physical ground state of the cell. It is in an
obvious manner that the two electrons will tend to occupy
different dots because of the Coulombic force associated
with bringing them together in close proximity on the same
dot. By these concepts, it is concluded that the ground state
of the system will be an equal superposition of the two ba-
sic configurations with electrons at opposite corners, as
shown in Fig. 1 [3, 4].
Figure 1. QCA cell and its ground states
The physical interactions between cells may be used to
realize elementary Boolean logic functions. The basic logic
gates in QCA are the Majority logic function and the In-
verter gate as illustrated in Fig. 2 (a) and Fig. 2 (b), respec-
tively. The Majority logic function can be realized by only
5 QCA cells [5]. The logic AND function can be realized
through a Majority logic function by setting one of its in-
puts permanently to logic level 0 and the logic OR function
can be implemented through a Majority logic function by
setting one of its inputs permanently to logic level 1 [6].
(a) (b)
Figure 2. (a) Majority logic gate and (b) Inverter gate
As an application of QCA technology, we have imple-
mented the A5/1 stream cipher. The Section 2 will describe
the A5/1 algorithm shortly. In Section 3, the implemented
modules are explained and Section 4 concludes the paper.