A Novel Realization of Reversible LFSR for its
Application in Cryptography
Prasoon Lata Singh, Alak Majumder, Barnali Chowdhury, Ranvijay Singh, Nikhil Mishra
Department of Electronics & Communication Engineering
National Institute of Technology, Arunachal Pradesh
Yupia, India – 791112
prasoonsingh8@gmail.com , majumder.alak@gmail.com , barnali.cse92@gmail.com ,
singhranvijay419@gmail.com , nikhilmishra445@gmail.com ,
Abstract— One-to-one mapping from input to output is the
necessary condition for a reversible computational model
transiting from one state of abstract machine to another.
Probably, the biggest motivation to study reversible
technologies is that, it is considered to be the best effective way
to enhance the energy efficiency than the conventional models.
The research on reversibility has shown greater impact to have
enormous applications in emerging technologies such as
Quantum Computing, QCA, Nanotechnology and Low Power
VLSI. In this paper, we have realized novel reversible
architecture of Linear Feedback Shift Register (LFSR) and
Parallel Signature Analyzer (PSA) and have explored these in
terms of delay, quantum cost and garbage. While approaching
for LFSR, we have shown new reversible realization of Serial
Input Serial Output (SISO) and Serial Input Parallel Output
(SIPO) registers up to N-bit and analyzed their delay, quantum
cost & garbage in terms of some lemmas, which will
outperform the existing designs available in literature.
Keywords– Reversible Logic; SISO; SIPO; Reversible
LFSR; Reversible PSA.
I. INTRODUCTION
The power dissipation of devices is increasing with the
technological advancement day-by-day, thereby making it
the major limitation of technology. Reversible logic gates
due to its ability to reduce power dissipation attracted
researcher’s attention. Irreversible gates produce energy loss
due to the information bits lost during computation process.
Information loss occurs due to less no. of generated output
signals than what is applied. According to R. Landauer’s
principle[1], given in 1961, irreversible logic gates
dissipates KTln2 joules of energy for the loss of 1-bit
information, where K is the Boltzmann constant and T is the
absolute temperature at which operation is performed which
means that the power dissipation is directly proportional to
the number of information bit loss. Charles Bennet, in 1973
[2], proposed that, to avoid heat dissipation, logic circuit
must be built from reversible circuit since there no
information loss occurs. At first, in the design of reversible
logic circuits, design was limited to combinational logic
circuits and it was just because of the convention that the
feedback is not allowed in the reversible computing [19].
But, in 1980, Toffoli [4] has shown that the feedback is
allowed in reversible computing. According to Toffoli [11],
a sequential network is reversible if its combinational part is
reversible. The recent works focus on optimizing the
reversible sequential designs in terms of number of
reversible gates and garbage outputs. The shift registers are
the most exhaustively used functional devices in digital
system design for multiple bits storing & shifting of the
same if required.
In this paper, we are presenting reversible
realization of two shift registers naming Serial-in Serial-out
and Serial-in Parallel-out for their application in designing
sequence pulse generator. We will also present novel
reversible architecture of Linear Feedback Shift Register
(LFSR) and Parallel Signal Analyzer (PSA). In computing,
the input bit of LFSR is a linear function of its last state.
The starting value of the LFSR is termed seed, and due to
the deterministic operation of the register, the bit stream
produced is completely determined by its current (or
previous) state.
The paper is organized as follows. Section II gives
an overview of the related work & the purpose of the work.
Section III highlights the basic reversible gates which
includes a new MF gate with its quantum representation.
Reversible shift register are discussed in section IV with a
comparison of them against previous works. Using
reversibility, how pulse generation can be done is shown on
section V using a particular example. Section VI & VII
describes Reversible LFSR & PSA respectively thereby
mentioning how they can generate random bit pattern.
Conclusion with future scope is discussed on section VIII.
II. RELATED WORK
The concept of a reversible memory cell was first
shown by Fredkin and Toffoli [5], in 1982, where, design of
a JK latch was introduced. Later, in 1996, Picton [7]
developed a design of clock less SR-latch using two cross-
coupled NOR gate, where NOR gates were designed from
Fredkin gate. All the reversible latches such as D-Latch, T-
Latch etc. along with their flip-flop and master-slave
configuration were introduced for the first time in 2005 by
Thapliyal et.al.[9]. In 2006, Rice [10] introduced a SR-latch
without fan-out problem available in the design by Picton
and subsequently designed other latches from SR. In 2007,
Thapliyal and Vinod [11] proposed a better design of
reversible flip-flops than by Rice in terms of number of
reversible gates being used and garbage outputs. A more
detailed analysis of SR-latch was presented by Rice [12] in
2008. A better design of all reversible latches (except SR-
latch) along with their flip-flops than that of Thapliyal
2015 2nd International Conference on Signal Processing and Integrated Networks (SPIN)
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