International Journal of Computer Applications (0975 – 8887)
Volume 111 – No 2, February 2015
1
Text Encryption Algorithms based on Pseudo Random
Number Generator
Mina Mishra
Ph. D. Scholar
Electronics & Telecommunication, Nagpur
University, Nagpur, Maharashtra, India
V.H. Mankar
Lecturer
Department of Electronics Engineering,
Government Polytechnic, Nagpur,
Maharashtra, India
ABSTRACT
This paper presents algorithms for encryption and decryption
developed using pseudo random number generator (PRNG)
and non-Linear functions. PRNG used in the work are matlab
random number generator (RNG) and Linear congruential
generator (LCG). The developed algorithms are named
according to PRNG used in it. State of PRNG is considered as
secret key of the cipher. The encryption schemes have been
cryptanalyzed for four different methods to test its strength
like key space analysis, plaintext and key sensitive test.
Known plaintext attack is also performed by taking into
consideration a small string of plaintext and the complete
cipher text for small text. The analysis is performed on
different keys selected randomly from key space for various
texts and files.
Key sensitivity up to 50 % and plaintext sensitivity ranging
from 3% to 50 % have been obtained in the developed
ciphers. It is concluded that proposed encryption algorithms
have strength against linear, differential and statistical attacks.
Keywords
Cryptography, Pseudo random number generator (PRNG),
Random number generator, Linear Congruential Generator.
1. INTRODUCTION
Cryptography has remained important over the centuries, used
mainly for military and diplomatic communications. With the
advent of the internet and electronic commerce, cryptography
has become vital for the functioning of the global economy,
and is something that is used by millions of people on a daily
basis. Various schemes of encryption using different
techniques have been proposed in recent years. The Pseudo
random number generators have been used for design of
ciphers and found to be fundamental tool in many
cryptographic applications like key generation, encryption,
masking protocols and for internet gambling [1]- [4].
A pseudorandom number generator (PRNG), also known as a
deterministic random bit generator (DRBG) is an algorithm
for generating a sequence of numbers that approximates the
properties of random numbers. The sequence is not truly
random in that it is completely determined by a relatively
small set of initial values, called the PRNG's state, which
includes a truly random seed. Good statistical properties are a
central requirement for the output of a PRNG, and common
classes of suitable algorithms include linear congruential
generator, lagged fibonacci generator, and linear feedback
shift register [5], [6].
This paper aims to develop a number of algorithms for
-linear
functions. The encryption techniques are crypt analyzed for
linear and differential attacks to test their validity. Various
methods of cryptanalysis used in this work are key space,
plaintext and key sensitive test. Known plaintext attack is also
performed by taking into consideration a small string of
plaintext and the complete cipher text for small text. Simple
pseudorandom number generator like matlab random number
generator (RNG) and linear congruential generator (LCG)
have been used here. The developed algorithms are named
according to PRNG used in it.
The analysis is performed on different keys selected randomly
from key space for various texts and files. Key sensitivity up
to 50 % and plaintext sensitivity ranging from 3% to 50 %
have been obtained in the developed ciphers. It is concluded
that proposed encryption algorithms have strength against
linear, differential and statistical attacks.
The rest of the paper is organized as follow. Section II,
developed algorithm. Next section presents and discusses
about the algorithm. In section IV, analysis and results have
been discussed. Section V gives conclusion of the work.
2. PSEUDORANDOM NUMBER
GENERATOR
PRBG plays an important role in cryptography. They have
been frequently used in the designing of the ciphering
methods. Two of the simple PRBG used in designing of
encryption algorithm have been discussed in brief here:
A. Random Number Generator (RNG)
Matlab Rand produces uniformly distributed pseudorandom
numbers, scalar value drawn from a uniform distribution on
the unit interval.
number corresponding to state k, which is the seed (also
known as initial condition) of generator, acting as key for
cryptosystem.
B. Linear Congruential Generator (LCG)
A Linear Congruential Generator (LCG) represents one of the
oldest and best-known pseudorandom number generator
algorithms. The generator is defined by the recurrence
relation:
x(k+1) = (ax(k)+b) mod c
Where, x(k) is the sequence of pseudorandom values, and c,0
< c - -
< c - -
period of a general LCG is at most c, and for some choices of
a much less than that. Provided that b is nonzero, the LCG
will have a full period for all seed values if and only if:
b and c are relatively prime,
( a -1) is divisible by all prime factors of c,
International Journal of Computer Applications (0975 – 8887)
Volume 111 – No 2, February 2015
2
(a -1) is a multiple of 4 if c is a multiple of 4.
Parameter b is the best choice as encryption key for chaotic
cryptosystem.
3. ENCRYPTION AND DECRYPTION
ALGORITHM
This section discusses the algorithms of various encryption
methods. Encryption process for each of the method has been
explained using algorithm. Decryption process is just reverse
secret key in the method.
A. RNG Method
Encryption Algorithm:
Step-1. Read the plain text as p and key as k, which is the
state of the random number generator.
Step-2. Convert each text into its ASCII values.
Step-3. Transform each character of text using the expressions
given as:
y = p + 2 sin (100)
c = y + 10 r
k = k + 1.
Where, p is input text; c is output text; r = random number
Matlab random number
generator;
Step-4. Plot output of the system.
Step-5. Convert integer values into its character values.
Step-6. Read c as output text as cipher text.
B. LCG Method
Encryption Algorithm:
Step-1. Read plaintext as p, key as b and length as n.
Step-2. Change the character values of text into its ASCII
values.
Step-3. Each ASCII values are transformed into five
corresponding values using the following transformations:
y = p + sin (b);
c = y + r;
y is intermediate variable.
r is the random numbers generated corresponding to the key; b
is state of LCG; c is any variable.
Step-
Step-5. The sequences of numbers in c are then converted into
character values.
Step-6. Read the output text (cipher text).
Algorithm For Linear Congruential Generator:
Step-1. Read iteration as N, initial condition as x (1), values of
parameters a, b and c where b is considered as key for the
system.
Step-2. Calculate, for k=1: N
x(k+1) = mod (a x(1) + b, c)
Step-3. Read output states as x.
A. Modified RNG Method:
Encryption Algorithm:
Step-1. Input plaintext as p, key as k.
Step-2. Convert p into ASCII form.
Step-3. Read length of plaintext as n.
Step-4. Read index of iterations as i and index of length of
plaintext as m.
Step-5.
(a) For i = 1, do following steps:
i. Convert each number into its binary form, which
forms matrix of dimension containing rows equal to
the length of text and number of columns is eight.
ii. Above matrix dimension is changed into dimension
where no. of rows is half the length of text and no. of
columns is sixteen.
iii. For each column, elements of each row are circularly
shifted by one in anticlockwise direction. Element of
first row of each column is shifted to last row.
iv. From second row to last row, for each row elements of
each column is shifted by one in right direction.
v. Again matrix dimension is changed into dimension of
matrix as in (a) (i).
vi. Binary form of numbers is changed into decimal form.
vii. Read output sequence of numbers as p.
(b) For m = 1, do following steps:
i. Generate random number corresponding to key (state).
ii. Do Xor operation between random number and p and
store the result in p.
iii. Increment key by one, go to (b)(i) and the loop
continues till m = n is completed. The loop outputs new
values of p having length n.
(c) i = i+1 and go to step (5) (a) (i). Repeat process till i = 16
is completed.
Step-6. For i = 1, do following steps.
i. Generate random number r corresponding to value of
key (state).
ii. Calculate = p + mod (r, 128).
iii. Convert each number of p into its binary form, which
forms matrix of dimension containing rows equal to
the length of text and number of columns is eight.
iv. Above matrix dimension is changed into dimension
where no. of rows is half the length of text and no. of
columns is sixteen.
v. Matrix is partitioned into two equal halves, first and
second.
vi. Mix both matrix and obtain new matrix of same
dimension. Mixing is done in such a way that elements
of second column of new matrix becomes elements of
first column of second matrix, third columns elements
becomes elements third column of first matrix, fourth
columns elements becomes elements of second
column of second matrix and so on.
International Journal of Computer Applications (0975 – 8887)
Volume 111 – No 2, February 2015
3
vii. Dimension of new mixed matrix is changed into
dimension i.e., equal to the dimension of matrix as
instep (6) (iii).
viii. Binary forms of numbers in matrix are changed into
decimal form.
ix. Read output as p.
x. Again key is incremented by one, k = k + 1.
xi. i = i + 1, go to step (6) (i). The process repeats until i =
16 is completed.
Step-5. Read output generated by completion of above steps
as c and plot it.
Step-6. Convert integer values of c into character form.
Step-7. Read c as cipher text.
4. ANALYSIS AND RESULTS
The analysis part consists of testing the validity of methods
against the most basic attacks like linear, statistical and
differential attacks. Cryptanalysis is the necessary for testing
the strength of the developed ciphers. The cryptanalytic
procedures used in this work include:
A. Key Space Analysis: The size of the key space is the
number of encryption/decryption key pairs that are available
in the cipher system. In the proposed method, the key space
(range of keys) is defined clearly. Once the key has been
defined and key space has been properly characterized, the
good key is chosen randomly from the large key ranges [7].
B. Plaintext sensitivity: This method corresponds to the
percentage of change in bits of cipher text obtained after
encryption of plaintext, which is derived by changing single
bit from the original plaintext from the bits of cipher text
obtained after encryption of original plaintext. With the
change in single bit of plaintext, there, must be ideally 50%
change in bits of cipher text to resist differential cryptanalysis
(chosen-plaintext attack) and statistical analysis, corresponds
to plaintext sensitivity test [8].
C. Key sensitivity: This method corresponds to the
percentage of change in bits of cipher text obtained after
encryption of plaintext using key, which is flipped by single
bit from the original key, from bits of cipher text obtained
after encryption of plaintext using original key, which
requires ideally 50% change in cipher text bits to resist Linear
and statistical attacks [9].
D. Known plaintext attack: It is assumed that the opponent
knows everything about the algorithm; he/she has the
corresponding cipher text of plaintext and some portion of
plaintext. With this much information, the opponent tries to
find out the secret key [10].
For each of the methods the analysis result is cited in tabular
form as follows:
Table 1: Analysis Table for RNG method
Sl.
No.
Plaintext
Key value
Cipher text
Plaintext
sensitivity
(in %).
Key
sensitivity
(in %).
Robustness
against known
plaintext attack
for p = [p1 p2].
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International Journal of Computer Applications (0975 – 8887)
Volume 111 – No 2, February 2015
4
Table 2: Analysis Table for LCG method
Sl.
No.
Plaintext
Key
value
Cipher text
Plaintext
sensitivity
(in %)
Key
sensitivity
(in %)
Robustness
against known
plaintext attack
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International Journal of Computer Applications (0975 – 8887)
Volume 111 – No 2, February 2015
5
Table 3: Analysis Table for Modified RNG method.
Sl.
No.
Plaintext
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sensitivity
(in %)
Key
sensitivity
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Robustness
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5. CONCLUSION
This paper proposes an encryption algorithm based on pseudo
random number generator (PRNG). The performance of
developed encryption scheme is evaluated by performing key
space analysis, plaintext and key sensitive test and known
plaintext attack on them. Known plaintext attack is performed
by taking into consideration a small string of plaintext and the
complete cipher text for small text.
The analysis is performed on different keys selected randomly
from key space for various texts and files. Developed
algorithm showed key sensitivity up to 50 %. Plaintext
sensitivity in modified algorithm has been increased from 3%
to 50 %.Thus, proposed encryption algorithm have shown
strength against linear, differential and statistical attacks. A
comparative result analysis is briefed in table 4. Modified
RNG possess good plaintext and key sensitivity property.
Table 4: Comparison between the three methods
Name of
cipher
Range of
plaintext
sensitivity
Range of
key
sensitivity
Robustness
against
known
plaintext
tattack
RNG
0.5 to 1.5 %
22 to 30 %
Yes
LCG
0.5 to 3 %
23 to 39 %
Yes
MODIFIED
RNG
34 to 50 %
43 to 54%
Yes
International Journal of Computer Applications (0975 – 8887)
Volume 111 – No 2, February 2015
6
6. ACKNOWLEDGMENTS
The authors would like to thank the anonymous reviewers for
their valuable suggestions and the proposed references.
7. AUTHOR’S PROFILE
Mina Mishra, is pursuing Ph.D. (Engg) from Nagpur
University, Maharashtra, India. She received M.E. degree
specialization in communication in the year 2010. Her
research area covers chaotic systems, chaotic cryptology,
network security and secure communication.
Vijay H. Mankar received M. Tech. degree in Electronics
Engineering from VNIT, Nagpur University, India in 1995
and Ph.D. (Engg) from Jadavpur University, Kolkata, India in
2009 respectively. He has more than 16 years of teaching
experience and presently working as a Lecturer (Selection
Grade) in Government Polytechnic, Nagpur (MS), India. He
has published more than 45 research papers in international
conference and journals. His field of interest includes digital
image processing, data hiding and watermarking.
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[4] J
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[7]
Proceedings of IEEE 4th International Conference on
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algorithm: Robustness against Brute-
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