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Pentaplicative Cipher Technique
Neelansh Garg, Harshit Bhatia and Rahul Johari
Abstract The traditional cipher techniques employ the use of limited keys for asym-
metric and symmetric cryptography. Most of the encoding schemes use single key
function to encrypt the critical data before transmitting it over an insecure network.
Increasing the number of keys and number of encryption functions increases the
strength of a symmetric technique. This paper presents a symmetric key technique
that uses five keys for encryption and decryption.
Keywords Cryptography ·Symmetric ·Encryption ·Decryption ·Cipher
1 Introduction
With the constant increase in network traffic, the need for automated security tools
has also increased. Nowadays, a lot of techniques are available for providing the
security of the data and necessary information that need protection. But to preserve the
criticality of the data and information many symmetric and asymmetric techniques
have been proposed. Hence, the techniques are introduced by cryptography [1,2]to
achieve the task of communicating in a secure manner. Highly sensitive areas which
have the need to secure their data are fond of new and better techniques that can
keep their data safe thus making them invulnerable to attacks. Along the same lines,
the proposed technique is an approach that is aimed at providing high security to the
data.
N. Garg ·R. Johari
USICT, GGSIPU, Delhi, India
e-mail: neelansh5@gmail.com
R. Johari
e-mail: rahul.johari.in@ieee.org
H. Bhatia (B)
Reval India Private Limited, Gurugram, India
e-mail: droid.harshit@gmail.com
© Springer Nature Singapore Pte Ltd. 2019
S. Bhattacharyya et al. (eds.), International Conference on Innovative Computing
and Communications, Lecture Notes in Networks and Systems 55,
https://doi.org/10.1007/978-981-13-2324-9_24
241
242 N. Garg et al.
2 Proposed System
The proposed system is an extension of [3] and uses five keys instead of three keys
to successively encrypt the plaintext and decrypt the ciphertext. The Pentaplicative
cipher technique is a symmetric key cipher that makes use of the same set of keys
to encrypt and decrypt the text and uses mathematical operations carried out in a
pre-defined order. The proposed technique employs the use of a much cheaper math-
ematical operation, XOR, and uses the bit dispersion method to make it harder to
map the length of plaintext to that of ciphertext. It is harder to decipher multiple oper-
ations with multiple keys that correspond to the private social security information
of the user, and hence, this decreases the probability of breaking the cipher text.
Related Work
In [4], authors(s) introduce the Cross-Language Cipher (CLCT) Technique to provide
security to plaintext by mapping of characters. In [5], author(s) have designed a
Java-based tool to depict the utilization of injection through SQL injection attack
and broken authentication using brute force attack and dictionary attack.
3 Methodology
A. Explanation of Pentaplicative Encryption Technique
The paper presents a conjectural adoption of the proposed technique on a sample
plaintext. The proposed technique uses the ASCII character set encoded into their
corresponding decimal numbers. The five private keys (kept secret) used in the tech-
nique map to the social information of the user and have been symbolized as K1,
K2,K3,K4, and K5. The keys are namely AADHAR number (K1), PAN Number
(K2), Bank Account Number (K3), Voter Identification Number (K4), and Passport
Number (K5). Below example depicts the encryption and decryption process on a
sample plaintext and uses a sample system of five keys that form the user input.
Plaintext—CRYPTO
Let the private keys be: K117, K219, K317, K413, and K515 (assump-
tion: for simplification of the example, we have used smaller values of the five keys).
The technique uses the following operations in a sequential order to obtain a
ciphertext which is then transmitted to the receiver over an unsecured channel:
E1(PT XOR K1)
E2(E1+K2)mod 256
E3(E2∗K3)mod 256
E4(E3−K4)mod 256
E5(E4XOR K5)
Pentaplicative Cipher Technique 243
Table 1 Encryption table
P.T E1(P.T.
XOR K1)
E2(E1+
K2) mod 256
E3(E2*
K3) mod 256
E4(E3−
K4) mod 256
E5(E4
XOR K1)
C(67) (67 XOR
17) 82 (R)
(82 + 19) mod
256 101 (e)
(101 * 17)
mod 256
181
(181 −13)
mod 26 168
(¿)
(168 XOR
15) 167 (º)
R(82) (82 XOR
17) 67 (C)
(67 + 19) mod
256 86 (V)
(86 * 17) mod
256 182
(182 −13)
mod 256
169
(169 XOR
15) 166 (ª)
Y(89) (89 XOR
17) 72 (H)
(72 + 19) mod
256 91 ([)
(91 * 17) mod
256 11
(11 −13)
mod 256
254 ()
(254 XOR
15) 241 (±)
P(80) (80 XOR
17) 65 (A)
(65 + 19) mod
256 84 (T)
(84 * 17) mod
256 148 (ö)
(148 −13)
mod 256
135 (ç)
(135 XOR
15) 136 (ê)
T(84) (84 XOR
17) 69 (E)
(69 + 19) mod
256 88 (X)
(88 * 17) mod
256 216
(216 −13)
mod 256
203
(203 XOR
15) 196 (−)
O(79) (79 XOR
17) 94 (ˆ)
(94 + 19) mod
256 113 (q)
(113 * 17)
mod 256
129 (ü)
(129 −13)
mod 256
116 (t)
(116 XOR
15) 123 ({)
Table 2 Bit dispersion operation
Obtained
E5
167 166 241 136 196 123
E5
binary
10100111 10100110 11110001 10001000 11000100 01111011
Cipher 101001 111010 011011 110001 100010 001100 010001 111011
Cipher
text
41 58 27 49 34 12 17 59
Final transmitted ciphertext for CRYPTO plaintext is ):←1”♀◄;
C.T.bit dispersion(E5)
Bit dispersion function converts the characters to their 8-bit ASCII code and then
groups the entire stream of binary bits for characters into a group of 6 bits. Remainder
bits, if any, are padded with trailing zeroes to make the sequence a complete group
of 6 bits. Further, each group of 6 bit is encoded back to an ASCII character which
is the final ciphertext.
The table describes the process with the help of an example and briefs the working
of the Pentaplicative technique (Tables 1and 2).
B. Explanation of Pentaplicative Decryption Technique
The decryption process begins with reverse bit dispersion process wherein the group
of 6 binary bits is converted to a character stream. Then, the group of 8 bits is
244 N. Garg et al.
Table 3 Reverse bit dispersion operation
Obtained
C
41 58 27 49 34 12 17 59
Cin
binary
101001 111010 011011 110001 100010 001100 010001 111011
Re-
dispersed
10100111 10100110 11110001 10001000 11000100 01111011
Dispersed
ASCII
167 166 241 136 196 123
Dispersed text to be used to obtain plaintext is ºª ±ê {
formed from the stream and extra padding of trailing zeroes discarded. The binary
bits are converted into their ASCII decimal value and character, and this forms the
input for further mathematical operations to counter effect the encryption operation.
Mathematically, the process is carried out as follows:
•Ciphertext, C is ):←1”♀◄;
•Keys, K117, K219, K317, K413 and K515.
•The modulo multiplicative inverse of the key for decryption is specified below:
K317 and K−1
3241 (K3must be co-prime with 256 for inverse to exist.).
The final plaintext message can be computed at the receiver’s end using the fol-
lowing steps as specified by the text that follows:
Dcreverse bit dispersion(C)
D1(DcXOR K5)
D2(D1+K4)mod 256
D3D1∗K−1
3mod 256
D4(D3−K2)mod 256
P.T(D4XOR K1)
D1,D2,D3, and D4are intermediate texts obtained during decryption, and Cis
ciphertext input to the decryption algorithm along with five keys. Dcis the output of
the reverse bit dispersion function (Tables 3and 4).
The final plaintext is received by D5and can be computed at the receiver’s end.
The five keys and order in which mathematical operations are performed must be
kept secret between sender and receiver to secure the crypto-system. The length of
ciphertext and plaintext is different, thus avoiding the linear mapping of characters.
Pentaplicative Cipher Technique 245
Table 4 Decryption table
DcD1= (CXOR
K5)
D2(D1+
K4) mod 256
D3(D2*
K−1
3)mod
256
D4(D3−
K2) mod 256
D5(D4
XOR K5)
º (167) (167 XOR
15) 168 (¿)
(168 + 13)
mod 256
181
(181 * 241)
mod 256
101 (e)
(101 −19)
mod 256 82
(R)
(82 XOR
15) 67 (C)
ª (166) (166 XOR
15) 169
(169 + 13)
mod 256
182
(182 * 241)
mod 256 86
(V)
(86 −19)
mod 256 67
(C)
(67 XOR
15) 82 (R)
±(241) (241 XOR
15) 254 ()
(254 + 13)
mod 256 11
(11 * 241)
mod 256 91
([)
(91 −19)
mod 256 72
(H)
(72 XOR
15) 89 (Y)
ê (136) (136 XOR
15) 135 (ç)
(135 + 13)
mod 256
148 (ö)
(148 * 241)
mod 256 84
(T)
(84 −19)
mod 256 65
(A)
(65 XOR
15) 80 (P)
(196) (196 XOR
15) 203
(203 + 13)
mod 256
216
(216 * 241)
mod 256 88
(X)
(88 −19)
mod 256 69
(E)
(69 XOR
15) 84 (T)
{ (123) (123 XOR
15) 116 (t)
(116 + 13)
mod 256
129 (ü)
(129 * 241)
mod 256
113 (q)
(113 −19)
mod 256 94
(ˆ)
(94 XOR
15) 79 (O)
4 Mathematical Modeling
As stated above, the technique encodes the encountered characters into their corre-
sponding ASCII numbers. The process of encryption follows the equation that output
encryption function, Tn(y), is obtained from the input cipher function, C(y), upon
applying some mathematical computations over the latter. The cipher’s encryption
mechanism deploys the following equations:
C(y)Bit_Dispersion(E5(y))where,E5(y)(E4(y) XOR K5(x)),
and,E4(y)(E3(y)−K4(x))mod 256,and,E3(y)(E2(y)∗K3(x))mod 256,
and,E2(y)(E1(y)+K2(y))mod 256,and,E2(y)(P(y)XOR K1(y))
where P(y) is the length of plaintext Nnand K(y) is the encryption key method
that is used in the encryption process, and mentioned K1(y), K2(y), K3(y), K4(y),
and K5(y) are the key functions that are used individually through all characters of
plaintext with length Nn. Since the operation does not do one-to-one mapping with
characters, hence the obtained length of ciphertext C(y)isM*
n
(1) Upon successful application of the operations, the result obtained needs to be
decoded from numbers back into the original ASCII character set from which
it was earlier encoded. The functional integral values for C(y) are obtained
individually as C0(y), C1(y), C2(y), C3(y)… Cn(y)fornlength n belonging to
246 N. Garg et al.
natural number set {1, 2 … N} and specified range 0 <C(y) < 255. Conclusively,
the numbers are mapped back to the original character set via their ASCII code
values that pertain to yias (y0,y1,…yn) where the ASCII values are in Base10
order.
(2) The integers thus obtained would first be converted into their respective binary
Base2 form, and this decimal to binary conversion is carried out for all the values
yiby following the below-mentioned procedure: Q0=yi/2 (remainder value x0),
Q1=y0/2 (remainder value x1), Q2=1/2 (remainder value x2), and so on……Rn
(x0,x1,…x7) until the quotient is 0, where nbelongs to natural number integer
set I, i.e., R1R2…R
n, and this goes on to the number of characters in input
plaintext.
(3) The obtained Base10 values for each individual character are then mapped into
corresponding binary values denoted as a function Rn(y) and left shift operation
follows:
LnRn(y+Ki)where the 0 <Ki<number of characters in plaintext,n
The encoded character set is treated with a special bit dispersion operation
wherein the number of bits of each character is mapped from 8 bits to 6 bits
of new character. The new characters are depicted as (l0l1l2…l*
n). h0…h5
denote the 6-bit character value of each integer.
(4) The bit dispersion operation returns a 6-bit binary number which needs to be
transformed into a decimal number of Base10. This Base2 to Base10 conversion
makes use of the following transformation steps as depicted:
W∗
nh0×20+h1×22+···+hk×2k
h0+(h1×2)+(h2×4)+···+hk×2k,
where (n*belongs to the set of integers, I) up till the length of plaintext.
h0+(2×h1)+(2×(h2×2)) +···+2×hk×2k−1
h0+2
h1+(h2×2)+···+hk×2k−1.
(5) Conclusively, these transformed decimal numbers are then individually mapped
into an ASCII character. The above equation shows each decimal number being
represented as W*
n. Applying such mapping gives the final encrypted text, and
the function Tn(y) gives the ciphertext with length (n*), which is greater than
length of plaintext.
(6) The average execution time is given by equation, T(T0+T1+T2+
T3+T4+T5+T6+T7+T8+T9+T10 )/11.
(7) The time complexity can be computed and depicted in Big-Oh notation as O(n)
where the number of characters in the input plaintext is depicted by n.
(8) The calculation of the time taken for various processes is specified in Table 5.
Pentaplicative Cipher Technique 247
Table 5 Time calculation S. No. Operations Time taken
1. E1(y)T0
2. E2(y)T1
3. E3(y)T2
4. E4(y)T3
5. E5(y)T4
6. C(y)T5
7. ASCII convert T6
8. Base10 to Base2 T7
9. The bit dispersion T8
10. Base2 to Base8 T9
11. Reverse ASCII T10
5 Result
A comparison is drawn between the running time of Triplicative and Pentaplicative
technique, and to mark the difference, an illustrative graph is shown (Fig. 1). The
running time comparison was done on the same set of data for both the techniques,
and the difference in running time of the two techniques reveals that the Pentaplicative
cipher technique outperforms Triplicative technique in terms of running time. Even
though Pentaplicative uses more number of keys , the results favor Pentaplicative
Fig. 1 Comparison of the running time results of Triplicative and Pentaplicative [3]
248 N. Garg et al.
Fig. 2 Encryption flowchart
Table 6 Simulation table Simulation environment
OS used Windows 10 Pro 64 bit
Processor Intel Core i5 3230M
RAM 8GB
Simulation IDE NetBeans
Ver s i o n of I D E 8.2.0 build 201403101706
Development language Java
Java version 1.8.0 build 25.25-b02
technique which takes smaller processing time. Increasing the number of keys makes
the technique arithmetically stronger as well as secure, while reducing the running
time of technique. The space complexity of both techniques remains constant at Big-
Oh of n−O(n), where n denote the number of input characters for carrying out the
process of encryption/decryption. The simulation was carried out as is specified in
the mentioned environment details (Table 6), and the output is shown (Fig. 3). The
summarized methodology is depicted pictorially as a flowchart (Fig. 2).
Pentaplicative Cipher Technique 249
Fig. 3 Output for Pentaplicative technique
6 Conclusion
The Pentaplicative technique is a lightweight and a robust crypto technique that has a
small running time. The crypto-system is cheaper to implement and set up as it does
not require heavier hardware for the operations. The results draw a clear picture in
terms of improvement of performance with its predecessor—Triplicative technique.
Moreover, the selection of confidential social security information as keys makes the
technique more difficult to decipher and hence makes for a strong cipher technique.
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Sci 78:217–223
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on security in computing and communication. Springer International Publishing, pp. 217–227
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