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INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 10, OCTOBER 2019 ISSN 2277-8616
1777
IJSTR©2019
www.ijstr.org
Hybrid Cryptosystem Using RSA, DSA, Elgamal,
And AES
Levinia B. Rivera, Jazzmine A. Bay, Edwin R. Arboleda, Marlon R. Pereña and Rhowel M. Dellosa
Abstract— The integration and combination of an asymmetric and symmetric algorithm such as RSA, ElGamal, DSA, and AES were
presented. Hybrid encryption has been used to ensure integrity in terms of data exchanged between the sender and receiver. The strength
of the asymmetric algorithm such as RSA depends on the difficult process of factorization of large prime integers while the ElGamal’s
security lies on Discrete Logarithm Problem (DLP). The symmetric algorithm is known to process the encryption faster than the asymmetric
algorithm. Key generation of DSA is merged in the proposed algorithm. DSA is recognized for its fast signature algorithm while the AES S-
Box is used to hash the ciphertext obtained. AES strength is its fast expansion key tone. Experiment’s result is presented to analyze the
effectiveness of the proposed algorithm.
Index Terms—AES, Algorithm, El Gamal, DSA, RSA, Encryption, Symmetric, Asymmetric
—————————— ——————————
1 INTRODUCTION
The art of reading and writing secret information is
Cryptography, comprises the uses of mathematics and science
in order for the protection of original information[1-3].
Cryptography covers the method of encrypting the raw
information into an unintelligent form and hard to decipher
by just anyone. The extraction of the original message is done
through decrypting the encrypted message through the use of
the key pair, public and private key[4,5]. Most Encryption
Algorithms are commonly available for use in information
security. Encryption algorithm has two types; namely, the
Asymmetric (public) keys [6] and the Symmetric (private)
keys[7]. Encryption in Symmetric key is also called secret key
encryption. This type of encryption involves the use of only
one key to decrypt and encrypt plaintext or data[8]. On the
other hand, Asymmetric key requires the use of two keys, one
is a public key typically used for encrypting while the other
one is the private key, serves as the decryption key[9]. In
encryption algorithm such as RSA (Rivest-Shamir-Adleman),
the public key is used for encryption and the private key is
used for decryption. Public key encryption is based on
computationally extensive mathematical functions[10]. Data
Encryption Standard (DES) and Advanced Encryption
Standard (AES) are examples of cryptography algorithms that
have their own strengths and weaknesses[11]. DES algorithm
uses one 64-bits key, in contrast to the AES algorithm where it
uses various bits‘ keys such as 128, 192 and 256. In encryption
algorithm, one of the apparent issues is the problem regarding
key distribution, Asymmetric key encryption or public-key
encryption resolves this problem. Examples of Asymmetric
key algorithm are the RSA and DSA where both use public
and private keys; each for encryption and decryption,
respectively. Users of this algorithm have to use two keys;
where one key-public key, is known to the public for it used
for encryption of the data while the other key-private key, is
only known to the user and is used for decrypting the
encrypted data [12].
2 TECHNICAL ASPECTS
Developed by Ron Rivers, Adi Shamir, and Leonard Adleman
is public-key encryption known as RSA [13]. RSA was first
recognized in use for signing and encryption. The three main
steps in RSA are Key Generation, Encryption and Decryption.
The weakness of RSA manifests when small encryption
exponent in sending the same message to the different
recipient is used. The second loophole is when same key is
used for signing and encryption.
2.1 Related Studies
RSA is the acronym for Ron Rivest, Adi Shamir, and Leonard
Adleman algorithm. These are the names of MIT students
who first proposed an explanation of the said algorithm to the
general public, the year 1977[14]. RSA is one of the
Asymmetric cryptography used. RSA algorithm follows that
the user must choose two prime numbers from these a
supplementary value is derived. The prime number must be
kept hidden from anyone but the user. The public key is used
for encryption of message and from the name itself it is known
to the public. There have been improvements in the algorithm
of the RSA, and with the currently published methods it is
difficult to crack the private key if the public key is large
enough[15,16]. It takes great knowledge about prime numbers
before someone (hacker) can decode the message [17-19]. The
study of [26] make use of closest coordinates to develop an
algorithm for indoor positioning system to improve its
efficiency. The present standard for secret key encryption is
the Advanced Encryption Standard Algorithm (AES). Vincent
Rijmen and Joan Daemen, originated from Belgium, are the
cryptographers who are the creator of the AES algorithm[20].
————————————————
Levinia B. Rivera is from the Department of Computer and Electronics Engineering, College of
Engineering and Information Technology of Cavite State University.
Jazzmine A. Bay is from the Department of Computer and Electronics Engineering, College of
Engineering and Information Technology of Cavite State University.
Edwin R. Arboleda is from t he Department of Computer and Electronics Engineering, College of
Engineering and Information Technology of Cavite State University.
Marlon R. Pereña is from the Department of I nformation Technology, College of Engineering and
Information Technology of Cavite State University.
Rhowel M. Dellosa is from the Computer Engineering Department of A sia Technological School of
Science and Arts.
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The advent of AES replaced the old Data Encryption Standard
(DES). AES is easy to implement and processes fast in a very
reasonable amount of time on a regular computer, this paves
way for its success in setting the standard in asymmetric
algorithm. In AES, the standardized version of the Rijndael
algorithm is used by the Federal Information Processing
Standard 197. The algorithm established the incorporation of
Exclusive-OR operations (XOR), octet substitution with an S-
box, row and column rotations, and a Mix Column in the flow
of algorithm. The cipher uses number of encryption sequences
which converts plain text to ciphertext. The output of each
sequence algorithm is the input to the next algorithm. The
output of the final algorithm is the encrypted plain text known
as ciphertext. The input set by the user is entered into a matrix
known as State Matrix[21] On the principle of public-key
cryptography, that‘s where Digital Signature operates. The
idea of key pairs, private and public key, is where public
cryptography is constructed on. Large prime numbers make
up the public and private keys. These prime numbers are
produced by a mathematical algorithm. In DSA, the key pairs
are primarily involved both for the process of signing and
encrypting the message. The application of DSA key pairs is to
authenticate the identity of the user. The Digital Signature has
the same reliability as of a document and handwritten
signatures[22]. In network security, DSA is acclaimed to be
one of its major developments. The rapid growth of digital
communications resulted in a significant need for Digital
Signature. The integrity of the assigned data and the identity
of the signatory is authenticated by the Digital Signal
algorithm. The process of the authentication in DSA is
whereby the receiver of the digital message is assured and can
ensure the integrity of the identity of the sender and the
message. On the other hand, RSA encryption algorithm takes
up longer time due large key size and modular exponentiation
operations in fortifying security. This is the reason behind the
slow process in RSA‘s Digital Signature. There is a direct
proportion between the length of the transmitted signature
and the length of the transmitted message. Hence, the longer
the message also create longer digital signature [23]. ElGamal
is an asymmetric key algorithm. This algorithm is developed
in the year 1984 by Taher Elgamal. This algorithm is an
improvement to the Diffie-Hellmen key exchange protocol
and works over finite fields. Foundation of the security of this
algorithm is the Discrete Logarithm Problem. Thus, the
ElGamal is one of the many encryption schemes that use
randomization in encryption process [24]. The propositions
presented in this paper is the combination of the asymmetric
and symmetric encryption into one algorithm, which intends
to provide a comprehensive yet secure encryption method.
The prominent characteristics of RSA and ElGamal have been
considered and implemented in the proposed algorithm. The
use of prime numbers and the modular function is one of the
powerful advantages of these algorithms. The randomization
in producing keys makes it difficult to be cracked by
attempters. In order to confuse hackers, the proposed
algorithm is diversified with symmetric cryptosystem, DSA,
and AES. The key generation of DSA is used to provide keys
for ElGamal encryption, while AES provides hashing function
for messages, thus producing various hexadecimal
combinations to cipher the text.
RSA
The steps of the RSA algorithm are as follows: A. Generation
of Public and Private keys
A. Generation of Public and Private Keys
Following are the steps for the generation of public and
private keys:
1. Choose two distinct prime numbers p1 and p2.
2. Multiply them to get ‗n‘. \
3. Calculates (p1 -1) * (p2 -1) and mention it as ᴓ(n).
4. Select ‗e‘ as a public key, such that e and ᴓ(n) are
relatively prime.
5. Compute e*d = 1(mod ᴓ(n)) and consider ‗d‘ as the
private key.
B. Encryption Scheme
1. The message M is encrypted into ciphertext C using
the public key ‗e‘ such that C = Me mod n.
C. Decryption
2. The ciphertext C is decrypted back to its original form
M with the help of the private key ‗d‘ such that M=
Cd mod n.
ELGAMAL
Elgamal is an asymmetric key algorithm developed by Taher
Elgamal in the year 1984[24]. It is based on the Diffie-Hellman
key exchange algorithm and works over finite fields. The
security of this algorithm is based on the Discrete Logarithm
Problem (DLP). The steps of RSA algorithm are as follows: A.
Generation of Public and Private keys
A. Initialization
Before the encryption and decryption process can start, the
following initialization is done:
3. Choose a random prime p and a primitive root
element ‗a‘ ԑ Fa.
4. Private key ‗x‘ is chosen as a random number such
that ‗x‘ ԑ ᴜ Fa-1.
5. Public key ‗y‘ is computed using the private key
‗x‘. Therefore, y = ax mod p.
B. Encryption Scheme
1. The sender chooses a random integer k ԑ ᴜ Fa-1
and computes one-time key K = yk mod p.
2. The message M is encrypted into two parts (C1 and
C2) as ak mod p and K*M mod p respectively.
C. Decryption
1. The ciphertext is decrypted as M = C2 K-1 mod p
using one-time key K = C1x mod p.
DSA
Key pair generation:
p: a prime number between 512 to 1024bits long
q: a prime factor of p−1, 160bits long
g ≡ h(p−1)/q (mod p) > 1, and h <p−1
(p,q and g): public parameters
x<q: the private key, 160bits long
y ≡gx (mod p): the public key, 160bits long
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Signing process (sender): k<q: a random number
r ≡ (gk mod p) (modq)
s ≡k−1 (h+xr) (modq), h=H(m) is a one-way hash
function of the message m.
(r,s): signature
Verifying signature (receiver):
w ≡ s−1 (mod q)
u1≡h×w (mod q)
u2≡r ×w (mod q)
v ≡ (gu1yu2 (mod p)) (mod q)
If v =r, then the signature is verified.
AES
The Advanced Encryption Standard (AES) otherwise known
as the Rijndael algorithm is a FIFS-accepted cryptographic
algorithm established by Daemen and Rijmen. It is an AES
candidate algorithm in 1999. The Rijndael algorithm specified
as a symmetric block cipher that can process data blocks of 128
bits using cryptographic keys of 128, 192 and 256 bits [25].
3 PROPOSED ALGORITHM
The proposed algorithm is a combined method of Digital
Signature Algorithm (DSA), Rivest-Shamir-Adleman
Algorithm (RSA), El Gamal, and Advanced Encryption
Standard (AES) cryptosystem with their unique strengths.
DSA which is known for its fast signature generation and
discrete logarithm problem is same as ElGamal. RSA strength
lies in the difficult factorization of large integers and its use of
different key for encryption and decryption. While fast
expansion key time for AES S-Box. Figure 1 displays the block
diagram of the proposed algorithm.
Fig. 1. Block Diagram of the Proposed Algorithm
4 METHODOLOGY
4.1 Key Generation:
1. Alice‘s message Mn is any mix of characters from the
ASCII table. And each character of her message is
converted to its ASCII decimal equivalent.
2. Alice then assigns a key p1 which is a prime number
greater than the highest ASCII decimal equivalent of
her characters being chosen.
3. Alice also assign a random prime number q1
4. Generate the value of n by multiplying p1 and q1.
And Øn by multiplying p1-1 and q1-1.
5. Alice picks a number of encryption keys en, such that
the value must be a prime number and gcd(e, фn)=1.
Public keys can be less than or equal to the number of
the message.
6. Value of d can be calculated using the Euclidean
Algorithm: d = e-1 mod Øn
7. Alice again assigns a key p2 and q2, which are prime
numbers.
8. Alice then chooses a random number h, equal to the
number of e.
9. And generate the value of gn using the formula:
gn = hnp2-1/q mod p2
10. Choose a prime number p3 which is greater than Cn.
11. Bob chooses a private key x and keeps it a secret. He
then sends gnx to Alice.
12. Alice computed yn using the formula:
yn = gnx mod p3
13. Choose k which is a random number such the gcd (k,
p3-1).
14. Generate the value of rn, which is the decryption key
and also a private key using the formula:
rn = gnk mod p3
For Encryption:
1. To encrypt the message, Alice computes for the value
of C using the formula:
Cn = Mn mod n
2. Alice then computes again for Sn using the formula:
Sn = (ynk mod p3) [C mop (p3-1)]
3. The value of Sn will be hidden using AES S-Box
4. The proposed algorithm uses a repetitive cycle of key
pairs that make it unique. For example, there are 6
key pairs chosen: the seventh character will apply the
public key g7 = g1 and y7 = y1, so r7 = r1; the eighth
character will apply the public key g8 = g2 and y8 =
y2, so r8 = r2; and so on and so forth.
For Decryption:
1. To decrypt the message, Bob uses the Inverse AES S-
Box.
2. Bob uses the private key x: and apply the formula:
rnx mod p3
3. Compute for C using: C = Sn / rnx mod p3
4. And Bob will get the message using:
Mn = Cd mod n
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5 RESULTS AND ANALYSIS
Table 1 shows the avalanche effect of the proposed hybrid
algorithm on the random number keys. It proved that with the
multiple numbers of k used, the ciphertext will be a lot
different compared to single k. Although it is more secure to
use multiple keys yet at some point, the system would be
slower.
TABLE 1
THE AVALANCHE EFFECT OF THE HYBRID ALGORITHM
Message
Parameters
Random Key
Cipher Text
A large fawn
jumped
quickly
over
white
zinc
boxes
p1 = 131
p2 = 79
p3 = 3001
q1 = 23
q2 = 13
e1 = 83
e2 = 61
e3 = 59
e4 = 37
e5 = 23
e6 = 29
g1 = 52
g2 = 38
g3 = 64
g4 = 10
g5 = 46
g6 = 13
x = 18
k = 7
7dadcd2c,
7783d1cd,
f2fc2653,
63c4d16b,
7cf53fa7,
63aa5b3f,
63ca6301,
7783d1cd,
f2206f77,
63c4d16b,
6347014f,
63fa9a9d,
f25a5b30,
6f13e205,
f2881359,
7b460151,
7c07963f,
63936353,
6320e56f,
7783d1cd,
c545dc23,
f2881359,
770c0c97,
7b44c412,
6312fc53,
7cf90ccd,
6bef4f05,
6b135130,
772692dc,
7b1abc53,
63936353,
63c44638,
7783d1cd,
c5474ff0,
63ca2251,
6b7bdcc7,
63926a9d,
63ca6301,
7783d1cd,
6f00dcfa,
770c0c97,
7b18404f,
7777473f,
f25a5b30,
7b9682cd,
7bcd82c4,
7c3f964d,
7c4693fa,7c3f9d3f
A large
fawn
jumped
quickly
over
white
zinc
boxes
p1 = 131
p2 = 79
p3 = 3001
q1 = 23
q2 = 13
e1 = 83
e2 = 61
e3 = 59
e4 = 37
e5 = 23
e6 = 29
g1 = 52
g2 = 38
g3 = 64
g4 = 10
g5 = 46
g6 = 13
x = 18
k1 = 9
k2 = 11
k3 = 13
k4 = 17
k5 = 19
k6 = 21
f243edc4,
7c967c92,
f25afc53,
7c5146f5,
77bcaa00,
7ca59307,
63fa5bf7,
7c967c92,
f26e09f7,
7c5146f5,
633f04b1,
63a5f993,
6f53a3c9,
7b0cc340,
f2c4232a,
c5f965bc,
77f0a063,
f26e1b1b,
63b6ca5f,
7c9b7c92,
f2a51712,
f2c4232a,
6b1b2cf9,
6f30c900,
630c455f,
77524f07,
7bfafaa0,
6ba3cbf2,
f22336f2,
6b090763,
636e1b1b,
7ca53343,
7c967c92,
c57b3ffd, 63fdfabc,
c581cb30,
7c207b51,
637d45f2,
7c967c92,
6f095913,
6b1b2cf9,
6bf7fab1,
f2f05304,
6f53a3c9,
7c171897,
7b26131b,
772c470c,
7b825b00,
77cb5193
6 CONCLUSION
Encryption protects information from unwanted and
unauthorized access. In this paper, the proposed combination
of ElGamal, DSA, RSA, and AES algorithm using multiple
keys proves a more secure and efficient way of cryptosystem
encryption. The used of multiple keys will confuse the
attackers from cracking the ciphered text. Along the process,
the message has been twice encrypted by Asymmetric
algorithm RSA and ElGamal which enhances the system of
encryption. Through the use of AES, the ciphertext has been
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 8, ISSUE 10, OCTOBER 2019 ISSN 2277-8616
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hashed into hexadecimal.
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