Elgamal Cryptosystem - An Overview

Running head: ELGAMAL CRYPTOSYSTEM
Elgamal Cryptosystem
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1ELGAMAL CRYPTOSYSTEM
Elgamal cryptosystem
Taher Elgamal first introduced and described the technique of the Elgamal cryptosystem
in the year of 1985. The system was closely related to the Diffie-Hellman key exchange which
provides the sharing of the secret key between Bob and Alice, but neither has the permission to
communicate otherwise. ElGamal abridged the Diffie-Hellman key exchange algorithm by
introducing a random exponent k. It is a public key cryptosystem which works on top of discrete
logarithm procedure (Balasubramaniam & Muthukumar, 2014). That is suppose every person has
a pair of key Sk, Pk, where Sk is the secret key and Pk is the public key. The task is to find the
secret key using the public key only. The cryptosystem has both the encryption and the
decryption schemes. The encryption system helps to people to send message in a unsecured
channel with the help of the secret key (Enriquez & Arboleda, 2017). The signature schemes like
the Schnorr signature scheme and Digital Signature Algorithm (DSA) are based on Elgamal
signature scheme but with shorter keys.
Key Generation Technique
The key generation technique used by the used by the Elgamal cystography is somewhat
similar to the general public key generators. In order to generate the key, the basic cryptographic
requirement are two keys for the asymmetrical and at least key for the symmetrical
algorithms.The receiver needs create the public key which can be passed through any public
channel in advance and publish it through the channel (Rao, 2017). Explaining the procedure of
the key generation technique suppose that Bob is generating the key and Alice is accepting the
key.

2ELGAMAL CRYPTOSYSTEM
Bob will have to follow these following steps geniting the keypair.
1. Prime key and the group generation:
Initially Bob will have to generate a large prime number p and the generator g of a
multiplicative group (Z ∗ p) of the numerals modulo p.
2. The second task is to select the private key for the process.
In order to select the private key for the process Bob needs to select an integer b
from the group z randomly and with the help of the constraint 1 ≤ b ≤ p – 2 will
create the private exponent for the task (Kahate, 2013).
3. Public key assembling
After the above process is completed the and the private exponent is created, Bob
now can compute the public key part gb mod p. Here the Elgamal cryptosystem is
the triplet (p, g,pb) where b is the private key for the process.
4. Public key publishing
Now the private key b, public key p and is ready bob needs to transfer the public key
though any server or channel to Alice for advancing.
Encryption
In order to encrypt a message M for Bob, Alice will first require the public key triplet of
from any server or via any other medium. There is no security issue in this process, as the only
secret part b is sent as gb.
For the encryption of the plain text M Alice needs to follow the following: