Their scheme is based on the ElGamal encryption
construction and it is CPA secure under the Decisional Diffie-Hellman assumption.
Lin and Tzeng  proposed a two-round protocol using the multiplicative homomorphism of the ElGamal encryption
scheme, with the computational cost of (5b lg N + 44 - 6) modular multiplications.
Jakobsson, "Security of signed ElGamal encryption
," in Advances in cryptology--ASIACRYPT2000, vol.
To fulfil both the functions of encryption and signature as the proposed immune based blind signeryption, the above signature schemes must be improved with a secure symmetric encryption/decryption algorithm, for which the typical ElGamal encryption
algorithm is selected with its simplicity and security.
Reference  has shown that the ElGamal encryption
scheme is semantically secure  under a standard cryptographic assumption.
The security of the above encryption scheme is essentially similar to the security of the well-known Elgamal encryption
The classical ELGamal encryption
scheme is one of the most widely used public-key cryptosystems.
The ElGamal encryption
scheme consists of three algorithms, for initialization, encryption, and decryption, respectively.
Vallent et.al  proposed an efficient public key encryption with keyword search protocol which is pairing-free and is resilient against offline keyword guessing attack based on the Diffie-Hellman problem and the ElGamal encryption
scheme in 2014.
If Csize is the size of a ciphertext generated by an encryption algorithm E, then an adversary A required [2.sup.Csize] attempts to forge a value "c." With any standard secure algorithm (i.e., 160-bit ECEL (ECC based Elgamal Encryption
) (as public key Y of SS is an element from a group of points of an elliptic curve, any ECC based encryption algorithm must be used)), the probability of an adversary A to guess a valid (c' = c) is 1/([2.sup.160]).
The party who had the smaller set interacted with at least t servers to compute the subset problem based on the standard variant of the ElGamal encryption
. The overall cost for the computation is O(t[absolute value of A][absolute value of B]), and the communication is O(t[absolute value of A][absolute value of B] log p) bits.
Universal Re-Encryption is based on the ElGamal encryption