Their scheme is based on the ElGamal encryption
construction and it is CPA secure under the Decisional Diffie-Hellman assumption.
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.
Compound scheme 1 is the scheme of blind signature^ Elgamal encryption; Compound scheme 2 is the scheme of ECDSA+ Elgamal encryption.
Zheng original construction is built on a modification of ElGamal signature and carefully exploits randomness reuse to authenticate and encrypt the message more efficienty than simply encrypting the message using ElGamal encryption
The ElGamal encryption scheme consists of three algorithms, for initialization, encryption, and decryption, respectively.
An interesting property of the ElGamal encryption scheme is that it is multiplicatively homomorphic.
The classical ELGamal encryption scheme is one of the most widely used public-key cryptosystems.
As with the classical elgamal encryption, the security of the generalized elgamal encryption scheme is based on the intractability of the discrete logarithm problem in the grop G.
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.
Universal Re-Encryption is based on the ElGamal encryption