The ElGamal encryption system is an asymmetric public-key cryptosystem based on the computational difficulty of the discrete logarithm problem. Its design is a direct extension of the Diffie-Hellman key exchange protocol, adapting the key agreement mechanism for encryption. In ElGamal, a sender uses the recipient's public key to generate a shared secret key for one-time use, which is then used to encrypt the plaintext. This direct lineage from the principles of Diffie-Hellman distinguishes it from other common asymmetric algorithms like RSA, which is based on the difficulty of integer factorization.

1. Elgamal

T. (1985). A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory

31(4)

469–472. The paper's abstract states the system is "based on the discrete logarithm problem

" the same mathematical foundation as Diffie-Hellman. DOI: https://doi.org/10.1109/TIT.1985.1057074

2. Katz

J.

& Lindell

Y. (2014). Introduction to Modern Cryptography (2nd ed.). CRC Press. In Chapter 11

Section 11.3

"The El Gamal Encryption Scheme

" the text explicitly states

"The El Gamal encryption scheme...is closely related to the Diffie-Hellman key-exchange protocol...".

3. Rivest

R. L. (2017). Lecture 10: Public-Key Cryptography: Diffie-Hellman

ElGamal

RSA. MIT OpenCourseWare

6.857 Computer and Network Security

Fall 2017. The lecture notes describe the ElGamal encryption scheme as being "based on Diffie-Hellman key exchange."

4. Menezes

A. J.

van Oorschot

P. C.

& Vanstone

S. A. (1996). Handbook of Applied Cryptography. CRC Press. In Chapter 8

Section 8.4

"ElGamal public-key encryption" (page 294)

the algorithm is presented

and its relationship to the discrete logarithm problem and Diffie-Hellman is established.