ElGamal Public Key Encryption

Synonyms

ElGamal encryption

Related Concepts

Decisional Diffie–Hellman Assumption; ElGamal Decryption; Elliptic Curve Cryptography; E-Voting; Public Key Cryptography; Security Reduction; Threshold Cryptography

Definition

The ElGamal public key encryption scheme is characterized by having as ciphertext, $({c}_{1},{c}_{2}) := ({g}^{k},m \cdot{y}_{A}^{k})$, which details are explained further on.

Theory

In the ElGamal public key encryption scheme [1] $\langle g\rangle$ is a finite cyclic group of large enough order. q, (a multiple of) the order of g, denoted as $\mathrm{ord}(g)$ (not necessarily a prime), is public. In the original ElGamal scheme, $\langle g\rangle = {Z}_{p}$, p a prime and $q = p - 1$. Today, q is usually a prime and g a point on an elliptic curve over a finite field or an element from Z _p .

If Alice wants to make a public key, she chooses $a {\in }_{R}{Z}_{q}$ and she computes y _A : = g ^a in the group $\langle g\rangle$. Her public key will be (g, q, y...