ElGamal—Encryption and Decryption

RSA is not the only public-key cryptosystem despite its relatively high profile—it’s simply the most well-established one. The security of RSA, the best-known public-key cryptosystem, is assumed to be based on the difficulty of factoring. Several other proposed public-key cryptosystems are based on different versions of the discrete logarithm problem. Some of the most important variants of these are based on elliptic curves and offer significant practical benefits over RSA. Rather than describing approaches based on elliptic curves directly, we’ll discuss the ElGamal cryptosystem for several important reasons listed below:

1. ElGamal is the public-key cryptosystem on which elliptic curve variants are based.

2. ElGamal doesn’t require further significant mathematical concepts.

3. ElGamal forms the basis for several other important cryptographic primitives, such as the Digital Signature Algorithm.