Security and Performance of ElGamal Encryption Parameters

ElGamal encryption/decryption algorithm is based on the difficulty of discrete logarithm problem where it is strait forward to raise numbers to large powers but it is much harder to do the inverse computation of the discrete logarithm. The ElGamal algorithm depends on certain parameters which are affecting the performance, speed and security of the algorithm. Here, the importance of these parameters and the role it takes in the security and complexity of the system are analyzed, particularly the effect of changing the length of the modulo number and the private key number are investigated.