SHAHID MEHMOOD,FA16-RMT-008Dr. Tariq Javed Zia, Assistant ProfesorLHR TP 52642026-04-282018https://repository.cuilahore.edu.pk/123456789/3720In this dissertation, in general we have studied the implementation of inite groups in cryptography, especially theoretical based being have mathematical background. In particular the Elgamal encryption scheme based on finite groups has been used being more robust and efficient. It operates on a cyclic group for which the decisional Diffi-Hellman (DDH) assumption holds. This group is the subgroup of Quadratic residue Gq < Zp* of prime order q, where p = 2q + 1 is a safe prime. It is obvious from the definition of Elgamal encryption, which is public key encryption scheme, that the keys generated by the multiple parties (of course finite in numbers) can be combined to form a single (common) public key. The corresponding private keys can be regarded as key shares and, are used in collaborative manner. Consequently we have studied the implementation of modulo groups (Elgamal Algorithm) in particular, in electronic voting by presenting the construction of receipt free protocol from a given primary voting scheme. After applying this construction to the voting protocol we obtain an efficient receipt free 1-out-of-L voting protocol based on homomorphic encryption.endepartment of mathematicsImplementation of Elgamal Encryption in Electronic VotingDr. Tariq Javed Zia:SHAHID MEHMOODFA16Thesis