This book contains An Efficient MOR Public Key Cryptosystems Using Finite Groups , Public Key Cryptographic Technique Based on Suzuki 2-Group, An IND-CCA2 Secure Public Key Cryptographic Protocol Using Suzuki 2-Group, An IND-CPA Secure PKC Technique Based on Dihedral Group, An IND-CCA2 Secure PKC Protocol Using Dihedral Group. We demonstrated and examine the security of presented public key cryptographic technique in the indistinguishabilty adaptive chosen cipher text attack (IND-CCA2) in the random oracle model. This makes it attractive for application in resource-constrained environments where saving in computation, communication and implementation code area is a premium.