Authentication and Encryption with Key Exchange are the key concepts in Cryptography, which have been continuously being targeted. Many Security Algorithms are developed as research outcome and they are broadly classified into Symmetric and Asymmetric algorithms. Symmetric Algorithms are conventional which use a common secret key that is transmitted by using physical or other communication channel. Data Encryption Standard, Triple Data Encryption Algorithm, International Data Encryption Algorithm, Blowfish and AES are the algorithms that are categorized into Symmetric. In order to make key distribution easy, Asymmetric Key algorithms such as Rivest Shamir Adleman, Diffie Hellman, Elgamal, Digital Signature Algorithm and Elliptic Curve Cryptography, are used for Encryption and Authentication where secret key remains with generating user. Rivest Shamir Adleman, ElGamal and Elliptic Curve Cryptography are the most widely used public key algorithms that perform Key Exchange and used for both authentication and confidentiality. Digital Signature Algorithm is a generally applied digital signature system where as Diffie Hellman is used only for Key Exchange. This paper presents a review of the renowned Symmetric and Asymmetric algorithms. The specified algorithms are developed and test results are presented comparing the performance and key sizes.