The main aim of this paper is to provide a broad review of network security and cryptography, with particular regard to digital signatures. Network security and cryptography is a subject too wide ranging to coverage about how to protect information in digital form and to provide security services. However, a general overview of network security and cryptography is provided and various algorithms are discussed. A detailed review of the subject of network security and cryptography in digital signatures is then presented. The purpose of a digital signature is to provide a means for entity to bind its identity to a piece of information. The common attacks on digital signature were reviewed. The first method was the RSA signature scheme, which remains today one of the most practical and versatile techniques available. Fiat-Shamir signature schemes, DSA and related signature schemes are two other methods reviewed. Digital signatures have many applications in information security, including authentication, data integrity, and non-repudiation was reviewed.