A digital signature scheme is the process of signing an electronic message that can be transmitted over a computer network. Digital signatures provide message authentication that can be proved to a third party. With the rise of electronic communications over the Internet, digital signatures are becoming increasingly important, especially for the exchange of messages of legal significance. In 1988, Goldwasser, Micali and Rivest (GMR) [31] defined a signature scheme as a collection of algorithms: key generation, signature generation and signature verification. They defined a signature scheme as secure if it was existentially unforgeable against a chosen-message attack. These general definitions suited most signatures at the time, however, over the last decade digital signatures have emerged for which the GMR definitions are unsuitable. These signature schemes, together with their applications and security and efficiency considerations, will be explored in this thesis. These signature scheme variations have been classified by the additional services they provide to ordinary signature schemes, namely increased efficiency, increased security, anonymity, and enhanced signing and verifying capabilities.

A digital signature scheme is the process of signing an electronic message that can be transmitted over a computer network. Digital signatures provide message authentication that can be proved to a third party. With the rise of electronic communications over the Internet, digital signatures are becoming increasingly important, especially for the exchange of messages of legal significance. In 1988, Goldwasser, Micali and Rivest (GMR) [31] defined a signature scheme as a collection of algorithms: key generation, signature generation and signature verification. They defined a signature scheme as secure if it was existentially unforgeable against a chosen-message attack. These general definitions suited most signatures at the time, however, over the last decade digital signatures have emerged for which the GMR definitions are unsuitable. These signature schemes, together with their applications and security and efficiency considerations, will be explored in this thesis. These signature scheme variations have been classified by the additional services they provide to ordinary signature schemes, namely increased efficiency, increased security, anonymity, and enhanced signing and verifying capabilities.