  In this thesis, we propose some directed signature schemes. In addition, we
have discussed their applications in different situations. In this thesis, we
would like to discuss the security aspects during the design process of the
proposed directed digital signature schemes. The security of the most digital
signature schemes widely use in practice is based on the two difficult
problems, viz; the problem of factoring integers (The RSA scheme) and the
problem of finding discrete logarithms over finite fields (The ElGamal scheme).
The proposed works in this thesis is divided into seven chapters.
