This thesis is about applications of admissible billinear maps (coming from the Weil pairing), in digital signature cryptographic protocols. We present the Diffie-Hellman and the Discrete Logarithm problems and then we give the definition of an admissible billinear map. We define identity-based digital signature schemes, attacks and forgeries on them and explain what it means for such a scheme to be secure. We give several examples of digital signature schemes (not only identity-based) and prove their security in the Random Oracle Model (ROM). Finally, we present a new identity-based signature scheme from the Weil pairing which provides the extra ability of recovering the message from the signature.
(EN)
University of Crete
