Some digital signature schemes with collective signers
PhD. Thesis, Universitat Politècnica de Catalunya, Barcelona. April 15, 2005.
Author: Javier Herranz.
Supervisor: Germán Sáez.
Digital signatures are one of the most important consequences of
the appearance of public key cryptography, in 1976. These schemes
provide authentication, integrity and non-repudiation to digital
communications. Some extensions or variations of the concept of
digital signature have been introduced, and many specific
realizations of these new types of signature schemes have been
In this thesis, we deal with the basic definitions and required
security properties of traditional signature schemes and two of
its extensions: distributed signature schemes and ring signature
schemes. We review the state of the art in these two topics; then
we propose and analyze new specific schemes for different
Namely, we first study distributed signature schemes for general
access structures, based on RSA; then we show that such schemes
can be used to construct other cryptographic protocols:
distributed key distribution schemes and metering schemes. With
respect to ring signatures, we propose schemes for both a scenario
where the keys are of the Discrete Logarithm type and a scenario
where the public keys of users are inferred from their personal
identities. Finally, we also propose some distributed ring
signature schemes, a kind of schemes which combine the concepts of
distributed signatures and ring signatures.
We formally prove the security of all these proposals, assuming
that some mathematical problems are hard to solve. Specifically,
we base the security of our schemes in the hardness of either the
RSA problem, or the Discrete Logarithm problem, or the
Computational Diffie-Hellman problem.
Download the thesis in PDF.
Last Updated: August 16, 2010