RHUL-MA-2001-5

Cryptographic techniques, such as encipherment, digital signatures,
key management and secret sharing schemes, are important building 
blocks in the implementation of all security services.

In this thesis, we present a general model for online secret sharing
schemes and investigate the design of online secret sharing schemes
which are derived from this model such as Cachin and Pinch’s schemes. 
We propose a modified version of the Pinch multiple secret sharing
protocol, which identifies all cheaters, regardless of their number,
improving on previous results by Ghodosi et al.  A new scheme is then
proposed for computationally secure online secret sharing, in which
the shares of the participants can be reused.  The security of the
scheme is based on the intractability of factoring. This scheme has
the advantage that it detects cheating and it enables the
identification of all cheaters by an arbitrator, regardless of their
number.  The scheme does not rely on a 'last participant' who
reconstructs the secret on behalf of a minimal trusted set: the
responsibility is diffused among all participants.

In addition, we cryptanalyse the recently proposed signature scheme
by Shao, based on the discrete logarithm problem, and show it is
subject to homomorphism attacks, despite a claim to the contrary.
Moreover, we show that there are major differences between a digital
signature with message recovery scheme and an authenticated
encryption scheme and point out that the signature with message
recovery scheme that was recently proposed by Chen is actually not a
signature scheme.  It would more accurately be described as an
authenticated encryption scheme.

Furthermore, we propose a modification to the Helsinki protocol which
prevents attacks by an adversary.  Some of the material in Chapters
2, 3 and 4 of the thesis has appeared in published papers.