Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem
Abstract
The Boneh-Boyen signature scheme is a short signature scheme which is provably secure in the standard model under the q-Strong Diffie-Hellman (SDH) assumption.
The primary objective of this thesis is to examine the relationship between the Boneh-Boyen signature scheme and SDH. The secondary objective is to survey surrounding topics such as the generic group model, related signature schemes, intractability assumptions, and the relationship to identity-based encryption (IBE) schemes. Along these lines, we analyze the plausibility of the SDH assumption using the generic bilinear group model. We present the security proofs for the Boneh-Boyen signature scheme, with the addition of a small improvement in one of the probability bounds.
Our main contribution is to give the reduction in the reverse direction; that is, to show that if the SDH problem can be solved then the Boneh-Boyen signature scheme can be forged. This contribution represents the first known proof of equivalence between the SDH problem and Boneh-Boyen signatures. We also discuss the algorithm of Cheon for solving the SDH problem. We analyze the implications of Cheon's algorithm for the security of the Boneh-Boyen signature scheme, accompanied by a brief discussion on how to counter the attack.
Collections
Cite this version of the work
Kayo Yoshida
(2009).
Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem. UWSpace.
http://hdl.handle.net/10012/4219
Other formats
Related items
Showing items related by title, author, creator and subject.
-
On Pairing-Based Signature and Aggregate Signature Schemes
Knapp, Edward (University of Waterloo, 2009-01-21)In 2001, Boneh, Lynn, and Shacham presented a pairing-based signature scheme known as the BLS signature scheme. In 2003, Boneh, Gentry, Lynn, and Shacham presented the first aggregate signature scheme called the BGLS ... -
Signatures of New Physics from the Primordial Universe
Ashoorioon, Amjad (University of Waterloo, 2007-08-29)During inflation quantum fluctuations of the field driving inflation, known as inflaton, were stretched by inflationary expansion to galactic size scales or even larger. A possible implication of inflation -- if it is ... -
Unconditionally Secure Cryptography: Signature Schemes, User-Private Information Retrieval, and the Generalized Russian Cards Problem
Swanson, Colleen M (University of Waterloo, 2013-05-23)We focus on three different types of multi-party cryptographic protocols. The first is in the area of unconditionally secure signature schemes, the goal of which is to provide users the ability to electronically sign ...