Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem
MetadataShow full item record
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.
Cite this work
Kayo Yoshida (2009). Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem. UWSpace. http://hdl.handle.net/10012/4219
Showing items related by title, author, creator and subject.
Masárová, Zuzana (University of Waterloo, 2014-01-22)Code-based cryptography is an area of classical cryptography in which cryptographic primitives rely on hard problems and trapdoor functions related to linear error-correcting codes. Since its inception in 1978, the area ...
Lacharité, Marie-Sarah (University of Waterloo, 2014-05-26)Aggregate signature schemes combine the digital signatures of multiple users on different messages into one single signature. The Boneh-Gentry-Lynn-Shacham (BGLS) aggregate signature scheme is one such scheme, based on ...
Schanck, John (University of Waterloo, 2015-12-22)Public key cryptography, as deployed on the internet today, stands on shaky ground. For over twenty years now it has been known that the systems in widespread use are insecure against adversaries equipped with quantum ...