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http://hdl.handle.net/10012/4219
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| Title: | Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem |
| Authors: | Yoshida, Kayo |
| Keywords: | cryptography
digital signatures
signature scheme
Diffie-Hellman
Strong Diffie-Hellman
SDH
Boneh-Boyen signatures
Pollard rho
Pollard lambda
baby-step giant-step
assumptions
short signatures
random oracle
generic group
BLS
Waters
Okamoto
identity-based encryption
IBE
Cheon's algorithm
partial fraction
security
existential forgery |
| Approved Date: | 22-Jan-2009 |
| Date Submitted: | 2009 |
| 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. |
| Program: | Combinatorics and Optimization |
| Department: | Combinatorics and Optimization |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/4219 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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