Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem
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Date
2009-01-22T16:15:47Z
Authors
Yoshida, Kayo
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Journal ISSN
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Publisher
University of Waterloo
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.
Description
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