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1	Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem Yoshida, Kayo January 2009 (has links) 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. 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 Combinatorics and Optimization
2	Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem Yoshida, Kayo January 2009 (has links) 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. 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 Combinatorics and Optimization

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Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem

Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem