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Fuchun Guo , Yi Mu, Willy Susilo
In Eurocrypt 2009, Hohenberger and Waters pointed out that a complex-
ity assumption, which restricts the adversary to a single correct response,
seems inherently more reliable than their flexible counterparts. The q-SDH
assumption is less reliable than standard assumptions because its solution
allows exponential answers. On the other hand, the q-SDH assumption ex-
hibits the nice feature of tight reducion in security proof. In this paper, we
propose a variant of the q-SDH assumption, so that its correct answers are
polynomial and no longer exponentially many. The new assumption is much
more reliable and weaker than the original q-SDH assumption. We propose
a new digital signature scheme that can tightly reduce the security to the
proposed assumption in the standard model. We show that our signature
scheme shares most properties with the q-SDH based signature schemes.
We also propose a new approach to construct fully secure signatures from
weakly secure signature against known-message attacks. Although our se-
curity transformation is conditional and not completely generic, it offers
another efficient approach to construct fully secure signatures.
Keywords:
Digital Signatures, q-SDH Assumption, Security Proof
Digital signatures are a central primitive in modern cryptography. The
security proof of a signature scheme is usually based on a complexity as-
sumption. The q-Strong Diffie-Hellman (q-SDH) assumption [4] has become
a common assumption used for a catalogue of signatures. Digital signatures
[4, 5, 12] based on the q-SDH assumption have many good properties. For
example, the
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