[Resource Topic] 2004/076: Group Signatures: Provable Security, Efficient Constructions and Anonymity from Trapdoor-Holders

Welcome to the resource topic for 2004/076

Group Signatures: Provable Security, Efficient Constructions and Anonymity from Trapdoor-Holders

Authors: Aggelos Kiayias, Moti Yung


To date, a group signature construction which is efficient,
scalable, allows dynamic adversarial joins, and proven secure in a
formal model has not been suggested. In this work we give the first
such construction in the random oracle model.
The demonstration of an efficient construction proven secure in
a formal model that captures all intuitive security properties of a certain
primitive is a basic goal in cryptographic design.
To this end we adapt a formal model for group signatures
capturing all the basic requirements that have been identified as desirable
in the area and we construct an efficient scheme and prove its security.
Our construction is based on the Strong-RSA assumption
(as in the work of Ateniese et al.). In our system, due to
the requirements of provable security in a formal model, we
give novel constructions as well as innovative extensions of
the underlying mathematical requirements and properties.
Our task, in fact, requires the investigation of
some basic number-theoretic techniques for arguing
security over the group of quadratic residues modulo a composite
when its factorization is known. Along the way we
discover that in the basic construction, anonymity
does not depend on factoring-based assumptions, which, in turn, allows
the natural separation of user join management and anonymity
revocation authorities. Anonymity can, in turn, be shown even against
an adversary controlling the join manager.

ePrint: https://eprint.iacr.org/2004/076

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