Cryptology ePrint Archive: Report 2005/282

Spreading Alerts Quietly and the Subgroup Escape Problem

James Aspnes and Zoë Diamadi and Kristian Gjøsteen and René Peralta and Aleksandr Yampolskiy

Abstract: We introduce a new cryptographic primitive called the blind coupon mechanism (BCM). In effect, the BCM is an authenticated bit-commitment, which is AND-homomorphic. It has not been known how to construct such commitments before. We show that the BCM has natural and important applications. In particular, we use it to construct a mechanism for transmitting alerts undetectably in a message-passing system of n nodes. Our algorithms allow an alert to quickly propagate to all nodes without its source or existence being detected by an adversary, who controls all message traffic. Our proofs of security are based on a new subgroup escape problem, which seems hard on certain groups with bilinear pairings and on elliptic curves over the ring Zn.

Category / Keywords: AND-homomorphic bit commitment, Blind coupon mechanism, Elliptic curves over composite moduli, Subgroup escape problem, Anonymous communication.

Publication Info: Extended abstract is to appear in ASIACRYPT 2005

Date: received 22 Aug 2005

Contact author: aleksandr yampolskiy at yale edu

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Version: 20050825:074136 (All versions of this report)

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