Paper 2005/282

Spreading Alerts Quietly and the Subgroup Escape Problem

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


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.

Available format(s)
Publication info
Published elsewhere. Extended abstract is to appear in ASIACRYPT 2005
AND-homomorphic bit commitmentBlind coupon mechanismElliptic curves over composite moduliSubgroup escape problemAnonymous communication.
Contact author(s)
aleksandr yampolskiy @ yale edu
2005-08-25: received
Short URL
Creative Commons Attribution


      author = {James Aspnes and Zoë Diamadi and Kristian Gjøsteen and René Peralta and Aleksandr Yampolskiy},
      title = {Spreading Alerts Quietly and the Subgroup Escape Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2005/282},
      year = {2005},
      note = {\url{}},
      url = {}
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