International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Spreading Alerts Quietly and the Subgroup Escape Problem

James Aspnes
Zoë Diamadi
Kristian Gjøsteen
René Peralta
Aleksandr Yampolskiy
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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.
  title={Spreading Alerts Quietly and the Subgroup Escape Problem},
  booktitle={IACR Eprint archive},
  keywords={AND-homomorphic bit commitment, Blind coupon mechanism, Elliptic curves over composite moduli, Subgroup escape problem, Anonymous communication.},
  note={Extended abstract is to appear in ASIACRYPT 2005 13018 received 22 Aug 2005},
  author={James Aspnes and Zoë Diamadi and Kristian Gjøsteen and René Peralta and Aleksandr Yampolskiy},