Spreading Alerts Quietly and the Subgroup Escape Problem

摘要

We introduce a new cryptographic primitive called the blind coupon mechanism (BCM). In effect, the BCM is an authenticated bit commitment scheme, 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 Z_n.