Efficient Interval Check in the Presence of Malicious Adversaries.

Abstract

Abstract. We consider the following problem: Assuming that Alice and Bob have an integer interval [a, e] and an integer b respectively, for a commitment c to b, Alice and Bob jointly check whether b is within [a, e] without revealing their inputs, where either party may behave malicious-ly. A special case of the problem is the secure integer comparison in the malicious model. This problem mainly arises from location-based access control systems where one party needs to assure to the other party that its location is within some definite area. Our main result is a constant-round protocol that exhibit the square of log e communication and the square of log e exponentiations with simulation-based security. At the heart of the construction is perfec-t k-ary index and corresponding zero-knowledge proof techniques. We consider a more general case of the problem where the interval is substi-tuted by a union of intervals.