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**2014/690**

**Title:**

Efficient Interval Check in the Presence of Malicious Adversaries

**Authors:**
Genqiang Wu, Yeping He, Yi Lu, Liping Ding

**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 maliciously. 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 perfect k-ary index and corresponding zero-knowledge proof techniques. We consider a more general case of the problem where the interval is substituted by a union of intervals.

**ePrint:**
https://eprint.iacr.org/2014/690

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