Efficient Commitment Schemes with Bounded Sender and Unbounded Receiver

Omer Horvitz, Jonathan I. Katz

Dowon Hong, Ku-Young Chang, Heuisu Ryu

Abstract. In this paper we propose an efficient OT N 1 scheme in the bounded storage model, which is provably secure without complexity assumptions. Under the assumption that a public random string of M bits is broadcasted, the protocol is secure against any computationally unbounded dishonest receiver who can store τM bits, τ < 1. The protocol requires the sender and the receiver to store N · O ( √ kM) bits, where k is a security parameter. When N = 2, our protocol is similar to that of Ding [10] but has more efficient round and communication complexities. Moreover, in case of N> 2, if the sender and receiver can store N ·O ( √ kM) bits, we are able to construct a protocol for OT N 1 which has almost the same complexity as in OT 2 1 scheme. Ding’s protocol was constructed by using the interactive hashing protocol which is introduced by Noar, Ostrovsky, Venkatesan and Yung [15] with very large roundcomplexity. We propose an efficiently extended interactive hashing and analyze its security. This protocol answers partially an open problem raised in [10]. 1

Carlo Blundo, Barbara Masucci, Douglas R. Stinson +1 more

Rafael Pass, Alon Rosen

We present a nonmalleable commitment scheme that retains its security properties even when concurrently executed a polynomial number of times. That is, a man-in-the-middle adversary who is simultaneously participating in multiple concurrent commitment phases of our scheme, both as a sender and as a receiver, cannot make the values to which he commits depend on the values to which he receives commitments. Our result is achieved without assuming an a priori bound on the number of executions and without relying on any setup assumptions. Our construction relies on the existence of standard claw-free permutations and requires only a constant number of communication rounds.

Marc Fischlin, Roger Fischlin

Rafael Pass, Alon Rosen

We present a non-malleable commitment scheme that retains its security properties even when concurrently executed a polynomial number of times. That is, a man-in-the-middle adversary who is simultaneously participating in multiple concurrent commitment phases of our scheme, both as a sender and as a receiver cannot make the values he commits to depend on the values he receives commitments to. Our result is achieved without assuming an a-priori bound on the number of executions and without relying on any set-up assumptions. Our construction relies on the existence of standard collision resistant hash functions and only requires a constant number of communication rounds.