Abstract
When commitment schemes are used in complex environments, e.g., the Internet, the issue of malleability appears, i.e., a concurrent man-in-the-middle adversary might generate commitments to values related to ones committed to by honest players. In the plain model, the current best solution towards resolving this problem in a constant number of rounds is the work of Ostrovsky, Persiano and Visconti (TCC’ 09). They constructed a constant-round commitment scheme that is concurrent non-malleable with respect to both commitment and decommitment. However, the scheme is only computationally binding. For application scenarios where the security of receivers is of a great concern, computational binding may not suffice.
In this work, we follow the line of their work and give a construction of statistically binding commitment scheme which is concurrent non-malleable with respect to both commitment and decommitment. Our work can be seen as a complement of the work of Ostrovsky et al. in the plain model. Our construction relies on the existence of a family of pairs of claw-free permutations and only needs a constant number of communication rounds in the plain model. Our proof of security uses non-black-box techniques and satisfies the (most powerful) simulation-based definitions of non-malleability.
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Cao, Z., Visconti, I., Zhang, Z. (2010). Constant-Round Concurrent Non-Malleable Statistically Binding Commitments and Decommitments. In: Nguyen, P.Q., Pointcheval, D. (eds) Public Key Cryptography – PKC 2010. PKC 2010. Lecture Notes in Computer Science, vol 6056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13013-7_12
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