Abstract
We investigate commitment schemes whose messages, keys, commitments, and decommitments are elements of bilinear groups, and whose openings are verified by pairing product equations. Such commitments facilitate efficient zero-knowledge proofs of knowledge of a correct opening. We show two lower bounds on such schemes: a commitment cannot be shorter than the message and verifying the opening in a symmetric bilinear group setting requires evaluating at least two independent pairing product equations. We also present optimal constructions that match the lower bounds in symmetric and asymmetric bilinear group settings.
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Abe, M., Haralambiev, K., Ohkubo, M. (2012). Group to Group Commitments Do Not Shrink. In: Pointcheval, D., Johansson, T. (eds) Advances in Cryptology – EUROCRYPT 2012. EUROCRYPT 2012. Lecture Notes in Computer Science, vol 7237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29011-4_19
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DOI: https://doi.org/10.1007/978-3-642-29011-4_19
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