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These constructions are tightly related to and based on the algebraic properties of the underlying groups, and the notion originally seemed to be very much related to the algebra. However, it was shown that basing statistically binding commitment schemes on general unstructured assumption is possible, via the notion of interactive hashing
for commitments from general complexity assumptions (specifically and originally, based on any one way permutation) as in.<ref>Moni Naor, Rafail Ostrovsky, Ramarathnam Venkatesan, Moti Yung:
Perfect Zero-Knowledge Arguments for NP Using Any One-Way Permutation. J. Cryptology 11(2):
===A perfectly hiding commitment scheme based on RSA===
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