Homomorphic Signatures for Polynomial Functions

Authors: D. Boneh and D. Freeman

We construct the first homomorphic signature scheme that is capable of evaluating multivariate polynomials on signed data. Given the public key and a signed data set, there is an efficient algorithm to produce a signature on the mean, standard deviation, and other statistics of the signed data. Previous systems for computing on signed data could only handle linear operations. For polynomials of constant degree, the length of a derived signature only depends logarithmically on the size of the data set.

Our system uses ideal lattices in a way that is a ``signature analogue'' of Gentry's fully homomorphic encryption. Security is based on hard problems on ideal lattices similar to those in Gentry's system.

In proceedings of Eurocrypt 2011, LNCS 6632, pp. 149-168, 2011.   [BIBTEX]

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Related papers: The paper builds on results from our earlier paper on linearly homomorphic signatures from lattices.