# Homomorphic Signatures for Polynomial Functions

**Authors:**

*D. Boneh and D. Freeman*

** Abstract: **

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.

** Reference:**

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

**Full paper:**
pdf

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