Advances in Cryptology – EUROCRYPT 2011

Volume 6632 of the series Lecture Notes in Computer Science pp 149-168

Homomorphic Signatures for Polynomial Functions

  • Dan BonehAffiliated withStanford University
  • , David Mandell FreemanAffiliated withStanford University


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.


Homomorphic signatures ideals lattices