Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2011: Advances in Cryptology – EUROCRYPT 2011 pp 149-168

Homomorphic Signatures for Polynomial Functions

  • Dan Boneh
  • David Mandell Freeman
Conference paper

DOI: 10.1007/978-3-642-20465-4_10

Volume 6632 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Boneh D., Freeman D.M. (2011) Homomorphic Signatures for Polynomial Functions. In: Paterson K.G. (eds) Advances in Cryptology – EUROCRYPT 2011. EUROCRYPT 2011. Lecture Notes in Computer Science, vol 6632. Springer, Berlin, Heidelberg


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 signaturesidealslattices
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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Dan Boneh
    • 1
  • David Mandell Freeman
    • 1
  1. 1.Stanford UniversityUSA