Chapter

Advances in Cryptology – CRYPTO 2010

Volume 6223 of the series Lecture Notes in Computer Science pp 483-501

Improved Delegation of Computation Using Fully Homomorphic Encryption

  • Kai-Min ChungAffiliated withSchool of Engineering & Applied Sciences, Harvard University
  • , Yael KalaiAffiliated withMicrosoft Research New England
  • , Salil VadhanAffiliated withSchool of Engineering & Applied Sciences, Harvard University

Abstract

Following Gennaro, Gentry, and Parno (Cryptology ePrint Archive 2009/547), we use fully homomorphic encryption to design improved schemes for delegating computation. In such schemes, a delegator outsources the computation of a function F on many, dynamically chosen inputs x i to a worker in such a way that it is infeasible for the worker to make the delegator accept a result other than F(x i ). The “online stage” of the Gennaro et al. scheme is very efficient: the parties exchange two messages, the delegator runs in time poly(logT), and the worker runs in time poly(T), where T is the time complexity of F. However, the “offline stage” (which depends on the function F but not the inputs to be delegated) is inefficient: the delegator runs in time poly(T) and generates a public key of length poly(T) that needs to be accessed by the worker during the online stage.

Our first construction eliminates the large public key from the Gennaro et al. scheme. The delegator still invests poly(T) time in the offline stage, but does not need to communicate or publish anything. Our second construction reduces the work of the delegator in the offline stage to poly(logT) at the price of a 4-message (offline) interaction with a poly(T)-time worker (which need not be the same as the workers used in the online stage). Finally, we describe a “pipelined” implementation of the second construction that avoids the need to re-run the offline construction after errors are detected (assuming errors are not too frequent).

Keywords

verifiable computation outsourcing computation worst-case/average-case reductions computationally sound proofs universal argument systems