Constant Query Locally Decodable Codes against a Computationally Bounded Adversary

We consider the problem of Locally Decodable Codes against an adversary that is computationally bounded in terms of running time. Many times the computational limitations of the adversary help in designing better codes. In this paper we prove (using some standard cryptographic assumptions) that in the case of constant query locally decodable codes the computational constraint does not make the adversary less powerful, unless both the sender and the receiver shares a secret key. We show, if either the receiver or the sender has a secret key (that is not known to the other) then designing LDCs against computationally bounded adversary is as hard as designing smooth codes unless some standard cryptographic assumptions are false. ∗Indian Statistical Institute, Kolkata. Email: {rishi r}@isical.ac.in †Chennai Mathematical Institute. Email: {sourav}@cmi.ac.in. A part of the work was done when Sourav Chakraborty was at Technion, Israel Institute of Technology