We introduce a method for proving Sum-of-Squares (SoS)/ Lasserre hierarchy lower bounds when the initial problem formulation exhibits a high degree of symmetry. Our main technical theorem allows us to reduce the study of the positive semidefiniteness to the analysis of ``well-behaved'' univariate polynomial inequalities.

We illustrate the technique on ... more >>>

We introduce the notion of a database system that is information theoretically "secure in between accesses"--a database system with the properties that 1) users can efficiently access their data, and 2) while a user is not accessing their data, the user's information is information theoretically secure to malicious agents, provided ... more >>>

We present an adaptive and non-interactive protocol for verifying arbitrary efficient computations in fixed polynomial time. Our protocol is computationally sound and can be based on any computational PIR scheme, which in turn can be based on standard polynomial-time cryptographic assumptions (e.g. the worst case hardness of polynomial-factor approximation of ... more >>>