Some open questions aggregation and privacy protection Coding

Some open questions: aggregation and privacy protection Coding, information theory and signal processing Du, Kargupta, Vora Poorvi Vora/CS/GWU

Is this the question? Allowed queries of form Closureh({hi(x): minimum support of = }) Require responses of the form that enable accurate determination of What is f(x): minimum support of = ’ typically >> While preventing determination of g(x) x or g(x) if g(x) an outlier, i. e. x an outlier Privacy should be representation-invariant 1/31/2022 Poorvi Vora/CS/GWU minimal information required for the “legitimate” activity? 2

Privacy is related to data-representation Data representation questions • Modelling of data relationships – Entropy/mutual information (often used for discrete-valued data) – Number of principal components (often used for continuous-valued data) – Clustering into separate regimes in appropriate representations/codes: Fourier, Walsh, etc. • Consequent question: optimal source code – What is a good source code? – For example, jpeg is a decent compression, though lossy, of images – Walsh transform: similar band-limitedness notion in terms of decision tree lengths, data points used in a single query 1/31/2022 Poorvi Vora/CS/GWU 3

Adversary modelling What we know is if – the adversary is allowed any kind of adaptive query, and – the adversary wants error to go to zero the minimum cost per bit is bounded below, tightly, if – both adversary and database are willing to participate in an unbounded number of queries. So – make it expensive to ask a question, – stop questioning (bound number of queries) – make it such that the capacity for allowed patterns is high, and capacity for private information is low How? – Can one limit the adversary in any other ways to obtain anything more interesting? (polynomial time is not enough of a limitation) 1/31/2022 Poorvi Vora/CS/GWU 4

• Instead of uniform perturbation • Allow a total of np lies to n binary questions • What kinds of shapes can the ellipse be made to look like by computationally bounded Alice and Bob • What would be preserved? The “average” shape? 1/31/2022 Poorvi Vora/CS/GWU 5

Lying in a multiparty function evaluation 1/31/2022 Poorvi Vora/CS/GWU 6