*10:17* [Pub][ePrint]
Aggregate Pseudorandom Functions and Connections to Learning, by Aloni Cohen and Shafi Goldwasser and Vinod Vaikuntanathan
In the first part of this work, we introduce a new type of pseudo-random function for which ``aggregate queries\'\' over exponential-sized sets can be efficiently answered. An example of an aggregate query may be the product of all function values belonging to an exponential-sized interval, or the sum of all function values on points for which a polynomial time predicate holds. We show how to use algebraic properties of underlying

classical pseudo random functions, to construct aggregatable pseudo random functions for a number of classes of aggregation queries under cryptographic hardness assumptions. On the flip side, we show that certain aggregate queries are impossible to support.

In the second part of this work, we show how various extensions of pseudo-random functions considered recently in the cryptographic literature, yield impossibility results for various extensions of machine learning models, continuing a line of investigation originated by Valiant and Kearns in the 1980s and 1990s. The extended pseudo-random functions we address include constrained pseudo random functions, aggregatable pseudo random functions, and pseudo random functions secure under related-key attacks.

*19:17* [Pub][ePrint]
Aggregatable Pseudorandom Functions and Connections to Learning, by Aloni Cohen and Shafi Goldwasser and Vinod Vaikuntanathan
In the first part of this work, we introduce a new type of pseudo-random function for which ``aggregate queries\'\' over exponential-sized sets can be efficiently answered. An example of an aggregate query may be the product of all function values belonging to an exponential-sized interval, or the sum of all function values on points for which a polynomial time predicate holds. We show how to use algebraic properties of underlying

classical pseudo random functions, to construct aggregatable pseudo random functions for a number of classes of aggregation queries under cryptographic hardness assumptions. On the flip side, we show that certain aggregate queries are impossible to support.

In the second part of this work, we show how various extensions of pseudo-random functions considered recently in the cryptographic literature, yield impossibility results for various extensions of machine learning models, continuing a line of investigation originated by Valiant and Kearns in the 1980s and 1990s. The extended pseudo-random functions we address include constrained pseudo random functions, aggregatable pseudo random functions, and pseudo random functions secure under related-key attacks.