Aggregate Pseudorandom Functions and Connections to Learning

In the first part of this work, we introduce a new type of pseudo-random function for which ``aggregate queries\u27\u27 over exponential-sized sets can be efficiently answered. We show how to use algebraic properties of underlying classical pseudo random functions, to construct such ``aggregate pseudo-random functions\u27\u27 for a number of classes of aggregation queries under cryptographic hardness assumptions. For example, one aggregate query we achieve is the product of all function values accepted by a polynomial-sized read-once boolean formula. On the flip side, we show that certain aggregate queries are impossible to support. Aggregate pseudo-random functions fall within the framework of the work of Goldreich, Goldwasser, and Nussboim on the ``Implementation of Huge Random Objects,\u27\u27 providing truthful implementations of pseudo-random functions for which aggregate queries can be answered. 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. 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

Statically Aggregate Verifiable Random Functions and Application to E-Lottery

Cohen, Goldwasser, and Vaikuntanathan (TCC\u2715) introduced the concept of aggregate pseudo-random functions (PRFs), which allow efficiently computing the aggregate of PRF values over exponential-sized sets. In this paper, we explore the aggregation augmentation on verifiable random function (VRFs), introduced by Micali, Rabin and Vadhan (FOCS\u2799), as well as its application to e-lottery schemes. We introduce the notion of static aggregate verifiable random functions (Agg-VRFs), which perform aggregation for VRFs in a static setting. Our contributions can be summarized as follows: (1) we define static aggregate VRFs, which allow the efficient aggregation of VRF values and the corresponding proofs over super-polynomially large sets; (2) we present a static Agg-VRF construction over bit-fixing sets with respect to product aggregation based on the q-decisional Diffie-Hellman exponent assumption; (3) we test the performance of our static Agg-VRFs instantiation in comparison to a standard (non-aggregate) VRF in terms of costing time for the aggregation and verification processes, which shows that Agg-VRFs lower considerably the timing of verification of big sets; and (4) by employing Agg-VRFs, we propose an improved e-lottery scheme based on the framework of Chow et al.\u27s VRF-based e-lottery proposal (ICCSA\u2705). We evaluate the performance of Chow et al.\u27s e-lottery scheme and our improved scheme, and the latter shows a significant improvement in the efficiency of generating the winning number and the player verification

Aggregate Pseudorandom Functions and Connections to Learning

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. We show how to use algebraic properties of underlying classical pseudo random functions, to construct such “ag-gregate pseudo-random functions ” for a number of classes of aggregation queries under crypto-graphic hardness assumptions. For example, one aggregate query we achieve is the product of all function values accepted by a polynomial-sized read-once boolean formula. On the flip side, we show that certain aggregate queries are impossible to support. Aggregate pseudo-random func-tions fall within the framework of the work of Goldreich, Goldwasser, and Nussboim [GGN10] on the “Implementation of Huge Random Objects, ” providing truthful implementations of pseudo-random functions for which aggregate queries can be answered. 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 exten-sions of machine learning models, continuing a line of investigation originated by Valiant and Kearns in the 1980s. The extended pseudo-random functions we address include constraine

Pseudorandom functions with structure : aggregate pseudorandom functions and connections to learning

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.Title as it appears in MIT Commencement Exercises program, June 5, 2015: Pseudorandom functions with structure : aggregate pseudorandom functions and connections to learning Cataloged from PDF version of thesis.Includes bibliographical references (pages 79-82).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. We show how to use algebraic properties of underlying classical pseudo random functions, to construct such "aggregate pseudo-random functions" for a number of classes of aggregation queries under cryptographic hardness assumptions. For example, one aggregate query we achieve is the product of all function values accepted by a polynomial-sized read-once boolean formula. 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. 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. In the third part of this work, we demonstrate limitations of the recent notions of constrained pseudo-random functions and cryptographic watermarking schemes. Specifically, we construct pseudorandom function families that can be neither punctured nor watermarked. This is achieved by constructing new unobfuscatable pseudorandom function families for new ranges of parameters.by Aloni Cohen.S.M