Aloni Cohen

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 “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. Aggregate pseudo-random functions 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.

Cryptography with Updates

Starting with the work of Bellare, Goldreich and Goldwasser [CRYPTO’94], a rich line of work has studied the design of updatable cryptographic primitives. For example, in an updatable signature scheme, it is possible to efficiently transform a signature over a message into a signature over a related message without recomputing a fresh signature.

The GGM Function Family Is a Weakly One-Way Family of Functions

We give the first demonstration of the cryptographic hardness of the Goldreich-Goldwasser-Micali GGM function family when the secret key is exposed. We prove that for any constant

Watermarking cryptographic capabilities

\epsilon >0

Watermarking Cryptographic Capabilities.

, the GGM family is a

What about Bob? The Inadequacy of CPA Security for Proxy Reencryption.

1/n^{2+\epsilon }