Machine learning applications gain more and more access to highly sensitive information while simultaneously requiring more and more computation resources. Hence, the need for outsourcing these computational expensive tasks while still ensuring security and confidentiality of the data is imminent. In their seminal work, Tramer and Boneh presented the Slalom protocol for privacy-preserving inference by splitting the computation into a data-independent preprocessing phase and a very efficient online phase. In this work, we present a new method to significantly speed up the preprocessing phase by introducing the Carnival protocol. Carnival leverages the pseudo-randomness of the Subset sum problem to also enable efficient outsourcing during the preprocessing phase. In addition to a security proof we also include an empirical study analyzing the landscape of the uniformity of the output of the Subset sum function for smaller parameters. Our findings show that Carnival is a great candidate for real-world implementations.

The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.

Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.

In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage.