International Association
for Cryptologic Research

Streaming functional encryption (sFE), recently introduced by Guan, Korb, and Sahai [Crypto 2023], is an extension of functional encryption (FE) tailored for iterative computation on dynamic data streams. Unlike in regular FE, in an sFE scheme, users can encrypt and compute on the data as soon as it becomes available and in time proportional to just the size of the newly arrived data. As sFE implies regular FE, all known constructions of sFE and FE for P/Poly require strong cryptographic assumptions which are powerful enough to build indistinguishability obfuscation (iO). In contrast, dynamic bounded-collusion FE, in which the adversary is restricted to making at most Q function queries for some Q determined during encryption (but not fixed at time of setup), can be built from the minimal assumptions of identity-based encryption (for public-key FE) [Agrawal, Maitra, Vempati and Yamada, Crypto 2021;\; Garg, Goyal, Lu and Waters, Eurocrypt 2022] and one-way functions (for secret-key FE), as secret-key IBE is implied by one-way functions (folklore). In this paper, we introduce and build dynamic bounded-collusion streaming FE from the same minimal assumptions of identity-based encryption (for public-key sFE) and one-way functions (for secret-key sFE). Similarly to the original sFE paper of Guan, Korb, and Sahai, our scheme satisfies semi-adaptive-function-selective security which is similar to standard adaptive indistinguishability-based security except that we require all functions to be queried before any of the challenge messages. Along the way, our work also replaces a key ingredient (called One-sFE) from the original work of Guan, Korb, and Sahai with a much simpler construction based on garbled circuits. In contrast, the original approach relied on the powerful object of compact FE (which is known to imply iO) to construct this primitive.

In recent breakthrough results, novel use of grabled circuits yielded constructions for several primitives like Identity-Based Encryption (IBE) and 2-round secure multi-party computation, based on standard assumptions in public-key cryptography. While the techniques in these different results have many common elements, these works did not offer a modular abstraction that could be used across them. Our main contribution is to introduce a novel notion of obfuscation, called Reach-Restricted Reactive-Program Obfuscation (R3PO) that captures the essence of these constructions, and exposes additional capabilities. We provide a powerful composition theorem whose proof fully encapsulates the use of garbled circuits in these works. As an illustration of the potential of R3PO, and as an important contribution of independent interest, we present a variant of Multi-Authority Attribute-Based Encryption (MA-ABE) that can be based on (single-authority) CP-ABE in a blackbox manner, using only standard cryptographic assumptions (e.g., DDH) in addition. This is in stark contrast to the existing constructions for MA-ABE, which rely on the random oracle model and supports only limited policy classes.

We introduce Leakage-Resilient Incompressible cryptography, which simultaneously addresses two variants of side-channel attacks that have been tackled in theoretical cryptography. Leakage-resilience seeks to provide security against an adversary who learns a part of the secret-key and the entire ciphertext or signature; conversely, incompressible cryptography provides security against an adversary who learns the entire secret-key, but only a part of the ciphertext or signature. However, constructions in either of these security models can fail against an attack in the other model. In this work, we define a new model of security that subsumes both leakage-resilient cryptography and incompressible cryptography, and we present several non-trivial positive and negative results. On the positive side, first we present a transformation from incompressible symmetric-key encryption (SKE) to leakage-resilient incompressible SKE in the information-theoretic setting. Next, as one of our main results, we construct a leakage-resilient incompressible public-key encryption (PKE), combining an incompressible SKE and a new primitive that we call leakage-resilient non-committing key encapsulation mechanism (LR-NC-KEM). While an incompressible SKE suitable for use in both these constructions already exists in the literature (Dziembowski, CRYPTO 2006), we present a new construction with better parameters, using an appropriate notion of invertible extractors; this leads to corresponding improvements in the final parameters we obtain in these constructions. We also design a leakage-resilient incompressible signature scheme. On the negative side, we show barriers to significantly improving the parameters we obtain, by showing impossibility of basing the security of such improved schemes on blackbox reductions. Apart from the general framework and the specific results we obtain, some of the intermediate tools that we define and instantiate, like LR-NC-KEM and invertible extractors, may be of independent interest.

Secure Non-Interactive Reductions (SNIR) is a recently introduced, but fundamental cryp- tographic primitive. The basic question about SNIRs is how to determine if there is a SNIR from one 2-party correlation to another. While prior work provided answers for several pairs of correlations, the possibility that this is an undecidable problem in general was left open. In this work we show that the existence of a SNIR between any pair of correlations can be determined by an algorithm. At a high-level, our proof follows the blueprint of a similar (but restricted) result by Khorasgani et al. But combining the spectral analysis of SNIRs by Agrawal et al. (Eurocrypt 2022) with a new variant of a “junta theorem” by Kindler and Safra, we obtain a complete resolution of the decidability question for SNIRs. The new junta theorem that we identify and prove may be of independent interest.