Laconic Function Evaluation for Turing Machines
Laconic function evaluation (LFE) allows Alice to compress a large circuit C into a small digest d. Given Alice’s digest, Bob can encrypt some input x under d in a way that enables Alice to recover C(x), without learning anything beyond that. The scheme is said to be laconic if the size of d, the runtime of the encryption algorithm, and the size of the ciphertext are all sublinear in the size of C. Until now, all known LFE constructions have ciphertexts whose size depends on the depth of the circuit C, akin to the limitation of levelled homomorphic encryption. In this work we close this gap and present the first LFE scheme (for Turing machines) with asymptotically optimal parameters. Our scheme assumes the existence of indistinguishability obfuscation and somewhere statistically binding hash functions. As further contributions, we show how our scheme enables a wide range of new applications, including two previously unknown constructions: – Non-interactive zero-knowledge (NIZK) proofs with optimal prover complexity. – Witness encryption and attribute-based encryption (ABE) for Turing machines from falsifiable assumptions.
WhatsUpp with Sender Keys? Analysis, Improvements and Security Proofs
Developing end-to-end encrypted instant messaging solutions for group conversations is an ongoing challenge that has garnered significant attention from practitioners and the cryptographic community alike. Notably, industry-leading messaging apps such as WhatsApp and Signal Messenger have adopted the Sender Keys protocol, where each group member shares their own symmetric encryption key with others. Despite its widespread adoption, Sender Keys has never been formally modelled in the cryptographic literature, raising the following natural question: What can be proven about the security of the Sender Keys protocol, and how can we practically mitigate its shortcomings? In addressing this question, we first introduce a novel security model to suit protocols like Sender Keys, deviating from conventional group key agreement-based abstractions. Our framework allows for a natural integration of two-party messaging within group messaging sessions that may be of independent interest. Leveraging this framework, we conduct the first formal analysis of the Sender Keys protocol, and prove it satisfies a weak notion of security. Towards improving security, we propose a series of efficient modifications to Sender Keys without imposing significant performance overhead. We combine these refinements into a new protocol that we call Sender Keys+, which may be of interest both in theory and practice.