This report summarizes significant publications from our project, focusing on advancements in cryptographic primitive design to achieve optimal rates, advanced security guarantees, and practical efficiency.
Objective 1: New Compactness Tools
We have notably advanced cryptographic primitives that achieve optimal rates and security. Our focus areas were incompressible encryption, statistical sender privacy in oblivious transfer (OT), and advanced hashing techniques.
Incompressible Encryption:
We pioneered the first incompressible encryption scheme with an optimal rate under standard assumptions like the Learning with Errors (LWE) and Decisional Residuosity (DCR) problems [BDD22]. This encryption enhances security against mass surveillance by ensuring encrypted messages remain secure even if a small fraction of ciphertext is forgotten by an adversary. This scheme is efficient for large data volumes and addresses the limitations of previous schemes that had poor ciphertext rates or relied on strong assumptions.
Statistical Sender Privacy in Oblivious Transfer (OT):
We developed a new SSP OT construction based on Decisional Diffie-Hellman (DDH) and Learning Parity with Noise (LPN) assumptions [BDS23], achieving asymptotically optimal amortized communication complexity. This represents a significant enhancement over previous methods that required computationally intensive Fully Homomorphic Encryption (FHE).
Advanced Hashing Techniques:
We made breakthroughs with correlation intractability, providing a lower complexity bound for constructing correlation intractable hash functions and developing a new construction of somewhere statistically binding (SSB) hashing [BDSZ24]. This new hashing achieves a rate-1 BARG and RAM succinct non-interactive arguments (SNARG) with partial input soundness.
Two-Round Secure Batch Oblivious Transfer:
We tackled securing two-round protocols with minimal communication, introducing a batch OT protocol that is secure against malicious adversaries with near-optimal communication costs [BDS24].
Stealth Addresses:
We formalized stealth address mechanisms for private payments in blockchain-based cryptocurrencies, introducing SPIRIT, an efficient lattice-based stealth signature scheme with additional features like fuzzy tracking [PTDH23].
t-out-of-n Distributed Signatures:
We introduced a new construction specifically designed for applications with a small number of signers, overcoming efficiency issues of previous constructions [ADP24].
Objective 2: Advanced Laconic Functionalities
Laconic cryptography, allowing sublinear communication complexity, has been a key area of focus. We've made substantial progress in designing cryptographic systems that balance advanced security requirements with optimal performance.
Identity-Based Encryption (IBE):
We introduced big-key Identity-Based Encryption (bk-IBE) [DGSW22], enhancing security by facilitating large master secret keys while keeping user-specific keys small and portable.
Laconic Function Evaluation (LFE):
We presented the first LFE scheme for Turing machines with optimal parameters [DGM22], based on indistinguishability obfuscation and statistically binding hash functions, enabling advanced applications like non-interactive zero-knowledge (NIZK) proofs.
Laconic Encryption:
We demonstrated that laconic encryption does not require non-black-box techniques, introducing a practical black-box construction based on the LWE assumption [DKLLMR23].
Objective 3: Laconism and Obfuscation
Our work in witness encryption and obfuscation led to the development of Signature-Based Witness Encryption (SWE), enabling secure message encryption for future decryption [DHMW23]. We also addressed reducing ciphertext size in SWE schemes, achieving a sub-linear relationship between ciphertext size and the number of verification keys [ADMSW24].
Conclusion These publications have expanded the set of techniques for designing laconic cryptography protocols and introduced new research questions, particularly concerning the use of these techniques in threshold cryptography.
