Briefing
The paper addresses the pervasive challenge of achieving efficient and adaptively secure cryptographic primitives with minimal communication. It introduces Succinct Oblivious Tensor Evaluation (NI-OTE), a foundational breakthrough enabling two parties to compute an additive secret sharing of a tensor product with communication logarithmic in input size, secured by the Learning With Errors (LWE) assumption. This new mechanism fundamentally reshapes the landscape for constructing adaptively secure laconic function evaluation, trapdoor hash functions, and succinct homomorphic secret sharing, paving the way for more scalable and private decentralized architectures.
Context
Prior to this research, constructing cryptographic primitives like laconic function evaluation (LFE) and trapdoor hash functions (TDH) faced significant limitations regarding communication complexity and adaptive security. Existing LFE schemes struggled to achieve both adaptive security from standard assumptions and optimal communication rates simultaneously. Similarly, TDH constructions for general functions often incurred non-optimal encoding key sizes or relied on stronger, less falsifiable assumptions, leaving a gap in the theoretical framework for truly efficient and robust private computation.
Analysis
The core innovation is Non-Interactive Oblivious Tensor Evaluation (NI-OTE), a two-party protocol where Alice and Bob compute an additive secret sharing of a tensor product x ⊗ y with messages whose size is independent of the dimension of x. This is achieved through a two-step process ∞ initially, a “half-succinct” protocol is constructed where only one party’s message is short, then a generic bootstrapping procedure makes the scheme fully succinct. The security of NI-OTE is rooted in the standard Learning With Errors (LWE) assumption.
A key technical ingredient introduced is “adaptive lattice encodings,” a new variant of homomorphic lattice encodings that naturally supports adaptive security and enables homomorphic operations while circumventing prior attacks. This primitive then serves as a versatile building block, transforming into succinct Non-Interactive Matrix Oblivious Linear Evaluation (NI-MOLE) and enabling constructions of adaptively secure LFE with optimal rate, trapdoor hash functions for all functions with optimal parameters, and highly efficient succinct homomorphic secret sharing.
Parameters
- Core Concept ∞ Succinct Oblivious Tensor Evaluation
- New System/Protocol ∞ Non-Interactive Oblivious Tensor Evaluation (NI-OTE)
- Key Technical Ingredient ∞ Adaptive Lattice Encodings
- Underlying Assumption ∞ Learning With Errors (LWE)
- Key Authors ∞ Damiano Abram, Giulio Malavolta, Lawrence Roy
- Primary Applications ∞ Laconic Function Evaluation, Trapdoor Hashing, Homomorphic Secret Sharing
Outlook
This research establishes a new foundational primitive, opening several avenues for future work. The adaptive lattice encodings, as a novel variant, hold potential for broader applications across lattice-based cryptography, extending beyond the primitives discussed here. The ability to construct adaptively secure LFE and optimal trapdoor hashing from standard LWE assumptions paves the way for more practical and provably secure private computation frameworks. Future research will likely explore further optimizations of NI-OTE, its integration into more complex privacy-preserving protocols, and the development of new cryptographic schemes leveraging the enhanced properties of adaptive lattice encodings, potentially impacting the design of confidential smart contracts and scalable privacy layers in decentralized systems.
Verdict
This research fundamentally advances the theoretical underpinnings of private verifiable computation by introducing a highly efficient and adaptively secure cryptographic primitive from standard assumptions.
Signal Acquired from ∞ arxiv.org
