Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits

📅 2025-08-13
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🤖 AI Summary
This work addresses the construction of succinct oblivious tensor evaluation (OTE), proposing the first two-party OTE protocol based solely on the standard LWE assumption: two parties securely compute a shared secret representation of the tensor product of their private vectors via only two messages, with communication and CRS size independent of vector dimension. Building upon this, we achieve the first adaptively secure succinct function evaluation (SFE) with communication complexity $m+ell+Dcdot ext{poly}(lambda)$, where $m,ell$ are input/output lengths and $D$ is circuit depth. We introduce adaptive lattice coding—a novel unifying paradigm—enabling the construction of trapdoor hash functions, rate-optimal homomorphic secret sharing (HSS), and optimally succinct oblivious transfer (OT) for batched messages, all applicable to arbitrary functions. All primitives feature low communication overhead and provable security under standard assumptions.

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📝 Abstract
We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors $mathbf{x} otimes mathbf{y}$, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of $mathbf{x}$. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a host of cryptographic primitives, all with security reducible to LWE, such as: * Adaptively secure laconic function evaluation for depth-$D$ functions $f:{0, 1}^m ightarrow{0, 1}^ell$ with communication $m+ell+Dcdot mathrm{poly}(λ)$. * A trapdoor hash function for all functions. * An (optimally) succinct homomorphic secret sharing for all functions. * A rate-$1/2$ laconic oblivious transfer for batch messages, which is best possible. In particular, we obtain the first laconic function evaluation scheme that is adaptively secure from the standard LWE assumption, improving upon Quach, Wee, and Wichs (FOCS 2018). As a key technical ingredient, we introduce a new notion of emph{adaptive lattice encodings}, which may be of independent interest.
Problem

Research questions and friction points this paper is trying to address.

Efficient secure computation of tensor products
Achieving adaptive security from LWE
Enabling versatile cryptographic primitives succinctly
Innovation

Methods, ideas, or system contributions that make the work stand out.

Succinct oblivious tensor evaluation (OTE) from LWE
Adaptive lattice encodings for secure computations
Trapdoor hash functions for all circuits
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