secret sharing

This paper addresses the fundamental question of whether cryptography can reduce algorithmic time complexity. We propose the first framework that systematically leverages cryptographic trapdoor mechanisms to accelerate deterministic computation. Our core method constructs a provably secure trapdoor matrix distribution: under standard assumptions (LWE or DDH), it is computationally indistinguishable from a random matrix distribution, yet a holder of the trapdoor key can compute an $n imes n$ matrix–vector product in nearly linear time $ ilde{O}(n)$, breaking the classical $Omega(n^2)$ lower bound. The construction supports both finite fields and the real domain, integrating randomness elimination and efficient key derivation techniques. In canonical applications such as dimensionality reduction, it achieves asymptotic speedup while preserving exact correctness. Both the formal security guarantees and the asymptotic acceleration are rigorously proven.

Pure cryptographic approaches—such as fully homomorphic encryption (FHE)—for secure aggregation in mutually distrustful multi-party settings suffer from prohibitive computational overhead, hindering practical deployment. Method: This paper proposes a hybrid secure aggregation architecture integrating cryptography and trusted execution environments (TEEs), systematically designing and analyzing a layered, end-to-end trustworthy computing pipeline that synergistically combines secure multi-party computation (MPC), secret sharing, zero-knowledge proofs, and Intel SGX/ARM TrustZone. The scheme is rigorously formulated under the malicious adversary model. Contribution/Results: It achieves provably balanced security-performance trade-offs: over 100× faster than state-of-the-art FHE-based aggregation, while supporting real-time federated aggregation over million-scale datasets. Extensive experiments validate its practicality, robustness, and feasibility for real-world deployment.

To address gradient leakage, high communication overhead, and inefficient secure aggregation caused by dynamic client dropout in privacy-preserving federated learning, this paper proposes an in-network computing–based secure aggregation architecture. Our method jointly designs homomorphic pseudorandom masking—using client-local seeds—with P4-programmable switches (Intel Tofino), enabling seed aggregation directly in the network fabric. This eliminates the need for key agreement and threshold secret sharing, thereby overcoming traditional threshold-based fault-tolerance constraints. The approach supports graceful handling of client dropouts without requiring a trusted third party. Experiments demonstrate that, compared to state-of-the-art schemes, our solution achieves up to 77× reduction in end-to-end runtime and cuts total client communication cost by 50%. We validate efficiency and practicality on both real server clusters and the Tofino hardware platform.

This work addresses the high communication overhead and security risks inherent in existing single-server secure aggregation protocols, which rely on the server to relay sensitive data among users. To overcome these limitations, the authors propose a novel two-layer secret sharing protocol that integrates Shamir’s secret sharing with 2-out-of-2 additive secret sharing, enhanced by pseudorandom functions (PRFs) and key-homomorphic PRFs (KhPRFs). This design enables secure aggregation without requiring direct user-to-user communication or server-mediated data forwarding. Furthermore, the protocol introduces an innovative encoding mechanism based on the Chinese Remainder Theorem, substantially reducing computational and communication costs for high-dimensional data. Experimental results demonstrate that, in a setting with 100 users and input length $2^{18}$, the approach reduces communication overhead by nearly 100×, decreases computation time by 51%–75%, and lowers overall computational cost by approximately 17%.

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.

This work proposes the first asymmetric two-server private aggregation protocol, addressing the high communication and computational overhead of existing schemes on high-dimensional data, which typically rely on symmetric server roles and trusted preprocessing. By offloading intensive high-dimensional computation to a primary server while keeping the auxiliary server lightweight, our protocol achieves malicious security with identifiable abort—without requiring any trusted setup—and features communication complexity independent of the input dimension. Built upon standard lattice assumptions (LWE/SIS), we introduce a novel and efficient lattice-based zero-knowledge proof to realize this asymmetric two-party computation framework. The design enables deployment of the auxiliary server on commodity hardware, substantially reducing overall overhead while enhancing security and robustness under the non-collusion assumption.

This work addresses the challenge of high communication overhead in existing secure aggregation methods for decentralized federated learning, which scales linearly with gradient dimension and thus struggles to support large models or operate efficiently under bandwidth constraints and unreliable nodes. Furthermore, Top-K sparsification—while reducing communication—hinders secure aggregation due to inconsistent gradient indices across users. To overcome these limitations, this paper presents the first information-theoretically secure decentralized aggregation protocol that natively supports Top-K sparsification. By offloading dimension-dependent costs to an offline phase and employing random masking and permutation to ensure privacy, the scheme robustly handles user dropouts and collusion attacks. Experimental results demonstrate that transmitting only 1% of the gradients achieves model accuracy comparable to full-gradient aggregation, substantially reducing communication costs while preserving security, efficiency, and accuracy.

This work addresses the challenge of computing the product of arbitrary M private inputs across a distributed system of N nodes while tolerating up to T colluding adversaries and guaranteeing ε-differential privacy, where perfect privacy and accuracy are inherently incompatible. The authors propose a differentially private secure multiplication framework based on coded polynomials and hierarchical noise injection, extending the privacy–accuracy trade-off theory from the two-input case to arbitrary M. By systematically canceling lower-order noise terms, the framework significantly improves estimation accuracy. The study characterizes the optimal privacy–accuracy trade-off for node counts satisfying (M−1)T+1 ≤ N ≤ MT, and for the minimal setting N = T+1, establishes asymptotically tight achievability and converse bounds in the high-privacy regime.

This work addresses the threat of malicious servers in federated learning, which may compromise privacy via gradient inversion or manipulate aggregation results. To counter this, the authors propose a verifiable secure aggregation scheme based on a dual non-colluding server architecture. By integrating pseudorandom functions with linear labeling techniques, the scheme constructs lightweight cryptographic primitives that provide end-to-end privacy protection and mutual verifiability while maintaining communication overhead comparable to plaintext aggregation. Experimental results demonstrate significant efficiency gains: at an input dimension of 20K, user computation time is reduced to 18 ms—7× faster than OPSA—and verification time drops to 9.5 ms, representing a 2.4× speedup, thereby substantially lowering both computational and verification costs.

This work investigates efficient constructions for compressive additive secret sharing of point functions among multiple parties and extends this approach to broader function classes to support diverse secure computation applications. By generalizing distributed point functions (DPFs) from single-point functions to generic function secret sharing (FSS) schemes, the study proposes lightweight and highly efficient protocols that substantially broaden the applicability of DPFs in privacy-preserving computation. The paper systematically reviews the theoretical foundations and core techniques underlying DPFs and FSS, and advances their practical deployment in real-world scenarios such as private information retrieval, anonymous communication, and secure multi-party computation, thereby enhancing both the security and practicality of the preprocessing phase.