Stochastic Gradient Descent (SGD) is the foundation of modern machine learning (ML). In privacy-sensitive settings, gradients can reveal details about individual data points. Differential Privacy (DP) protects sensitive data during ML training by clipping gradients and adding calibrated Gaussian noise. However, existing frameworks assume semi-honest participants, which fails in adversarial or federated environments where malicious actors can bypass or alter the noise addition process, breaking privacy guarantees. We present VeriDP, a framework for verifiable differentially private training that cryptographically enforces and proves the correct execution of differentially private stochastic gradient descent (DP-SGD) in zero knowledge. VeriDP integrates Zero-Knowledge Proofs (ZKPs) with polynomial commitments, sumcheck and GKR-based proofs, and incrementally verifiable computation (IVC) to generate compact proofs of correct gradient computation, clipping, averaging, and Gaussian noise generation—without revealing private data or randomness. Unlike previous systems that only verify the final privacy budget, VeriDP enables per-iteration verifiability of each model update, providing strong privacy assurances even in adversarial settings. This establishes a novel and complete Zero-Knowledge Proof of Differentially Private Stochastic Gradient Descent (ZK-DPSGD), uniting differential privacy and verifiable computation for secure and auditable ML. Our evaluation shows that prover time increases linearly with the number of input samples, while both verifier time (2–5 ms) and proof size (3–4 KB) remain compact and effectively constant.

Federated learning (FL) proposes to train a global machine learning model across distributed datasets. However, the aggregation protocol as the core component in FL is vulnerable to well-studied attacks, such as inference attacks, poisoning attacks [71] and malicious participants who try to deviate from the protocol [24]. Therefore, it is crucial to achieve both malicious security and poisoning resilience from cryptographic and FL perspectives, respectively. Prior works either achieve incomplete malicious security [76], address issues by using expensive cryptographic tools [22, 59] or assume the availability of a clean dataset on the server side [32]. In this work, we propose AlphaFL, a two-server secure aggregation protocol achieving both malicious security in the universal composability (UC) framework [19] and poisoning resilience in FL (thus malicious2) against a dishonest majority. We design maliciously secure multi-party computation (MPC) protocols [24, 26, 48] and introduce an efficient input commitment protocol tolerating server-client collusion (dishonest majority). We also propose an efficient input commitment protocol for the non-collusion case (honest majority), which triples the efficiency in time and quadruples that in communication, compared to the state-of-the-art solution in MP-SPDZ [46]. To achieve poisoning resilience, we carry out 𝐿∞ and 𝐿2-Norm checks with a dynamic L_2-Norm bound by introducing a novel silent select protocol, which improves the runtime by at least two times compared to the classic select protocol. Combining these, AlphaFL achieves malicious2 security at a cost of 25% − 79% more runtime overhead than the state-of-the-art semi-malicious counterpart Elsa [76], with even less communication cost.

In a secure pattern matching scheme, a client learns only the locations where his private pattern matches a server’s private text, while server learns nothing. In this article, we propose a secure pattern matching protocol for the semi-honest setting which is then enhanced to guarantee full simulation-based security in the presence of malicious parties. The proposed protocol supports exact pattern matching, approximate pattern matching and pattern matching with wildcards. It is analytically shown that the proposed protocol is considerably more efficient in the approximate matching with at most$k$permitted mismatches while it has the same speed in the exact matching case comparing with the recent work in the literature. The achievements are also experimentally evaluated on a case of secure Desoxyribo-Nucleic Acid (DNA) search over the NCBI dataset of the United States national library of medicine. The results show efficiency of the proposed protocol and particularly confirm low computation overhead for the client.