Paper 2026/878 Original: eprint.iacr.org/2026/878 ↗

Verifiable Anomaly and Similarity Detection Using Matrix Profile in Private Time-series

Abstract

Analyzing time-series databases in a privacy-preserving manner has gained significant attention, especially when the data contains sensitive personal information such as medical records or spatio-temporal data such as trajectories. Motivated by scenarios where a user must show whether an anomaly (or similarity) is detected in a time series containing sensitive data, we propose a toolkit for proving these properties on (committed) private time series. We leverage Matrix Profile (MP), a state-of-the-art data-mining structure, to detect subsequence anomalies and similarities in time series, in contrast to many works that only detect anomalies and similarities on complete time series. As recent findings have shown, the aggregated data used by MP (such as subsequence distances or MP values) leak critical information about the time series. It is therefore crucial to consider a strong adversary model where all information other than the presence or absence of anomalies/similarities remains protected. To guarantee this, we propose a combination of commitment and zero-knowledge proof systems that ensure both the validity of the proven result and the (unconditional) protection of the time series. The proposed schemes maintain reasonable execution times, even for large real-time time series.