Paper 2026/1477

PERSEPHONE: Zero-Knowledge Multiplicative Non-Negative Proof for Sequential Private Range Verification

Abstract

Numerous real-world systems in the FinTech space rely on zero-knowledge proof (ZKP) to verify information without revealing it. For example, range verification is an essential component of transaction systems to ensure that a payment amount does not exceed the payer's wallet balance. However, this verification requires to access the payer's account balance and transferred amount, which they may want to keep confidential. This drives the need for private range verification. In its simplest form, private range verification can be achieved with a zero-knowledge range proof (ZKRP) to verify that a secret value lies within public bounds. When the bounds are also private, ZKRP can still be used, but multiple ZKRPs are needed for each private range verification. This causes a considerable slowdown in the transaction system, which can not only delay transactions but also cause system failures when delays build up beyond control. To address this limitation, we consider the problem of Sequential Private Range Verification, which involves verifying in a sequence that a series of values fall within sequentially-linked private bounds, rather than verifying each private range independently. We propose a novel ZKP, which we call zero-knowledge multiplicative non-negative proof (ZK-MultNNP), and use it in our proposed framework PERSEPHONE to address this problem. We demonstrate experimentally that PERSEPHONE outperforms a ZKRP-based solution by 3x. Furthermore, we observe in a realistic digital payment system that transaction requests are always processed within the Doherty threshold of 400ms with the PERSEPHONE-based system, against only 9% for the ZKRP-based solution.