Stealth Address Schemes With Fast Retrievability Based On Subgroup Membership Assumptions Related To Factoring

Abstract

Abstract Stealth address is a known technique to ensure the privacy (anonymity) of a recipient participating in a certain transaction in a distributed blockchain scenario. However, most existing stealth address schemes require linear judge time and search time $\mathcal{O}(n)$, where $n$ is the number of transactions of a certain block, so the only way to claim transactions for a recipient is to traverse the transaction list to find out whether an ever-arrived transaction belongs to him. To overcome this drawback, we proposed the notion of Fast Stealth Address (FSA), a novel approach that simultaneously preserves privacy and improves search efficiency of recipients. We give a generic construction of FSA scheme under subgroup membership assumption related to factoring and instantiate concrete schemes based on specific number-theoretic assumptions. Our framework mainly improves on two aspects: (i) allowing constant recognize time $\mathcal{O}(1)$ to judge whether a certain block contains recipient’s transactions and (ii) allowing logarithmic search time $\mathcal{O}(\log{n})$ to find out the precise transactions intended for a recipient. We formalize the security model of an FSA scheme and provide provable security analysis to ensure the security of our constructions. Besides, we implement our schemes to measure their real-world performance on several metrics and give comparison results to stealth address scheme utilized by Monero.