Universally Composable Key-Insulated and Privacy-Preserving Signature Scheme with Publicly Derived Public Key

Abstract

In recent years, the rapid development of blockchain-based applications, such as cryptocurrencies, has raised concerns about privacy preservation within the blockchain community. One widely adopted technique for privacy preservation is the use of Stealth Address, which serves as a crucial component of Monero’s Ring Confidential Transaction (RingCT) protocol. Liu et al. (EuroS &P’19) introduced and formalized a new signature variant called the Key-Insulated and Privacy-Preserving Signature Scheme with Publicly Derived Public Key (PDPKS), and gave a systematically definition on the Stealth Address in both syntax and security definition. This signature variant goes beyond defining the necessary functionality but also capturing safety and privacy requirements, by introducing two game-based security definitions respectively.

Rather than in a standalone mode, PDPKS protocol is typically executed alongside other secure components within a complex blockchain system to achieve various security objectives. However, achieving security of a comprehensive system requires additional analysis on the entire system, considering mutual impacts among protocols. Hence, it is crucial to introduce a unified and systematic definition that can describe the security in a universally composable (UC) manner.

This paper focuses on formalizing the security of PDPKS in the UC framework, which provides a stronger security definition and ensures that the protocol can be designed and analyzed modularly, so that any specific constructions that satisfy the security requirements defined in the proposed UC model can be securely used as building blocks in complex blockchain systems, without any security concerns. To have a concrete construction that satisfies the UC-security proposed in this paper, we conducted an analysis of the conventional game-based security definitions put forth by Liu et al., and proved that the equivalence between the UC-security of PDPKS and the simultaneous satisfaction of the two game-based security definitions. As a result, this implies that the construction proposed by Liu et al. is a UC-secure PDPKS construction. Besides, the proved equivalence also contributes to a general framework wherein any PDPKS construction that satisfies Liu et al.’s security definition will also satisfies UC-security. This framework enables the use of these PDPKS constructions as secure building blocks in the design and implementation of UC-secure blockchain systems.