Single Proof for Multi-Authentication: Decentralized Anonymous Functional Credentials Based on fNIZK

Web3 has attracted considerable attention in fields including DeFi, DApps, and NFTs due to its decentralization, enhanced privacy, and user-centricity. However, interoperability and scalability challenges hinder its widespread adoption. While deploying anonymous credentials across Web3 networks to enable cross-network service access is a potential solution to these challenges, existing credential systems remain limited by centralized management, high energy consumption, and credential abuse, making them unsuitable for Web3 environments. To overcome these limitations, we propose a decentralized anonymous functional credential (DAFC) scheme that is efficient, privacy-preserving, and linkable. Unlike existing schemes, DAFC enables users to generate a single proof embedding attributes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> for requesting services under different access policies. Each provider can use the functional key <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$sk_{F}$</tex-math></inline-formula> associated with their respective access policy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F$</tex-math></inline-formula> to extract <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F(x)$</tex-math></inline-formula> for attribute verification. This significantly reduces authentication computational overhead. Furthermore, DAFC's linkability effectively mitigates credential abuse risks. As an additional contribution, we propose a novel construction of non-interactive zero-knowledge functional proof (fNIZK) based on one-out-of-many proofs and functional encryption for inner products, which is the building block of DAFC. Security analysis demonstrates that DAFC achieves anonymity, unforgeability, and linkability. Performance evaluation shows that DAFC outperforms prior schemes in both computational and communication overhead when requesting at least 6 services with distinct access policies.