From Σ-Protocol-Based Signatures to Ring Signatures: General Construction and Applications

Public Key Infrastructure (PKI) has gained widespread attention for ensuring the security and integrity of data communication. While existing PKI mainly supports digital signatures, it is lacking in crucial anonymity, leading to the leakage of a signer’s identity information. To alleviate the issue, ring signatures are a suitable choice to provide anonymity as they allow users to create their own rings without the need for an administrator. Unfortunately, the utilization of ring signatures in PKI may present compatibility challenges within the system. Thus, proposing a general mechanism to convert a standardized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula>-based signature to a ring signature is far-reaching. In this paper, we propose a general construction for converting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula>-based signatures into ring signatures. To achieve this, we first introduce a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula>-based general model, providing a general transformation to convert existing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula>-based signatures into a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Sigma $ </tex-math></inline-formula>-protocol form. Subsequently, we incorporate our redesigned one-out-of-many relation within our general model and proceed to devise ring signatures leveraging on one-out-of-many proofs. Furthermore, to reduce the signature size, we employ the Bulletproofs folding technique, enabling the attainment of logarithmic size ring signatures. To demonstrate the wide applicability of our general construction, we present four prominent signatures as case studies. Ultimately, we conduct a rigorous security analysis and benchmark experimental evaluation. The signing and verification times are 0.44 to 0.97 times and 0.27 to 0.91 times compared to other state-of-the-art schemes, respectively. Additionally, we exhibit the lowest signature size to date.