Blind ECDSA from the ECDSA Assumption

Abstract

Blind signatures have become a cornerstone for privacy-sensitive applications such as digital cash, anonymous credentials, and electronic voting. The elliptic curve variant of the Digital Signature Algorithm (ECDSA) is widely adopted due to its efficiency in resource-constrained environments, such as mobile devices and blockchain systems. Building blind ECDSA is hence a natural goal. One presents the first such construction relying solely on the ECDSA assumption. Despite the inherent complexities in integrating blindness with ECDSA, we design a protocol that ensures both unforgeability and blindness without introducing new computational assumptions and ensuring concurrent security. It involves zero-knowledge proofs based on the MPC-in-the-head paradigm for complex statements combining relations on encrypted elliptic curve points, their coordinates, and discrete logarithms.