SQIAsignHD: SQIsignHD Adaptor Signature
Farzin Renan, Péter Kutas
TL;DR
SQIAsignHD introduces a quantum-resistant adaptor signature by embedding secret randomness in an adaptor framework built on SQIsignHD and artificial orientation for SIDH-like isogenies on supersingular curves. The construction achieves aEUF-CMA security and witness extractability in the random oracle model, with a compact 1.26 KB signature at 128-bit security and scalable parameterization for higher security levels. By leveraging isogeny-based primitives and a formal ROM proof, the scheme addresses quantum threats to adaptor signatures and improves efficiency over prior SIDH-based designs. The work has direct implications for secure off-chain blockchain protocols, enabling efficient conditional payments and atomic swaps under post-quantum assumptions.
Abstract
Adaptor signatures can be viewed as a generalized form of standard digital signature schemes by linking message authentication to the disclosure of a secret value. As a recent cryptographic primitive, they have become essential for blockchain applications, including cryptocurrencies, by reducing on-chain costs, improving fungibility, and enabling off-chain payments in payment-channel networks, payment-channel hubs, and atomic swaps. However, existing adaptor signature constructions are vulnerable to quantum attacks due to Shor's algorithm. In this work, we introduce $\mathsf{SQIAsignHD}$, a new quantum-resistant adaptor signature scheme based on isogenies of supersingular elliptic curves, using SQIsignHD - as the underlying signature scheme - and exploiting the idea of the artificial orientation on the supersingular isogeny Diffie-Hellman key exchange protocol, SIDH, to define the underlying hard relation. We, furthermore, provide a formal security proof for our proposed scheme.