SQIAsignHD: SQIsignHD Adaptor Signature

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.