SQIAsignHD: SQIsignHD Adaptor Signature

2024-04-13

IACR Cryptology ePrint Archive

AI Summary

Existing adapter signatures are vulnerable to quantum attacks via Shor’s algorithm, posing a critical threat to post-quantum blockchain security. Method: This paper proposes SQIsignHD-Adapter, the first quantum-resistant adapter signature scheme, which uniquely integrates supersingular isogeny-based cryptography (SIDH) with artificially constructed directed hard relations. Its unforgeability and adaptability are rigorously proven in the Quantum Random Oracle Model (QROM). Built upon the SQIsignHD signature framework, it yields a fully Shor-resistant adapter signature primitive compatible with off-chain protocols such as atomic swaps and payment channels. Results: Experimental evaluation shows signatures of approximately 16 KB with efficient verification, establishing the first provably secure adapter signature primitive for post-quantum blockchain infrastructure.

Technology Category

Machine Learning: Quantum Machine LearningGame Theory and Economic Paradigms: Adversarial LearningMultiagent Systems: Adversarial Agents

Application Category

Security and Privacy: Blockchains and distributed ledgersEconomics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrenciesGraph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

Adaptor signatures can be viewed as a generalized form of the standard digital signature schemes where a secret randomness is hidden within a signature. Adaptor signatures are a recent cryptographic primitive and are becoming an important tool for blockchain applications such as cryptocurrencies to reduce on-chain costs, improve fungibility, and contribute to off-chain forms of payment in payment-channel networks, payment-channel hubs, and atomic swaps. However, currently used adaptor signature constructions are vulnerable to quantum adversaries 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, as the underlying hard relation. We, furthermore, show that our scheme is secure in the Quantum Random Oracle Model (QROM).

Problem

• Develops quantum-resistant adaptor signature scheme
• Addresses vulnerability to quantum attacks
• Enhances security for blockchain applications

Innovation

• Quantum-resistant adaptor signature scheme
• Based on supersingular elliptic curve isogenies
• Uses SQIsignHD and SIDH concepts