Post-quantum secure compact deterministic wallets from isogeny-based signatures with rerandomized keys

Abstract

A deterministic wallet is a specialized type of cryptocurrency wallet designed to simplify key management and enhance security. In their research presented at CCS'19, Das et al. introduced a general framework for building deterministic wallets based on signature schemes with rerandomizable keys (rerandomizable signatures). This advanced form of signature scheme allows for independent yet consistent rerandomization of signing and public key. Additionally, they provided an instantiation of their framework using rerandomizable signatures derived from BLS and ECDSA. However, these wallet schemes reveal vulnerability to quantum threats, primarily because of their reliance on the discrete logarithm problem which poses a significant challenge to the security landscape.

As signature schemes with perfectly rerandomizable keys are central to the construction of deterministic wallets, we begin by offering a generic construction of such scheme from signature schemes based on cryptographic (free) group actions. We present an in-depth security analysis of our scheme proving them secure against existential unforgeability under chosen-message attack with honestly rerandomized keys. To ensure post-quantum security, we instantiate our generic construction of rerandomizable signature from isogeny-based signature schemes Commutative Supersingular Isogeny based Fiat-Shamir signature (CSI-FiSh) and CSI-FiSh with Sharing-friendly Keys (CSI-SharK). We extend our techniques to adaptor signatures as well as to design an adaptor signature with rerandomizable keys from isogenies. Additionally, we seamlessly integrate our generic rerandomizable signature scheme into the development of the deterministic wallet. Finally, we instantiate our deterministic wallet from rerandomizable signature scheme from CSI-FiSh which gives the first isogeny-based deterministic wallet, distinguished by its compact key sizes.