Isogeny-Based Multi-signature Scheme

Multi-signatures are protocols that allow multiple signers to produce a joint signature on the same message. They are used in areas such as blockchains for cryptocurrencies. In recent years, multi-signature schemes have been proposed in lattice-based cryptography as well as pairing-based cryptography but there are currently no multi-signature schemes in isogeny-based cryptography. In this paper, we propose a multi-signature scheme by extending the Commutative Supersingular Isogeny based Fiat-Shamir signature (CSI-FiSh), as well as its variant CSI-FiSh with Sharing-friendly Keys (CSI-SharK) to the multiple signers setting. To adapt our scheme to the isogeny setting, we use a round-robin during both the key aggregation and the signature aggregation. We also prove the security of our scheme in the Random Oracle Model (ROM) by using the Double Forking Lemma Technique.