@techreport{oai:ipsj.ixsq.nii.ac.jp:00217007,
 author = {Yusen, Wang and Atsuko, Miyaji and Yusen, Wang and Atsuko, Miyaji},
 issue = {23},
 month = {Mar},
 note = {A threshold HHS [9] (Hard Homogeneous Spaces) signature scheme had been proposed by Luca De Feo et al [2]. Generally, CSI-FiSh [4] and its ancestors [1][8] can be adapted into this threshold scheme. In this work, we mainly focus on the basic version of CSI-FiSh proposed by Stolbunov [8]. In the isogeny-based threshold signature scheme sketched by Luca De Feo et al, a dealer is necessary in order to split the secret key into shares and to securely distribute them to all participants. However, in certain conditions, a trusted dealer which is a trusted third party is not permitted or does not exist. Therefore we proposed a dealer-less version based on the threshold scheme of Luca De Feo et al. We use Joint Random-Secret Sharing to let all participants exchange information with each other and thus can collaborate to generate a secret isogeny that is not revealed to any participants. In this work, we clarify some fundamental theories such as Hard Homogeneous Spaces, Joint Random-Secret Sharing, and Shamir's Secret Sharing. After that, we briefly take a review of the threshold HHS signature scheme proposed by Luca De Feo et al. We give the whole process of our dealer-less threshold scheme and then illustrate the comparison with the original one with a dealer. We believe that our dealer-less version has a wider range of applications., A threshold HHS [9] (Hard Homogeneous Spaces) signature scheme had been proposed by Luca De Feo et al [2]. Generally, CSI-FiSh [4] and its ancestors [1][8] can be adapted into this threshold scheme. In this work, we mainly focus on the basic version of CSI-FiSh proposed by Stolbunov [8]. In the isogeny-based threshold signature scheme sketched by Luca De Feo et al, a dealer is necessary in order to split the secret key into shares and to securely distribute them to all participants. However, in certain conditions, a trusted dealer which is a trusted third party is not permitted or does not exist. Therefore we proposed a dealer-less version based on the threshold scheme of Luca De Feo et al. We use Joint Random-Secret Sharing to let all participants exchange information with each other and thus can collaborate to generate a secret isogeny that is not revealed to any participants. In this work, we clarify some fundamental theories such as Hard Homogeneous Spaces, Joint Random-Secret Sharing, and Shamir's Secret Sharing. After that, we briefly take a review of the threshold HHS signature scheme proposed by Luca De Feo et al. We give the whole process of our dealer-less threshold scheme and then illustrate the comparison with the original one with a dealer. We believe that our dealer-less version has a wider range of applications.},
 title = {An Isogeny-based Dealer-Less Threshold Signature Scheme},
 year = {2022}
}