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In this paper, we construct the first provably-secure isogeny-based (partially) blind signature scheme. While at a high level the scheme resembles the Schnorr blind signature, our work does not directly follow from that construction, since isogenies do not offer as rich an algebraic structure. Specifically, our protocol does not fit into the linear identification protocol abstraction introduced by Hauck, Kiltz, and Loss (EUROCYRPT'19), which was used to generically construct Schnorr-like blind signatures based on modules such as classical groups and lattices. Consequently, our scheme is provably secure in the random oracle model (ROM) against poly-logarithmically-many concurrent sessions assuming the subexponential hardness of the group action inverse problem. In more detail, our blind signature exploits the quadratic twist of an elliptic curve in an essential way to endow isogenies with a strictly richer structure than abstract group actions (but still more restrictive than modules). The basic scheme has public key size 128 B and signature size 8 KB under the CSIDH-512 parameter sets—these are the smallest among all provably secure post-quantum secure blind signatures. Relying on a new ring variant of the group action inverse problem (rGAIP ), we can halve the signature size to 4 KB while increasing the public key size to 512 B. We provide preliminary cryptanalysis of rGAIP and show that for certain parameter settings, it is essentially as secure as the standard GAIP . Finally, we show a novel way to turn our blind signature into a partially blind signature, where we deviate from prior methods since they require hashing into the set of public keys while hiding the corresponding secret key—constructing such a hash function in the isogeny setting remains an open problem. [ABSTRACT FROM AUTHOR]

In blockchain-based systems usually there are two common concerns: one of them is privacy and other is key management. Besides privacy has been widely studied, nor key management has been done so deeply, moreover, the conjunction of both neither has be addressed. In this work we present a threshold blind signature scheme designed on the modified version of the Paillier cryptosystem presented by Yi et al. Our scheme guarantees four main characteristics of interest: Independence meaning that our scheme could be applied to any blockchain-based transaction system, allowing to adapt it to different application scenarios, i.e. electronic voting or founds administration; secure key storage which improves the key management security by recovering the whole signature instead of the private key and avoiding to have one single point of failure. In addition, we also provide anonymity as one of the best-evaluated features on online transactions. Finally, we achieve independence from mixers or trusted third parties, which most of the time are used to reach anonymity with inherent risks. All of these characteristics are achieved without increase computational and communication cost in comparison with related work.