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Communications in computer and information science

Lattice-Based Puncturable Blind Signature Scheme with Bidirectional Security

Junshuai Zhang, Zhenhua Liu, Dongdong Yao

Published Jan 1, 2024• 0 citations
Publisher
DOI
10.1007/978-981-96-0151-6_28

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Puncturable digital signatures, enable fine-grained revocation of signing authority but typically offer security only against static adversaries. To address this limitation, this paper construct a lattice-based signature scheme that supports private puncturing and achieves adaptive security in the random oracle model. This paper design integrates a private puncturable pseudorandom function (Private PRF), which allows secure secret key updates without revealing any information about the punctured messages or their corresponding signatures. This ensures existential unforgeability under adaptive chosen message attacks. The results demonstrate the feasibility of achieving adaptively secure, privacy-preserving puncturable signatures under post-quantum assumptions.
Blind signature offer the protection for sender's privacy and become an important primitive for electronic commerce. In this paper, we present a technique of matrix-vector-blinding for lattice-based blind signature. Building on this result, we propose two hierarchical ID-based blind signature schemes from lattice with and without random oracle, which are secure against quantum attacks. We apply the latest technique of "lattice basis delegation in fixed dimension" from ABB10's[1] scheme to our constructions which contribute to shorter public key and signature. Both of our blind signature schemes are proven to hold the properties of perfect blindness and one-more unforgeableability. Our hierarchical ID-based blind signature schemes are communicationally efficient and needs only one round data exchanges between the signer and the user, and with a shorter public key and signature in comparison with similar schemes[2, 3]. We prove that our scheme is secure assuming that the short integer solution (SIS) problem is hard.
Motivated by the need to have secure blind signatures even in the presence of quantum computers, we present two efficient blind signature schemes based on hard worst-case lattice problems. Both schemes are provably secure in the random oracle model and unconditionally blind. The first scheme is based on preimage samplable functions that were introduced at STOC 2008 by Gentry, Peikert, and Vaikuntanathan. The scheme is stateful and runs in 3 moves. The second scheme builds upon the PKC 2008 identification scheme of Lyubashevsky. It is stateless, has 4 moves, and its security is based on the hardness of worst-case problems in ideal lattices.