Abstract
Based on preimage sampleable functions and hard problems for lattices, we propose two lattice-based multi-signature schemes, which include the trivial broadcasting multi-signature scheme and the sequential multi-signature scheme. In the broadcasting multi-signature scheme, the length of the multi-signature varies linearly with the number of the signers. In the sequential multi-signature scheme, the length of the multi-signature is fixed and independent of the number of the signers. These two multi-signature schemes can allow multiple signers to sign the same message cooperatively.
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