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Abstract
To design an efficient post-quantum linearly homomorphic signature scheme, using the pre-image sampling function, a lattice-based linearly homomorphic signature scheme over a binary field is proposed in this paper. Linear homomorphism is achieved through the homomorphism of the lattice-based hash function used in the proposed signature scheme. It is shown that the proposed scheme satisfies the privacy property. Based on the hardness of the short integer solution problem, the proposed scheme is unforgeable against the type 1 and type 2 adversaries in the random oracle model. Moreover, compared with a presented linearly homomorphic signature scheme in 2011, the proposed scheme has some advantages with respect to the public key size, signature length and computational cost.
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