Leveled Lattice-Based Linearly Homomorphic Signature Scheme in the Standard Model for Network Coding

  • Fenghe WangEmail author
  • Shaoquan Shi
  • Chunxiao Wang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1105)


Linearly homomorphic signature scheme is an important cryptographic primitive which can be used to against the pollution attacks in network coding. To achieve the security protection for network coding even in quantum environment, an efficient lattice-based linearly homomorphic signature scheme in the standard model is proposed in this paper. Unlike the known lattice-based scheme in the standard model, in our construction, lattice-based delegation algorithm is not needed to achieve the standard security. Hence, all the messages are signed over the same lattice in the proposed scheme. Hence, the public key of the proposed scheme only consists as a group of vectors compared with that a group of public and random matrices are necessary in known construction used lattice-based delegation tool. As a result, the public key size of the proposed scheme is shorter than that of the known lattice-based schemes (standard model). Moreover, the proposed scheme also shares advantage about the signature length. Based on the hardness of the standard short integer solution problem, we prove that the proposed scheme is adaptively unforgeable against the type 1 and type 2 adversaries in the standard model. We also shown that the proposed scheme satisfies the weakly context hiding property.


Linearly homomorphic signature Standard model Lattice Short integer solution Pre-image sampling function 



This work was supported in part by the National Natural Science Foundation of China under Grant 61803228, Project of Shandong Province Higher Education Science and Technology Program under grant J18KA361.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of ScienceShandong Jianzhu UniversityJinanChina
  2. 2.School of ComputerShandong Jianzhu UniversityJinanChina

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