Research On Identity-Based Authorized Function Linearly Homomorphic Signature

With the rapid development of cloud computing,more and more resource-constrained users outsource complex computing tasks to cloud servers for computing.As a result,the verifiable problem of outsourced computation in remote untrusted environments becomes a hotspot for researchers.Authorized function homomorphic signature(AFHS)combines the characteristics of function signature and homomorphic signature.It can not only ensure the privacy of user data and verify the correctness of the calculation results,but also verify the honesty of cloud server computing behavior and realize verifiable outsourced computation.However,the existing AFHS schemes are constructed based on traditional number theory assumptions,with the continuous development of quantum algorithms,if quantum computers appear,these schemes will be solved in polynomial time.Lattice-based cryptography can not only resist the attack of quantum computer,but also has higher computational efficiency.In addition,the schemes based on public key infrastructure require expensive certificate management overhead.Therefore,this thesis studies AFHS schemes from lattices based on identity-based cryptography.The main works of this thesis as follows:(1)This thesis proposes the formal definition of identity-based authorized function linearly homomorphic signature(IB-AFLHS).It also proposes two security models of the signature system.Namely,existential unforgeability and weakly unforgeability against adaptive chosen-identity,chosen-message and chosen-function attacks,which are expressed as EUF-CIDA-CMA-CFA and WUF-CIDA-CMA-CFA.(2)This thesis proposes an IB-AFLHS scheme.The scheme combines the characteristics of identity-based signature,function signature and linearly homomorphic signature.IB-AFLHS can not only reduce the burden of signature calculations,verify the correctness of calculation results,but also verify the honesty of cloud server calculation behavior,prove that the cloud server only performs allowable computations on the data,prevent the cloud from acquiring unlimited signing ability,protect against the threat of disputes simultaneously,avoid the shortcomings of using public key certificates,and reduce the cost of communication and calculation.Based on the computational Diffie-Hellman assumption,the scheme satisfies WUF-CIDA-CMA-CFA in the random oracle model.(3)This thesis proposes an IB-AFLHS on lattices.The computational characteristics on lattices determine that the calculation speed of the scheme is relatively fast,and the calculation efficiency is relatively high.Moreover,the high-quality nature of the difficult problems on lattices makes the scheme resistant to quantum computer attacks.Based on the small integer solution problem(SIS),the scheme satisfies WUF-CIDA-CMA-CFA in the standard model.Compared with the scheme based on bilinear pairings,this scheme is safer,more efficient and more practical.