Reseach On Fully Homomorphic Signcryption Scheme From Lattices

With the continuous and rapid development of Cloud Computing,Big Data and Internet of Things,it is extremely critical to protect data with homomorphism,privacy and integrity.Fatemeh Rezaeibagha et al.proposed a new cryptographic concept of the homomorphic signcryption(HSC)and constructed an HSC scheme based on the Decisional Diffie-Hellman(DDH)assumption.However,their scheme is only linearly homomorphic.To overcome linear homomorphism,Shimin Li et al.constructed two(leveled)fully homomorphic signcryption(FHSC)schemes.However,their schemes can not be constructed from standard assumption since they employ the indistinguishability obfuscation(i O)which can not be built from standard assumption as far as we know.So,it is interesting to design a leveled FHSC scheme from the standard assumption.In this work,we present a leveled FHSC scheme from lattices.For this,we exert classical sign-then-encrypt method and surmount the difficulty of homomorphic multiplicative evaluation.Moreover,we prove its indistinguishability against chosen plaintext attacks(IND-CPA)and strong unforgeability under hard problems of standard lattices.In the process of constructing the scheme,we utilize two classical fully homomorphic signature(FHS)scheme and fully homomorphic encryption(FHE)scheme,that is to say,GVW scheme and GSW scheme.Combining these schemes,we could design the frame of FHSC scheme.During the course of researching,we encrypt every elements in the signature matrix to obtain corresponding signcryption.In oder to satisfies homomorphic evaluation on multiplication,we build the multiplicative operation according to the form of signature,and then we divide the signature following multiplicative homomorphism into two components,and perform GSW encryption on each of these two components.Besides,it is obvious for us to achieve additive homomorphic operation.In addition,we also analyse the noise-level of signcryption and then optimize it accordingly.With analysing the noise-level,we find that "biased multiplication" technique reduces the noise-level in the process of homomorphic evaluation.Additionally,we also present practical applications on signcryption in this paper.For example,smart power,QR code recognition and so on.