Research On Lattice Based Homomorphic Signature

With the rapid development of cloud computing,cryptography scheme of homomorphism property has received considerable attention from communities in academia,and homomorphic signature is a very important aspect,it has a wide range of application in the field of outsourcing computing and network coding.It is very important to design homomorphic signature to ensure homogeneity and security.With the rapid development of quantum computer,it can break based on number theory hard problem scheme,such as discrete logarithm,elliptic curve and diffie-hellman hard problem,based-lattice scheme can resist a quantum computer attack.Based-PKI constructions scheme incur certificate management procedures,and identity-based scheme can reduce the management overhead certificate management.Therefore,it is necessary to design the homomorphic properties,identity-based and secure signature scheme.This thesis construct three different homomorphic signature schemes using preimage sampling algorithm,bonsai tree algorithm,lattice basis delegation algorithm,and sampling algorithm.This schemes are based on the Small Integer Solution?SIS?hard problem in lattices,and satisfing the different of secure model.The detail is as follows.?1?This thesis proposes a linearly identity-based homomorphic signature scheme from lattices,namely LIBHS.Based-PKI schemes have some issues,but identity-based scheme can overcome these problems to improve efficiency and reduce management costs.Considering the advantage identity-based scheme,we design LIBHS scheme to use BF and WHW scheme and make use of lattice basis delegation algorithm in extracting the secret key.Then,the unforgeability of LIBHS scheme is against existential unforgeability on adaptive chosen the message and ID attack(EU-ACMA-Adaptive_idin the random oracle model,and this homomorphic signature scheme is weakly context hiding.Finally,we introduce the application of the LIBHS scheme,namely remote data integrity checking.?2?This thesis puts forword a linearly identity-based homomorphic signature scheme from lattices in the standard model.The thiesis designs a novel LIBHS scheme to use BF and Chen scheme,and it can prove secure in the standard model.This scheme meets privacy and unforgeable security model.Finally,the unforgeability of this scheme is against existential unforgeability on static chosen the message and adaptively ID attack(EU-SCMA-Adaptive_idin the standard model.Compared to the first LIBHS scheme,the key length of this scheme is longer and the efficiency is relatively low,but this scheme can prove unforgeability security in the standard model.?3?This thesis proposes an identity-based leveld fully homomorphic signature scheme from lattices,namely IBLFHS.This scheme takes advantage of the bonsai tree algorithm,lattice basis delegation algorithm,sampling algorithm,and combines with Boyen scheme and Gorbunov scheme to construct an identity-based leveld fully homomorphic signature scheme from lattices,which can prove secure in the standard model.The unforgeability of this scheme is against existential unforgeability on static chosen the message and selectively ID attack(EU-ACMA-Adaptive_id).