Research On The Attribute Signature Method Of Multi-attribute Authority Oriented To The Small Integer Solution Problem On The Lattice

With the rapid development of technologies in the Internet,the Internet has continuously and deeply penetrated into our life from all aspects.Although the Internet has brought us too many conveniences,it has also made the problems of information security increasingly prominent.Information security has become a major issue affecting national stability of politics,development of economy,security of defense and culture.As an important branch of cryptography to ensure information security,digital signatures play an increasingly important role.Attribute-based signatures(ABS)are a special type of digital signatures that were proposed in 2007.They can be used to finely divide identity characteristics,so that signatures schemes are not only one-to-one for signers and verifiers,but also can be one-to-many or many-to-many.ABS is widely used in access control,anonymous authentication,trust negotiation,etc.,and therefore,has become a hotspot to research.On the other hand,with the rapid development of quantum computing,gradually transforming the currently used cryptographic schemes into the type of resisting quantum attacks will become an inevitable trend.Meanwhile,signature schemes whose security based on the difficult problems from lattices has become another hotspot of public key cryptography,due to its more solid security foundation,higher computing efficiency,and ability to resist quantum attacks.In view of this,this paper conducts research on ABS in lattices,and proposes an ABS involving multi-attribute authorities whose security rely on SIS problem on lattices.The results are as follows:1.We introduce the concept of multi-attribute authorities(MA)into lattice,and with the access tree structure in the scheme proposed by Goyal et al.,construct access structure trees for each attribute authority,and a tree according to the access structure,whose leaf nodes are the values of attribute authorities' access structure trees.We can calculate the matrix corresponding to the signer's private key according to the final result of,thereby making access structures on lattices support access strategies of AND gate,OR gate and threshold,improving the efficiency of attribute comparison when there are many attributes and attribute authority involved in the access structure.2.Based on the proposed method of generating a signer's private key and the introduction of multi-attribute authorities,we design an ABS involving multi-attribute authorities on lattice,combining with the linear homomorphic technique on lattices.Its signatures' length is irrelevant to the number of attributes,and only linearly proportional to the number of attribute authorities involved in the access structure;We also prove its correctness and unforgeability,conditional anonymity and resistance to collusion attacks under the random oracle.3.On the basis of the ABS with multi-attribute authorities proposed by us,we propose another ABS with multi-attribute authorities on the lattice,using Lyubashevsky's rejection sampling technique.And we also analyze the shceme's correctness and its unforgeability,conditional anonymity and resistance to collusion attacks under the random oracle.Compared with the previous scheme,this scheme has a better performance in terms of public parameters and signature's length.