| With the arrival of the information age,cloud computing has emerged with the advantages of practicality,simple operation and low cost.In cloud services,tradi-tional cryptographic schemes cannot safely convert ciphertext.Therefore,it is of great significance to ensure the safe and effective storage and sharing of cloud data.However,we can use proxy re-encryption(PRE)technology to safely and efffec-tively share the ciphertext stored in the cloud.Identity-based proxy re-encryption(IB-PR E)is a significant extension of PRE.It is a public key crptography that can safely convert ciphertext and does not require a large number of public key cer-tificates for management.In an identity-based proxy re-encryption scheme,there are mainly three types of participants:delegator,proxy and delegatee.It allows a proxy to convert the ciphertext based on delegator’s identity into another cipher-text of the same message for delegatee.During the conversion process,the proxy cannot obtain any plaintext information.IB-PRE technology has good practica-bility’ and it is widely used in many areas of cloud computing,such as distributed file systems,access control and encrypted mail forwarding systems.Therefore,an efficient,safe and powerful IB-PRE schemes has important application value.In recent years,quantum technology has also achieved unprecedented develop-ment.Most cryptosystems are designed based on the difficult problems of tradi-tional number theory and cannot resist the attacks of quantum computers.There-fore,it is particularly important to design a quantum crptography that is resistant to data security.The lattice-based cryptography is an anti-quantum crptography with a complete theoretical system.It is mainly designed based on the following three types of difficult problems:SIS problem,LWE problem and NTRU problem.Most of the identity-based cryptosystems over NTRU lattices are constructed on the cyclotomic fields K=Q(ζl),where l＝2n.In this field,the number theoretic transforms algorithm(NTT)is used to make the multiplication rate on the field more effective.As we all know,cryptography schemes based on NTRU lattices have the following advantages:short keys,fast speed,simple operations and small storage space.So far,most of lattice-based IB-PRE schemes are designed based on LWE assumption.IB-PRE schemes designed over NTRU lattices have not been found.In this paper,the main contribution is to propose a provable secure IB-PRE scheme over NTRU lattices.We analyze the correctness,safety and multi-functional properties of the IB-PRE scheme.Meanwhile,we provide the adaptive IND-ID-CPA security proof in the random oracle based on Ring-LWE assumption.At the same time,the security of the IB-PRE scheme is based on the approximate shortest vector problem(SVPγ),and its approximation factor is O((?)/α).In the scheme,the multi-functional properties mainly include:anonymity,unidirec-tionality,backward collusion safeness,non-interaction and multi-hop.In addition,compared with the existing IB-PRE scheme,the IB-PRE schemes over NTRU lat-tices requires less key storage space.The key and ciphertext sizes of our IB-PRE scheme are short,only one or two ring elements,and our scheme could encrypt n bits in each encryption process. |
