A Study Of Hierarchical Identity Based Encryption On Lattice

Lattice-based cryptographic scheme is mainly base on the difficult issue of lattice, not only can resist quantum-computing attacks, but also has the advantage of public key cryptographic scheme. The difficulty of General public key cryptography is different under the different problems. However, the most difficult problem of Lattice-based cryptographic scheme is the equivalent of safety between samples and common samples. On the evidence that security problem, we can choose any example. As a result, the Lattice-based cryptographic schemes emerge in endlessly, the Lattice-based signature scheme and Lattice-based cryptographic scheme are especially rich.Identity-based encryption scheme has an important role in cloud computing and e-commerce areas, But with the increasing number of users’ identities, the certificate management problem increasingly prominent. The hierarchical identity-based encryption in lattice, can be better able to handle certificate management problems of excessive number of users, reduces the cost, and has higher computation efficiency.The thesis introduces the basic methods of public key cryptography based on lattice, and discussed the issues around the identity-based cryptosystem. Relevant theories about lattice were reviewed, mainly introduced the definition of lattice and its difficult problems, bonsai-tree principle, the original like sampling function, lattice base assignment algorithm, lattice generation algorithm. The algorithms mainly include the DTrap Gen trapdoor generation algorithm presented by Micciancio and Peikert,the algorithms also include two different Sample Left and Sample Right trapdoor generation algorithms presented by Agrawal and Boneh. At last, the thesis studies HIBE based on lattice, and propose a new scheme based on this issue.The new scheme use MP12 trapdoor generation algorithm and preimage sampling algorithm, based on the bonsai-tree principle, builds the hierarchical identity-based encryption scheme on lattice under the standard model. The new scheme is more simple, rapid and effective, in addition it makes parallel computing more easy to perform. Based on the learning difficult of lattice error, the scheme gives a security proof. The new scheme also use Waters’ method convert the first selective-ID secure lattice HIBEto adaptive-ID secure HIBE.The thesis also uses the trapdoor delegation technology presented by Micciancio and Peikert, compared with previous trapdoor delegate algorithm, delegating the new trapdoor in order to optimize and improve the fixed dimension and short secret HIBE scheme presented by Agrawal and Boneh in 2010.