Dual System And Spatial Encryption

Identity-Based Encryption, or IBE for short is a very hot field in modern cryptography. It decreases the complexity of public key and the management of the certificates in a public-key encryption system. Spatial Encryption was proposed as an instance of Generalized Indentity Based Encryption (GIBE) framework. It introduces the concept such as space, vector, matrix in linear algebra to support more features. It expands the traditional IBE in some fields. Dual System Encryption was proposed by B.Waters in 2009. In such system, the ciphertext and key was appeared in two forms: normal or semi-functional . The semi-functional part was not used in the real system, it only used for security proof. And the semi-functional part also interacted to mask the blinding factor by an additional element.This paper was based in Boneh, Hamburg [1] and Zhou, Cao[2] Spatial Encryption Scheme which used the feature of Dual System. Then we explore how to improve te security of spatial encryption. And in this paper, we will also review the history of Paring and IBE, The results of this paper include:1) Introduce Composite Order Bilinear Groups, based in Boneh Hamburg scheme. We added the third element of subgroup of this Composite Group, using Spatial Encryption. Reduce the hard problem to Subgroup decision problem fro 3 primes to achieve Adaptive Selective Plantext Attrack secure.2) Map element in group to vector, Construct a new scheme based in the original scheme, using dual system, to achieve the secure. Because of only computing in composite groups but without matrix, the efficiency gets improved.