Research On Identity-based Cryptography From Lattice

With the high-speed development of the computer，once we have quantumcomputers dealing with many quantum bits, existing cryptography schemes may be notsecure, so we have to design new cryptography schemes which are secure againstquantum attacks, The research on cryptography from lattice is one of the very importantresearch topics. A lattice is a collection of all integer linear combinations of linearlyindependent vectors and a discrete additive subgroup of vector space. Cryptographyschemes from lattice are not only more computational efficient but aslo securer. Studyon cryptography schemes which are based identity from lattice is the main content ofthis paper. In this paper, we give two schemes:1. We construct an identity-based encryption from lattice (i.e. L-IBE). Thisconstruction process identity as one chunk rather than bit-by-bit, and it can be regardedas a combination of two IBE schemes by the strongly unforgeable one-time signature.We show our scheme is secure against non-adaptive chosen-identity and chosen-ciphertext attack (IND-sID-CCA) based on LWE problem in the standard model. By thetechnique, i.e., imposing additional restrictions on the identities, presented by D. Bonehand X. Boyen, we also get the result that our IBE scheme is against adaptive chosen-identity and chosen-ciphertext attack (IND-ID-CCA) secure in the random oracle modeland in the standard model.2. We construct an identity-based key encapsulation mechanism form lattice (i.e.L-IBKEM). This scheme’s idea is similar to the previous one, and it is an IND-ID-CCAsecure scheme based on LWE problem in the standard model. Our L-IBKEMcombining with symmetric encryption can realize encrypt and decrypt more efficiently,and improve the performance of cryptosystem consequently.