The Identity - Based Cryptosystem Scheme

With the development of the computer science and information technology, quantum computing has been become more and more important. Under the quan-tum attack, factorizations and discrete logarithm problems are not hard, thus the cryptosystems based on these number theory problems are no longer secured. So looking for new public key cryptosystems against quantum attack has been become a burning issue.Public key cryptosystem based on lattice theory provides a new direction for the development of cryptography. Compared with bilinear pairing operations or exponent calculation, the operations in lattices are mostly linear operations which are simple and efficient. The hard problems in lattices, such as Shortest Vector Problem(SVP), Closest Vector Problem(CVP), Learning with Error(LWE) prob-lem, Small Integer Solution(SIS) problem, Inhomogeneous Small Integer Solu-tion(ISIS) problem, etc., are believed still secure under quantum computing. And the cryptosystems based on lattice theory have now become the hottest cryptosys-tems against quantum attack.The cryptosystems based on lattices have the advantage of the cryptosystem based on identity by putting them together. In the identity-based cryptosystem, the public keys of users can be extracted from their identity information, such as Email address or telephone numbers, while the corresponding private keys are generated by key generate center(KGC) which is a trusted third party. Identity-based cryp-tosystem reduces the dependent on public key certificates and the complexity of identification systems, and then increases the efficiency.Encryption and signature are two dominant parts of cryptography, and the cryptosystems based on lattices are no exception. This article studies the identity-based encryption and signature schemes from lattices and makes the following achievements:1. A forward-secure identity-based broadcast encryption scheme from lattice was constructed by incorporating the forward-security mechanism into broadcast encryption scheme. The scheme was proved semantic secure in random oracle model assuming the LWE problem is hard. Then the construction was extend to encrypt on t bits message simultaneously.2. An identity-based ring signature scheme from lattice was constructed by using the lattice basis delegation technique, and the signature conforms to the s-tandard form of classical ring signature schemes, namely, it forms a "head to tail" ring. It was proved anonymous and unforgeable. Then a more efficient ring sig-nature was constructed by modifying some parameters from the first one, and the sizes of ring public keys and signature are significantly reduced.3. An identity-based signature scheme from lattice was proposed and its se-curity is based on Small Integer Solution(SIS) assumption. The signature scheme conforms the "Hash and sign" form, establishes the system by using the trapdoor generation algorithm, generates the public key by using the identity information bit by bit, and computes the private key and signature by using the lattice basis delegation algorithm.4. Another identity-based signature scheme from lattice was proposed and its security is based on Inhomogeneous Small Integer Solution(ISIS) assumption. Compared with the previous signature scheme, this one is more practical because the method of generating the public key in this scheme is very simple. The public key is just a concatenation of 2ιmatrices without any computing.