Improved Towards Tightly Lattice-Based Short Signature And IBE Algorithm

With the current rapid development of quantum computing technology,traditional number-theory-based cryptographic constructions can be cracked by quantum algorithms,and this cryptographic structure is no longer absolutely safe.However,the cryptographic algorithm based on the lattice structure has many advantages.So far,there are no polynomial quantum algorithms to solve some lattice problems.The cryptographic system based on the lattice can provide strong anti-quantum characteristic and have important practical value.Although lattice-based cryptosystems have great potential in terms of design and security,there are still many aspects that need to be improved.For example,among the existing towards tightly secure lattice-based short signature and identity-based encryption algorithms,these schemes are either based on stronger assumptions,or require longer common parameters,or can only achieve weaker security guarantees.This requires further research and improvement by cryptographers so that tightly secure lattice-based cryptosystems can be widely used.The research in this thesis focuses on constructing two pseudorandom functions by using their pseudo-randomness based on verifiable random functions of division functions for improving towards tightly secure lattice-based short signature and identity encryption schemes.It is achieved to reduce the length of the public key parameters in the process of signature generation and identity-based encryption,to make the size of the ciphertext and private key optimal under the same assumptions,and to prove the almost tight security of the algorithm.The main results are as follows:(1)Verifiable random functions are constructed using the division function,and we obtain two improved pseudorandom functions by randomly mapping.(2)We improve the towards tightly secure short signature algorithm using the improved pseudorandom functions,and prove the security of the signature algorithm by reducing it to the lattice SIS hard problem.(3)We optimize the towards tightly secure identity-based encryption scheme using the improved pseudorandom function,and prove the security of the identity-based encryption scheme by reducing it to the lattice LWE problem,from which its security can be obtained.The improved towards tightly secure lattice-based short signature scheme and identity-based encryption scheme are well optimized for theoretical study and get a more significant reduction in computational effort compared to the original scheme.The improved towards tightly secure short signature algorithm and identity-based encryption scheme reduce the public key from linear order(is the security parameter)to logarithmic order.The algorithm achieves towards tight security.This reduces the parameters of the algorithm and improves the efficiency of the algorithm.Therefore,the improved lattice based short signature and identity-based encryption scheme are proposed in this theis.It solves the problem of large public key length in almost tight security signature and identity-based encryption algorithm based on lattice under the existing standard model.It can better meet the needs of practical applications in the field of network information security.