Research On Lattice-Based Digital Signature Schemes

Digital signature scheme is an essential component of the public key cryptography, which could be used to verify the identity of an entity as well as the integrity of data. With the popularity of network communications and the emergence of new applications, more and more security isssues need to be solved, and thus digital signature schemes are playing an increasingly important role in nowadays. Digiatl signature scheme based on intractable lattice problems is a special kind of digital signature scheme. Compeard with other digital signature schemes, it has more solid security foundation and enjoies higher computational efficiency. Additionally, lattice-based signature schemes can also withstand quantum computers’ attacks and are becoming a hotspot of the public key cryptography. However, there are only few lattice-based signature shemes, and most of them require great storage and communication overheads. That largely limits the application and popularity of lattice-based signature schemes.For the purpose of giving more types of attice-based signature shemes and improving the efficiency of them, in this paper we made the following research achievements:1. We have designed the first lattice-based message recovery signature scheme and proved its security in the random oracle model. Compaerd with other lattice-based signature schemes, this scheme is more efficient.2. We proposed a stronger security model for ring signatures and presented a lattice-based ring signature scheme provably secure in the model. Moreover, our lattice-based ring signature scheme is more efficient than others.3. A new identity-based signature scheme over lattices is proposed with a different approach from the conventional one. The new scheme is proven to be secure in the random oracle model and much more efficient than previous ones. Futhermore, we adapted the identity-based signature scheme and achieved the first identity-based message recovery signature scheme from lattices. We also showed the identity-based message recovery signature scheme is secure in the random oracle model and more efficient than the identity-based signature scheme.4. As the signing key size and signature length of the previous hierarchical identity-based signature schemes on lattices will increase rapidely when the depth of identity increases, it restricted those hierarchical identity-based signature schemes to be used by a small number of users. To address this problem, we presented two new hierarchical identity-based signature schemes from lattices. The two schemes are provably secure in the standard model and in the random oracle model respectively, and their signing key size and signature length are both constant. Therefore, they would be more suitable for daily applications.5. We extend the lattice-based signature schemes from traditional public key cryptography and identity-based public key cryptography to certificateless and certificate-based public key cryptography, and proposed the first certificateless signature scheme as well as the first certificate-based signature scheme from lattices. Since certificateless signature scheme and certificate-based signature scheme are more secure and more efficient than other ones, it means the lattice-based signature scheme makes another step forward to the direction of practical application.