An efficient fully dynamic group signature with message dependent opening from lattice

Cybersecurity

Table 1 Comparison of lattice-based group signature schemes in (Libert et al. 2016) and (Ling et al. 2017), in terms of efficiency and functionality

Schemes	Security level	Signature size	Group PK size	Signer’s SK size	Trapdoor?	Model
(Libert et al. 2016)	\(\left (\frac {2}{3}\right)^{\omega (\lambda)}\)	\(\tilde {O}(\lambda \cdot l)\)	\(\tilde {O}(\lambda ^{2}\cdot l)\)	\(\tilde {O}(\lambda)\)	yes	MDO
(Ling et al. 2017)	\(\left (\frac {2}{3}\right)^{\omega (\lambda)}\)	\(\tilde {O}(\lambda \cdot l)\)	\(\tilde {O}(\lambda ^{2}+\lambda \cdot l)\)	\(\tilde {O}(\lambda)+l\)	free	fully dynamic
Ours	2^−λ	O(lλ²)	O((λlogλ)²)	\(\tilde {O}(\lambda)+l\)	free	fully dynamic/MDO

The scheme in (Libert et al. 2016) is static and that in (Ling et al. 2017) is fully dynamic, the similarity is that both of them use the Stern-like protocol with a soundness error \(\frac {2}{3}\) as the underlying protocol. The scheme in this paper is fully dynamic and use a more efficient zero knowledge protocol with a soundness error \(\frac {1}{\max {(n,p)}+1}\) as the underlying protocol. Obviously, compared with the previous two schemes, our scheme has lower computational complexity when realize the same security level