Paper 2018/641

Membership Privacy for Fully Dynamic Group Signatures

Michael Backes, Lucjan Hanzlik, and Jonas Schneider

Abstract

Group signatures present a trade-off between the traditional goals of digital signatures and the signer's desire for privacy, allowing for the creation of unforgeable signatures in the name of a group which reveal nothing about the actual signer's identity beyond their group membership. Considering the desired properties formally opens up a possibility space of different security goals under various assumptions on trust placed in the designated entities of any scheme. Many models differ in their consideration of the variability of group membership as well, yet a formal treatment of the privacy of group membership status is lacking in all models, thus far. We address this issue, starting from the vantage point of the comprehensive model due to Bootle et al. (ACNS'16), who prove that any scheme secure in their model is also secure in the previous models. Their model allows for fully dynamic management of group membership by segmenting the scheme's lifetime into epochs during which group membership is static but between which users may join or leave the group. We extend the model of Bootle et al. by introducing formal notions of membership privacy. We then propose an efficient generic construction for a fully dynamic group signature scheme with membership privacy that is based on signatures with flexible public key (SFPK) and signatures on equivalence classes (SPSEQ). We instantiate the construction using a SFPK scheme based on the bilinear decisional Diffie-Hellman assumption and SPSEQ scheme by Fuchsbauer and Gay (PKC'18). The resulting scheme provides shorter signatures than existing schemes from standard assumption, while at the same time achieving stronger security guarantees.