Dynamic Threshold Cryptosystem without Group Manager

Abstract

In dynamic networks with flexible memberships, group signatures and distributed signatures are an important problem. Dynamic threshold cryptosystems are best suited to realize distributed signatures in dynamic (e.g. ad-hoc) networks. Without a group manager or a trusted third party even more flexible scenarios can be realized.

Gennaro et al. [6] showed, it is possible to dynamically increase the size of the signer group, without altering the public key. We extend this idea by removing members from the group, also without changing the public key. This is an important feature for dynamic groups, since it is very common, e.g. in ad-hoc networks that members leave a group.

Gennaro et al. used RSA and bi-variate polynomials for their scheme. In contrast, we developed a DL-based scheme that uses ideas from the field of proactive secret sharing (PSS). One advantage of our scheme is the possibility to use elliptic curve cryptography and thereby decrease the communication and computation complexity through a smaller security parameter.

Our proposal is an efficient threshold cryptosystem that is able to adapt the group size in both directions. Since it is not possible to realize a non-interactive scheme with the ability to remove members (while the public key stays unchanged), we realized an interactive scheme whose communication efficiency is highly optimized to compete with non-interactive schemes. Our contribution holds against passive and active information theoretic adversaries.