Group authentication is a method of confirmation that a set of users belong to a group and of distributing a common key among them. Unlike the standard authentication schemes where one central authority authenticates users one by one, group authentication can handle the authentication process at once for all members of the group. The recently presented group authentication algorithms mainly exploit Lagrange's polynomial interpolation along with elliptic curve groups over finite fields. As a fresh approach, this work suggests use of linear spaces for group authentication and key establishment for a group of any size. The approach with linear spaces introduces a reduced computation and communication load to establish a common shared key among the group members. The advantages of using vector spaces make the proposed method applicable to energy and resource constrained devices. In addition to providing lightweight authentication and key agreement, this proposal allows any user in a group to make a non-member to be a member, which is expected to be useful for autonomous systems in the future. The scheme is designed in a way that the sponsors of such members can easily be recognized by anyone in the group. Unlike the other group authentication schemes based on Lagrange's polynomial interpolation, the proposed scheme doesn't provide a tool for adversaries to compromise the whole group secrets by using only a few members' shares as well as it allows to recognize a non-member easily, which prevents service interruption attacks.

翻译：群组认证是一种确认一组用户同属一个群组并在他们之间分发共同密钥的方法。与标准身份验证方案（其中单一中心机构逐个验证用户）不同，群组认证能够一次性处理群组所有成员的认证过程。近期提出的群组认证算法主要利用有限域上的拉格朗日多项式插值与椭圆曲线群。作为全新的方法，本研究建议使用线性空间进行群组认证和任意大小群组的密钥建立。基于线性空间的方法通过降低计算和通信负载，可在群组成员间建立共同的共享密钥。利用向量空间的优势使所提方法适用于能源和资源受限的设备。除了提供轻量级认证和密钥协商外，该方案允许群组中的任意用户将非成员转化为成员，预计将适用于未来的自治系统。该方案的设计使得群组中任何人都能轻易识别此类成员的发起者。与基于拉格朗日多项式插值的其他群组认证方案不同，所提方案既不会为攻击者提供仅用少数成员份额即可危及整个群组秘密的工具，也能轻松识别非成员，从而防止服务中断攻击。