In an attribute-based signature (ABS), users sign signatures based on some predicate of attributes, using keys issued by a central authority. A signature reveals nothing about the attributes of the signer beyond the fact that they satisfy the signing predicate. This paper presents an ABS scheme for the case of threshold predicates from lattices. This scheme is existentially unforgeable against selective predicate and static chosen message attacks in the standard model, with respect to the hardness of the small integer solution problem. To the best of our knowledge, this work constitutes the first ABS scheme based on lattices, which is conjectured to thwart the quantum threat. Copyright © 2014 John Wiley & Sons, Ltd.