Resumen
Authentication has been adopted in many areas, but most of these authentication schemes are built using traditional cryptographic primitives. It is widely believed that such primitives are not resistant to quantum algorithms. To deal with those quantum attacks, lattice-based cryptography was introduced by Ajtai in 1996. To the best of our knowledge, the existing lattice-based authentication schemes are based on a lattice-based public key encryption called NTRU: a ring-based public key cryptosystem, proposed by Hoffstein, Pipher, and Silverman in 1998. However, these schemes only support the case of a single user. In view of the aforementioned issue, we propose the first lattice-based group authentication scheme. The proposed scheme is secure against replay attacks and man-in-the-middle attacks. Moreover, compared with the existing lattice-based authentication schemes, ours provides the most efficient method to agree upon a session key among a group of users after mutual authentication.