Abstract: A set of users who may authenticate is predefined and is associated, each, with a reference secret share. A first subset of users who has, each, to authenticate is predefined. The device defines a second subset of the users who has, each, to authenticate while further satisfying, each, to be physically proximate to the device and an authentication condition(s). The second user subset is comprised within the first user subset comprised within the user set. The device verifies whether each user of the second user subset satisfies to be physically proximate to the device and the authentication condition(s), if yes, requests, to each user device, the secret share and receives, from each user device relating to at least the first user subset, the secret share. The device reconstructs a secret with each received secret share, verifies whether the reconstructed matches the reference and, if yes, authenticates the user set.

Abstract: A set of users who may authenticate is predefined and is associated, each, with a reference secret share. A first subset of users who has, each, to authenticate is predefined. The device defines a second subset of the users who has, each, to authenticate while further satisfying, each, to be physically proximate to the device and an authentication condition(s). The second user subset is comprised within the first user subset comprised within the user set. The device verifies whether each user of the second user subset satisfies to be physically proximate to the device and the authentication condition(s), if yes, requests, to each user device, the secret share and receives, from each user device relating to at least the first user subset, the secret share. The device reconstructs a secret with each received secret share, verifies whether the reconstructed matches the reference and, if yes, authenticates the user set.