The　rapid　increase　in　user　base　and　technological　penetration　has　enabled　the　use　of　a　wide　range　of　devices　and　applications.　The　services　are　rendered　to　these　devices　from　single-server　or　highly　distributed　server　environments,　irrespective　of　their　location.　As　the　information　exchanged　between　servers　and　clients　is　private,　numerous　forms　of　attacks　can　be　launched　to　compromise　it.　To　ensure　the　security,　privacy,　and　availability　of　the　services,　different　authentication　schemes　have　been　proposed　for　both　single-server　and　multi-server　environments.　The　primary　performance　objective　of　such　schemes　is　to　prevent　most　(if　not　all)　attacks,　with　minimal　computational　costs　at　the　server　and　user　ends.　To　address　this　challenge,　this　paper　presents　a　secure　user　authentication　scheme　with　anonymity　(SUAA)　for　single-server　and　multi-server　environments.　It　works　on　3-factor　authentication,　involving　passwords,　smart　cards,　and　biometric　data.　We　use　symmetric　and　asymmetric　encryption　for　single-server　and　multi-server　architectures　respectively,　to　reduce　the　computational　costs.　Through　a　comprehensive　security　analysis,　we　show　that　the　proposed　scheme　is　reliable　through　mutual　authentication,　and　is　resilient　to　attacks　addressed　by　state　of　the　art　solutions.　Time　cost　analysis　also　shows　less　time　required　to　complete　the　authentication　process.　©　2018　Elsevier　Inc.