Sensor　networks　are　widely　used　in　a　variety　of　commercial　and　military　applications　due　to　their　self-organization　characteristics　and　distributed　nature.　As　a　fundamental　requirement　for　providing　security　functionality　in　sensor　networks,　key　predistribution　plays　a　central　role　in　authentication　and　encryption.　In　this　paper,　we　describe　the　hexagon-based　key　predistribution　scheme　and　show　how　it　can　improve　the　performance　of　key　predistribution　in　sensor　network　through　the　use　of　bivariate　polynomials　in　a　hexagonal　coordinate　system　based　on　the　deployment　information　about　the　expected　locations　of　the　sensor　nodes.　More　specifically,　we　show　that　the　hexagon-based　key　scheme　can　improve　the　probability　of　establishing　pairwise　keys　between　sensor　nodes　by　more　than　40%　over　previous　schemes.　©　Springer-Verlag　Berlin　Heidelberg　2006.