Yagan, OsmanMakowski, ArmandRandom key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the appearance of triangles, and identify the corresponding critical scaling. This is done by applying the method of first and second moments to the number of triangles in the graph.en-USRandom key graphsUniform intersection graphsExistence of trianglesZero-one lawsCritical scalingsTechnical Report