<p><b>Abstract</b>—The cryptographic key assignment problem is to assign cryptographic keys to a set of partially ordered classes so that the cryptographic key of a higher class can be used to derive the cryptographic key of a lower class. In this paper, we propose a <it>time-bound</it> cryptographic key assignment scheme in which the cryptographic keys of a class are different for each time period, that is, the cryptographic key of class <tmath>$C_i$</tmath> at time <tmath>$t$</tmath> is <tmath>$K_{i,t}$</tmath>. Key derivation is constrained not only by the class relation, but also the time period. In our scheme, each user holds some secret parameters whose number is independent of the number of the classes in the hierarchy and the total time periods. We present two novel applications of our scheme. One is to broadcast data to authorized users in a multilevel-security way and the other is to construct a flexible cryptographic key backup system.</p>