We prove a computational soundness theorem for symmetric-key encryption protocols that can be used to analyze security against adaptively corrupting adversaries (that is, adversaries who corrupt protocol participants during protocol execution). Our soundness theorem shows that if the encryption scheme used in the protocol is semantically secure, and encryption cycles are absent, then security against adaptive corruptions is achievable via a reduction factor of O(n · (2n)l ), with n and l being (respectively) the size and depth of the key graph generated during any protocol execution. Since, in most protocols of practical interest, the depth of key graphs (measured as the longest chain of ciphertexts of the form Ek1 (k2), Ek2 (k3), Ek3 (k4), · · · ) is much smaller than their size (the total number of keys), this gives us a powerful tool to argue about the adaptive security of such protocols, without resorting to non-standard techniques (like non-committing encryption). We apply ou...