Group Key Clause Samples

Group Key. Secrecy Before considering group key secrecy, we briefly examine key fresh- ness. Every group key is fresh, since at least one member in the group generates a new random key share for every membership change6. The probability that new group key is the same as any old group key is negligible due to bijectiveness of (f ◦ g) function. { } 6 Recall that insider attacks are not our concern. This excludes the case when an insider intentionally generates non-random numbers. We note that the root (group) key is never used directly for the purposes of encryption, au- thentication or integrity. Instead, special-purpose sub-keys are derived from the this key, e.g., by applying a cryptographically secure hash function, i.e. H(group key) is used for such applications. As discussed in Section 2.4, decisional group key secrecy is more meaningful if sub-keys are derived from a group key. Decisional group key secrecy of STR protocol is related to imbalanced tree decision ▇▇▇▇▇▇-▇▇▇▇▇▇▇ assumption mentioned in Section A.2. This assumption ensures that there is no information leakage other than public bkey information. We can also derive sub-keys based on the ▇▇▇▇▇’▇ hedge technique [25] and compute them as: H(group key) ⊕ H(group key) where H is a random oracle. It follows that, in addition to the security in the standard model based on the Imbalanced Tree Decision ▇▇▇▇▇▇-▇▇▇▇▇▇▇ assumption, the derived key is also secure in the random oracle model [6] based on the Imbalanced Tree Computational ▇▇▇▇▇▇-▇▇▇▇▇▇▇ assumption.