The Protocol P Sample Clauses

The Protocol P. Pas‌ To avoid cross-group attacks, we modify TTKEM so that a commit evolves all key pairs in the LT. For this, we first replace the standard encryption scheme by HIBE. That is, each node, instead of labels epk and esk, has two public mpk and i˙d, as well as one private label hsk. In the order listed, these labels contain a (master) HIBE public key, and a HIBE identity vector and the corresponding HIBE secret key for identity i˙d. Encryption for a node is done with mpk and i˙d. Whenever a new key pair is created for an internal node (e.g. during rekeying), the node’s i˙d is initialized to the empty string. For leaf nodes, the first ID in the vector i˙d is set to the ID of the user assigned to that leaf. Second, we can now evolve all keys with every commit: For nodes whose keys does not get replaced with the commit, we simply append the the hash of the commit message H3(c) to the HIBE ID vectors, and update all secret keys on the processor’s direct path (known by Invariant 2) accordingly. Intuitively, this provides forward secrecy for individual HIBE keys in the LT. First, HIBE schemes ensure that secret keys for an ID vector can not be used to derive secrets for prefixes of that ID vector. So, the HIBE key of a node can not be used to derive its keys from previous epochs. Second, this guarantees in the event the group is split into parallel epochs (by delivering different commit messages to different group members) that the keys of a node in one epoch can not be used to derive the keys for that node in any parallel epochs. That is because, more generally, HIBE schemes ensure that secret keys for an ID vector i˙d can not be used to derive keys for any other ID vector i˙dr unless i˙d is a prefix of i˙dr. But as soon as parallel epochs are created, the resulting ID vectors of any given node in both LTs have different commit messages in them at the same coordinate ensuring that no such vector is a prefix of another. We prove two statements about the security of our protocol. First, if the hash functions are modeled as non-programmable random oracles, then the protocol realizes the relaxed functionality that restricts the environment not to perform certain corruptions. Second, if we do allow pro- gramming the random oracles, then it achieves full UC security. Formally, we prove the following theorems.
Sample 1
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