Key-Homomorphic Encryption Clause Samples

Key-Homomorphic Encryption. ‌ The examples of TTKEM and pairwise channels show that an update should affect the whole state of a group. Indeed, this is what our protocol achieves with HIBE. However, one may ask if the same cannot be achieved without such inefficient primitives. This question was raised in the two-party setting by [21, 30], resulting in efficient, but sub-optimal constructions. We argue that extending their ideas to the group setting would also yield sub-optimal constructions, at least if we allow exposing commit randomness.