Embedding CGKA Ciphertexts in CKE Ciphertexts Sample Clauses

Embedding CGKA Ciphertexts in CKE Ciphertexts. With our proof that CGKA implies CKE, we directly lift the communication-cost lower bound for CKE from Section 4 to certain bad sequences in a CGKA execution. That means, our proof implies that such bad sequences in a CGKA execution lead to a linear communication overhead in the number of affected users. For this, we build a CKE construction that embeds specific CGKA ciphertexts in its CKE ciphertexts. Thus, a CGKA scheme that achieves sub-linear communication costs in the number of affected group members for these embedded ciphertexts results in a CKE with compact ciphertexts, which contradicts our lower bound from Section 4.