Secret Handshakes from CA-Oblivious Encryption

Secret handshakes were recently introduced [BDS + 03] to allow members of the same group to authenticate each other secretly, in the sense that someone who is not a group member cannot tell, by engaging some party in the handshake protocol, whether that party is a member of this group. On the other hand, any two parties who are members of the same group will recognize each other as members. Thus, a secret handshake protocol can be used in any scenario where group members need to identify each other without revealing their group affiliations to outsiders. The work of [BDS + 03] constructed secret handshakes secure under the Bilinear Diffie-Hellman (BDH) assumption in the Random Oracle Model (ROM). We show how to build secret handshake protocols secure under a more standard cryptographic assumption of Computational Diffie Hellman (CDH), using a novel tool of CA-oblivious public key encryption, which is an encryption scheme s.t. neither the public key nor the ciphertext reveal any information about the Certification Authority (CA) which certified the public key. We construct such CA-oblivious encryption, and hence a handshake scheme, based on CDH (in ROM). The new scheme takes 3 communication rounds like the [BDS + 03] scheme, but it is about twice cheaper computationally.