Brief announcement: secret handshakes from CA-oblivious encryption

Secret handshake protocols were recently introduced by Balfanz, et al. [1] 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 in the handshake protocol, whether his counterparty is a member of the group. On the other hand, any two parties who are members of the same group will recognize each other as members. Thus, secret handshakes can be used in any scenario where group members need to identify each other without revealing their group affiliations to outsiders. The secret handshake protocol of [1] relies on a Bilinear Diffie-Hellman assumption on certain elliptic curves. We show how to build secret handshake protocols secure under more standard cryptographic assumptions, like the RSA or the Diffie Hellman (DH) assumption, using a novel tool of CA-oblivious public key encryption, i.e. an encryption scheme where neither the public key nor the ciphertext reveal any information about the Certification Authority which certified the public key.