Structure Preserving CCA Secure Encryption and Its Application to Oblivious Third Parties
In this paper, the authors present the first public key encryption scheme that is structure preserving, i.e., the encryption scheme uses only algebraic operations. In particular, it does not use hash-functions or interpret group elements as bit-strings. This makes the scheme a perfect building block for cryptographic protocols where parties for instance want to prove, to each other, properties about ciphertexts or jointly compute ciphertexts. The scheme is also very efficient and is secure against adaptive chosen ciphertext attacks. They also provide a few example protocols for the scheme. For instance, a joint computation of a ciphertext, generated from two secret plaintexts from each party respectively, where in the end, only one of the parties learns the ciphertext.