CCAsecure publicly verifiable public key encryption scheme without pairings. (2015) - Liu, Zhen; Yang, Xiaoyuan; Pan, Feng; Wei, Yuechuan
Publicly verifiable encryption scheme is a very powerful tool to construct many other interesting cryptographic schemes or protocols, and the existing publicly verifiable encryption schemes are based on special characters of bilinear pairings. But the inefficient computing restricts its application badly. So it is quite attractive and significantly worthwhile to construct cryptographic algorithms without pairings. Hofheinz and Kiltz's (2009b) scheme is a ChosenCiphertext Attacks (CCA)secure public key encryption scheme under factoring assumption without pairings, but not a publicly verifiable construction. We improved Hofheinz and Kiltz's (2009b) scheme and realised publicly verifiable construct with CCA security by using the gap property that the decisional DiffieHellman problem is easy but the computational DiffieHellman problem is difficult as factoring over the group of signed quadratic residues. Furthermore, we improved the efficiency by instantiating this scheme over a semismooth subgroup. It can be used to construct threshold schemes without pairings.