New Construction of PVPKE Scheme Based on Signed Quadratic Residues

In SCN12, Nieto et al. [7] discussed an interesting property of public key encryption with chosen cipher text security, that is, cipher texts with publicly verifiability. Independently, we introduced a new cryptographic primitive: CCA Secure Publicly verifiable Public Key Encryption Without Pairings In the Standard Model (PVPKE) and discussed its application in proxy re-encryption (PRE) and threshold public key encryption (TPKE)[10]. In Crypto\´09, Hofheiz and Kiltz [6] introduced the group of signed quadratic residues and discussed its application, the most interesting feature of this group is its "gap" property, while the computational problem is as hard as factoring, and the corresponding decisional problem is easy. In this paper, we show that, if basing some of Nieto et al\´s schemes on signed quadratic residues, the resulting schemes can meet the requirements of PVPKE. Based on this observation, we give new constructions of PVPKE scheme based on signed quadratic residues and analysis its security.