CCA secure certificateless encryption schemes based on RSA

Certificateless cryptography, introduced by Al-Riyami and Paterson eliminates the key escrow problem inherent in identity based cryptosystem. In this paper, we present two novel and completely different RSA based adaptive chosen ciphertext secure (CCA2) certificateless encryption schemes. For the first scheme, the security against Type-I adversary is reduced to RSA problem, while the security against Type-II adversary is reduced to the CCDH problem. For teh second scheme both Type-I and Type-II security is related to the RSA problem. The new schemes are efficient when compared to other existing certificatless encryption schemes that are based on the costly bilinear pairing operation and are quite comparable with the certificateless encryption scheme based on multiplicative groups (without bilinear pairing) by Sun et al. (Sun et al., 2007) and the RSA based CPA secure certificateless encryption scheme by Lai et al. (Lai et al., 2009). We consider a slightly stronger security model than the ones considered in (Lai et al., 2009) and (Sun et al., 2007) to prove the security of our schemes.