Fully secure anonymous spatial encryption under affine space delegation functionality revisited

Recently, in Information Sciences, Zhang et?al. (2014) claimed that they proposed the first anonymous spatial encryption under affine space delegation functionality with full security, which solves the open problems of full security proposed in Boneh and Hamburg (2008) and anonymity left in Boneh and Hamburg (2008) and Moriyama and Doi (2011). In this paper, we show their construction cannot achieve recipient anonymity as the ciphertext terms leak information about the encryption vector. Hence realizing anonymous spatial encryption with full security is still an open problem. We propose a new fully secure anonymous spatial encryption under an affine space delegation mechanism that addresses the open problem positively. Our construction utilizes composite order bilinear groups where the group order is a product of four primes and achieves the same efficiency as that of the Zhang et?al. (2014) construction. Under some well-established cryptographic assumptions, the proposed construction is proven to be fully semantically secure with anonymity in the standard model within the dual encryption system framework.