Fuzzy Identity Based Encryption with a flexible threshold value

The issue of data and information security on the internet and social network has become more serious and pervasive in recent years. Cryptography is used to solve security problems. However, message encryption cannot merely meet the intended goals because access control over the encrypted messages is required in some applications. To achieve these requirements, attribute-based encryption (ABE) is used. This type of encryption provides both security and access structure for the network users simultaneously. Fuzzy Identity-Based Encryption (FIBE) is a special mode of ABE that provides a threshold access structure for the users. This threshold value is set by the authority for users, which is always fixed and cannot be changed. So, the sender (encryptor) will not play a role in determining the threshold value. The mentioned issue exists also in Key Policy Attribute Based Encryption (KP-ABE) schemes. In this paper, we present a FIBE scheme in addition to the authority, the sender also plays a role in determining the threshold value. Thus, the policy will be more flexible than previous FIBE schemes in that the threshold value is selected only by the authority. We can call the proposed scheme a dual-policy ABE. The proposed technique for flexibility of threshold value can be applied in most of the existing KP-ABE schemes. We use the (indistinguishable) selective security model for security proof. The hardness assumption that we use is the modified bilinear decision Diffie-Hellman problem