A Fully Secure KP-ABE Scheme on Prime-Order Bilinear Groups through Selective Techniques

Key-policy attribute-based encryption (KP-ABE) is the cryptographic primitive which enables fine grained access control while still providing end-to-end encryption. Although traditional encryption schemes can provide end-to-end encryption, users have to either share the same decryption keys or the data have to be stored in multiple instances which are encrypted with different keys. Both of these options are undesirable. However, KP-ABE can provide less key overhead compared to the traditional encryption schemes. While there are a lot of KP-ABE schemes, none of them simultaneously supports multiuse of attributes, adaptive security, monotone span programs, and static security assumption. Hence, we propose a fully secure KP-ABE scheme for monotone span programs in prime-order group. This scheme uses selective security proof techniques to obtain the requisite ingredients for full security proof. This strengthens the correlation between selective and full security models and enables the transition of the best qualities in selective security models to fully secure systems. The security proof is based on decisional linear assumption and three-party Diffie–Hellman assumption.

A CP-ABE Scheme Supporting Arithmetic Span Programs

Attribute-based encryption achieves fine-grained access control, especially in a cloud computing environment. In a ciphertext-policy attribute-based encryption (CP-ABE) scheme, the ciphertexts are associated with the access policies, while the secret keys are determined by the attributes. In recent years, people have tried to find more effective access structures to improve the efficiency of encryption systems. This paper presents a ciphertext-policy attribute-based encryption scheme that supports arithmetic span programs. On the composite-order bilinear group, the security of the scheme is proven by experimental sequence based on the combination of composite-order bilinear entropy expansion lemma and subgroup decision (SD) assumption. And, it is an adaptively secure scheme with constant-size public parameters.

Span program for non-binary functions

Span programs characterize the quantum query complexity of binary functions f:\{0,\ldots,\ell\}^n \to \{0,1\} up to a constant factor. In this paper we generalize the notion of span programs for functions with non-binary input/output alphabets f: [\ell]^n \to [m]. We show that non-binary span program characterizes the quantum query complexity of any such function up to a constant factor. We argue that this non-binary span program is indeed the generalization of its binary counterpart. We also generalize the notion of span programs for a special class of relations. Learning graphs provide another tool for designing quantum query algorithms for binary functions. In this paper, we also generalize this tool for non-binary functions, and as an application of our non-binary span program show that any non-binary learning graph gives an upper bound on the quantum query complexity.