Abstract
Functional encryption (FE) is a vast new paradigm for encryption scheme which allows tremendous flexibility in accessing encrypted data. In a FE scheme, a user can learn specific function of encrypted messages by restricted functional key and reveals nothing else about the messages. Besides the standard notion of data privacy in FE, it should protect the privacy of the function itself which is also crucial for practical applications. In this paper, we construct a secret key FE scheme for the inner product functionality using asymmetric bilinear pairing groups of prime order. Compared with the existing similar schemes, our construction reduces both necessary storage and computational complexity by a factor of 2 or more. It achieves simulation-based security, security strength which is higher than that of indistinguishability-based security, against adversaries who get hold of an unbounded number of ciphertext queries and adaptive secret key queries under the External Decisional Linear (XDLIN) assumption in the standard model. In addition, we implement the secret key inner product scheme and compare the performance with the similar schemes.
Highlights
Traditional public-key encryption provides all-or-nothing access to data: you can either recover the entire plaintext or reveal nothing from the ciphertext
Between two hybrid experiments, a hidden dimension can be used for reducing a difference of one coefficient in a secret key or a cipertext to a XDLIN instance
We introduce the definition of simulation-based secure secret key inner product encryption (IPE) (SSSK-IPE)
Summary
Traditional public-key encryption provides all-or-nothing access to data: you can either recover the entire plaintext or reveal nothing from the ciphertext. There are two notions of security for a FE scheme, i.e., indistinguishability-based security and simulation-based security The former one requires that an adversary cannot distinguish between ciphertexts of any two messages x0, x1 with access to a secret key skf for a function f such that f(x0) = f(x1). Note that an attacker who holds a secret key skf can always generate, on its own, the ciphertext for xi for message xi of her choice and use skf to learn f(xi) This can reveal nontrivial information about the function f. For the first time Zhao et al [19] presented a simulation-based secure secret key IPE scheme under the SXDH assumption in the standard model. Our scheme is simulation-based secure against adversaries who hold in an unbounded number of ciphertext queries and adaptive key queries. Between two hybrid experiments, a hidden dimension can be used for reducing a difference of one coefficient in a secret key or a cipertext to a XDLIN instance
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