The emergence of cloud computing enables users to upload data to remote clouds and compute them. This drastically reduces computing and storage costs for users. Considering secure computing for multilevel users in enterprises, the notion of hierarchical identity‐based inner product functional encryption (HIB‐IPFE) is proposed. In this cryptosystem, a sender can encrypt a vector into a ciphertext with a hierarchical identity, while a receiver who possesses a secret key corresponding to the same hierarchical identity and a vector can decrypt the ciphertext and obtain the inner product . However, HIB‐IPFE is not sufficient to capture flexible data sharing and forward security. In this study, we present a notion of hierarchical identity‐based puncturable HIBP‐IPFE. Furthermore, we present a formal definition and security model of HIBP‐IPFE to guarantee data confidentiality and receiver anonymity. Compared with HIB‐IPFE, our proposed scheme enables users to puncture keys on specific tags ensuring that the punctured keys cannot be used to decrypt the ciphertexts associated with those tags. The proposed scheme is provably secure under d ‐DBDHE assumption in the standard model. The experimental results indicate that our scheme is more practical in cloud computing, with superior functionality.
The emergence of cloud computing enables users to upload data to remote clouds and compute them. This drastically reduces computing and storage costs for users. Considering secure computing for multilevel users in enterprises, the notion of hierarchical identity‐based inner product functional encryption (HIB‐IPFE) is proposed. In this cryptosystem, a sender can encrypt a vector into a ciphertext with a hierarchical identity, while a receiver who possesses a secret key corresponding to the same hierarchical identity and a vector can decrypt the ciphertext and obtain the inner product . However, HIB‐IPFE is not sufficient to capture flexible data sharing and forward security. In this study, we present a notion of hierarchical identity‐based puncturable HIBP‐IPFE. Furthermore, we present a formal definition and security model of HIBP‐IPFE to guarantee data confidentiality and receiver anonymity. Compared with HIB‐IPFE, our proposed scheme enables users to puncture keys on specific tags ensuring that the punctured keys cannot be used to decrypt the ciphertexts associated with those tags. The proposed scheme is provably secure under d ‐DBDHE assumption in the standard model. The experimental results indicate that our scheme is more practical in cloud computing, with superior functionality.
Puncturable encryption (PE), introduced by Green and Miers at IEEE S$&$P 2015, allows recipients to update their decryption keys to revoke decryption capability for selected messages without communicating with senders. In general, it allows users to control which ciphertexts their keys may decrypt. The notion of PE has been found very useful in many applications, such as asynchronous messaging systems, group messaging systems, public-key watermarking schemes, secure cloud emails, and many more. In this paper, we introduce a new primitive called hierarchical identity-based puncturable encryption (HIBPE) that enhances the concept of PE by allowing more general key delegation and flexible key puncture. It enhances the capability of the data owner for multi-level encrypted data sharing within a group of users by delegating the decryption keys of the users in higher-levels to generate decryption keys for the users in lower-levels. Moreover, it allows users to puncture (update) their decryption keys on tags so that a decryption key punctured on a tag can no longer decrypt ciphertexts under this tag. In addition, to control access to the users' data, the higher-level users can further puncture the delegated keys (for lower-level users) with some tags such that the part of the owner's data is labeled by the punctured tags will no longer be accessible by the lower-level users. These features offer an efficient and flexible solution for encrypted data sharing as well as data-access control mechanisms in a hierarchical setting. We propose the formal definition and security model for HIBPE schemes and provide a concrete HIBPE scheme based on the hardness of the learning with errors problem in the standard model. Further, we provide a generic construction of forward secure hierarchical identity-based encryption (fs-HIBE) from HIBPE, which enables the first quantum-safe construction of fs-HIBE in the standard model. Moreover, this is the first fs-HIBE construction by exploring the concept of PE. The proposed fs-HIBE provides quantum-safe protection for secret keys from exposure in multi-level encrypted data sharing by evolving the keys with time.
Abstract Functional encryption (FE) is a novel paradigm for encryption scheme which allows tremendous flexibility in accessing encrypted information. In FE, a user can learn specific function of encrypted messages by restricted functional key and reveal nothing else about the messages. Inner product encryption (IPE) is a special type of functional encryption where the decryption algorithm, given a ciphertext related to a vector x and a secret key related to a vector y, computes the inner product x·y. In this paper, we construct an efficient private-key functional encryption (FE) for inner product with simulation-based security, which is much stronger than indistinguishability-based security, under the External Decisional Linear assumption in the standard model. Compared with the existing schemes, our construction is faster in encryption and decryption, and the master secret key, secret keys and ciphertexts are shorter.
Functional encryption provides a general access control over the encrypted data, where only the receiver with attribute that satisfies control policy function of policy parameter (i.e. ) can decrypt its ciphertext. Special cases of functional encryption include (anonymous-) (hierarchical) identity-based encryption, fuzzy identity-based encryption, attribute-based encryption, public key encryption with keyword search, spatial encryption, inner-product encryption, hidden-vector encryption and predicate encryption. In general functional encryption systems, the control policy function can be set flexibly. The main gap among these functional encryption schemes lies in the policy functions that associates with the secret keys. In this work, we first investigate several functional encryption schemes, and then formalize and unify the functionality description of the control policies for these schemes. After giving a general definition and security model, we present the relationship and transformations among functional encryption schemes when the equivalence of these different policy functions is employed.
Inner-product functional encryption (IPFE) is an exciting paradigm for non-interactively computing on encrypted data where a master secret key can be used to derive decryption keys associated with certain inner-product functions in such a way that the decryption operation reveals an inner-product result, and nothing else. Over the decades, all efforts regarding existing IPFE schemes have been dedicated to extending them to multi-input/multi-client scenarios, understanding the security concepts that can be achieved, and identifying a multitude of practical use cases. However, in the event of key compromise, a common issue in real-world applications, the existing IPFE schemes are unable to guarantee the confidentiality of past encryptions. This paper introduces a novel variant of IPFE that supports key updates, called updatable IPFE, potentially opening up a new avenue of research to address the common key exposure problem. In this setting, any sender can initiate the transition to the next period by computing a new public key and a special update. The special update can be processed by the system administrator and the receiver to compute the next-period master secret key and the next-period decryption key, respectively. If done honestly, future (regular) ciphertexts generated with the new public key can be decrypted with the new decryption key, but ciphertexts from the past cannot be decrypted with the new decryption key. To formally illustrate this, we formalize the notion of the indistinguishability-based security under chosen randomness chosen plaintext attacks (IND-CR-CPA). We further propose the first efficient construction of updatable IPFE in the standard model, based on Learning with Errors (LWE) assumption with polynomial modulus-to-noise rate. Finally, we conduct a comprehensive performance evaluation of our updatable IPFE, and the experimental results demonstrate its computational efficiency, making it a viable solution for real-world applications.
Inner product functional encryption (IPFE) is a subclass of functional encryption (FE), whose function class is limited to inner product. We construct an efficient private-key IPFE scheme with full-hiding security, where confidentiality is assured for not only encrypted data but also functions associated with secret keys. Recently, Datta et al. presented such a scheme in PKC 2016 and this is the only scheme that achieves full-hiding security. Our scheme has an advantage over their scheme for the two aspects. More efficient: keys and ciphertexts of our scheme are almost half the size of those of their scheme. Weaker assumption: our scheme is secure under the k-linear (k-Lin) assumption, while their scheme is secure under a stronger assumption, namely, the symmetric external Diffie-Hellman (SXDH) assumption. It is well-known that the k-Lin assumption is equivalent to the SXDH assumption when k=1 and becomes weak as k increases.
Abstract We propose a novel variant of functional encryption which supports ciphertext updates, dubbed ciphertext-updatable functional encryption. Such a feature further broadens the practical applicability of the functional encryption paradigm and allows for fine-grained access control even after a ciphertext is generated. Updating ciphertexts is carried out via so-called update tokens which a dedicated party can use to convert ciphertexts. However, allowing update tokens requires some care for the security definition. Our contribution is threefold: We define our new primitive with a security notion in the indistinguishability setting. Within CUFE, functional decryption keysandciphertexts are labeled with tags such that only if the tags of the decryption key and the ciphertext match, then decryption succeeds. Furthermore, we allow ciphertexts to switch their tags to any other tag via update tokens. Such tokens are generated by the holder of the main secret key and can only be used in the desired direction. We present a generic construction of CUFE for any functionality as well as predicates different from equality testing on tags which relies on the existence of indistinguishability obfuscation (iO). We present a practical construction of CUFE for the inner-product functionality from standard assumptions (i.e., LWE) in the random-oracle model. On the technical level, we build on the recent functional encryption schemes with fine-grained access control and linear operations on encrypted data (Abdalla et al., AC’20) and introduce an additional ciphertext updatability feature. Proving security for such a construction turned out to be non-trivial, particularly when revealing keys for the updated challenge ciphertext is allowed. Overall, such construction enriches the set of known inner-product functional encryption schemes with the additional updatability feature of ciphertexts.