Private Functional Encryption – Hiding What Cannot Be Learned Through Function Evaluation

Functional encryption (FE) is a generalization of many commonly employed crypto- graphic primitives, such as keyword search encryption (KS), identity-based encryption (IBE), inner-product encryption (IPE) and attribute-based encryption (ABE). In an FE scheme, the holder of a master secret key can issue tokens associated with functions of its choice. Possessing a token for f allows one to recover f(m), given an encryption of m. As it is important that ciphertexts preserve data privacy, in various scenarios it is also important that tokens do not expose their associated function. A notable example being the usage of FE to search over encrypted data without revealing the search query. Function privacy is an emerging new notion that aims to address this problem. The difficulty of formalizing it lies in the verification functionality, as the holder of a token for function f may encrypt arbitrary messages using the public key, and obtain a large number of evaluations of f.
Prior privacy models in the literature were fine-tuned for specific functionalities, did not model correlations between ciphertexts and decryption tokens, or fell under strong uninstantiability results. Our first contribution is a new indistinguishability-based privacy notion that overcomes these limitations and is flexible enough to capture all previously proposed indistinguishability-based definitions as particular cases.
The second contribution of this thesis is five constructions of private functional encryption supporting different classes of functions and meeting varying degrees of security: (1) a white-box construction of an Anonymous IBE scheme based on composite-order groups, shown to be secure in the absence of correlated messages; (2) a simple and functionality- agnostic black-box construction from obfuscation, also shown to be secure in the absence of correlated messages; (3) a more evolved and still functionality-agnostic construction that achieves a form of function privacy that tolerates limited correlations between messages and functions; (4) a KS scheme achieving privacy in the presence of correlated messages beyond all previously proposed indistinguishability-based security definitions; (5) a KS construction that achieves our strongest notion of privacy (but relies on a more expressive form of obfuscation than the previous construction).
The standard approach in FE is to model complex functions as circuits, which yields inefficient evaluations over large inputs. As our third contribution, we propose a new primitive that we call “updatable functional encryption” (UFE), where instead of circuits we deal with RAM programs, which are closer to how programs are expressed in von Neumann architecture. We impose strict efficiency constrains and we envision tokens that are capable of updating the ciphertext, over which other tokens can be subsequently executed. We define a security notion for our primitive and propose a candidate construction from obfuscation, which serves as a starting point towards the realization of other schemes and contributes to the study on how to compute RAM programs over public-key encrypted data.