Emerging neural networks based machine learning techniques such as deep learning and its variants have shown tremendous potential in many application domains. However, they raise serious privacy concerns due to the risk of leakage of highly privacy-sensitive data when data collected from users is used to train neural network models to support predictive tasks. To tackle such serious privacy concerns, several privacy-preserving approaches have been proposed in the literature that use either secure multi-party computation (SMC) or homomorphic encryption (HE) as the underlying mechanisms. However, neither of these cryptographic approaches provides an efficient solution towards constructing a privacy-preserving machine learning model, as well as supporting both the training and inference phases. To tackle the above issue, we propose a CryptoNN framework that supports training a neural network model over encrypted data by using the emerging functional encryption scheme instead of SMC or HE. We also construct a functional encryption scheme for basic arithmetic computation to support the requirement of the proposed CryptoNN framework. We present performance evaluation and security analysis of the underlying crypto scheme and show through our experiments that CryptoNN achieves accuracy that is similar to those of the baseline neural network models on the MNIST dataset.
Encryption is a well established technology for protecting sensitive data. However, once encrypted, data can no longer be easily queried aside from exact matches. We present an order-preserving encryption scheme for numeric data that allows any comparison operation to be directly applied on encrypted data. Query results produced are sound (no false hits) and complete (no false drops). Our scheme handles updates gracefully and new values can be added without requiring changes in the encryption of other values. It allows standard databse indexes to be built over encrypted tables and can easily be integrated with existing database systems. The proposed scheme has been designed to be deployed in application environments in which the intruder can get access to the encrypted database, but does not have prior domain information such as the distribution of values and annot encrypt or decrypt arbitrary values of his choice. The encryption is robust against estimation of the true value in such environments. We initiate the formal study of functional encryption by giving precise definitions of the concept and its security. Roughly speaking, functional encryption supports restricted secret keys that enable a key holder to learn a specific function of encrypted data, but learn nothing else about the data. For example, given an encrypted program the secret key may enable the key holder to learn the output of the program on a specific input without learning anything else about the program. We show that defining security for functional encryption is non-trivial. First, we show that a natural game-based definition is inadequate for some functionalities. We then present a natural simulation-based definition and show that it (provably) cannot be satisfied in the standard model, but can be satisfied in the random oracle model. We show how to map many existing concepts to our formalization of functional encryption and conclude with several interesting open problems in this young area. Predicate encryption is a generalized notion for public key encryption that enables one to encrypt attributes as well as a message. In this paper, we present a new inner-product encryption (IPE) scheme, as a specialized predicate encryption scheme, whose security relies on the well-known Decision Bilinear Diffie-Hellman (BDH) and Decision Linear assumptions. Our IPE scheme uses prime order groups equipped with a bilinear map and works in both symmetric and asymmetric bilinear maps. Our result is the first construction of IPE under the standard assumptions. Prior to our work, all IPE schemes known to date require non-standard assumptions to prove security, and moreover some of them use composite-order groups. To achieve our goal, we introduce a novel technique for attribute-hiding, which may be of independent interest. We introduce a new type of Identity-Based Encryption (IBE) scheme that we call Fuzzy Identity-Based Encryption. In Fuzzy IBE we view an identity as set of descriptive attributes. A Fuzzy IBE scheme allows for a private key for an identity, ω, to decrypt a ciphertext encrypted with an identity, ω ′, if and only if the identities ω and ω ′ are close to each other as measured by the “set overlap” distance metric. A Fuzzy IBE scheme can be applied to enable encryption using biometric inputs as identities; the error-tolerance property of a Fuzzy IBE scheme is precisely what allows for the use of biometric identities, which inherently will have some noise each time they are sampled. Additionally, we show that Fuzzy-IBE can be used for a type of application that we term “attribute-based encryption”. In this paper we present two constructions of Fuzzy IBE schemes. Our constructions can be viewed as an Identity-Based Encryption of a message under several attributes that compose a (fuzzy) identity. Our IBE schemes are both error-tolerant and secure against collusion attacks. Additionally, our basic construction does not use random oracles. We prove the security of our schemes under the Selective-ID security model. Decryption keys allow users to learn a specific function of the encrypted data and nothing else. We construct an Attribute-Based Encryption (ABE) scheme that allows a user's private key to be expressed in terms of any access formula over attributes. Previous ABE schemes were limited to expressing only monotonic access structures. We provide a proof of security for our scheme based on the Decisional Bilinear Diffie-Hellman (BDH) assumption. Furthermore, the performance of our new scheme compares favorably with existing, less-expressive schemes.