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.
. The concept of functional encryption was proposed by Amit Sahai and Brent Waters in @cite_42 , and the formal definition was presented by in @cite_48 . As a new technique for public-key cryptography @cite_45 , functional encryption can be viewed as the abstraction of most of the existing encryption schemes such as attribute-based encryption @cite_31 , inner production function @cite_55 , and order-revealing encryption @cite_36 . Generally, unlike traditional encryption schemes, where decryption reveals all or nothing, in a functional encryption scheme, the decryption keys may reveal only partial information about the plaintext, for instance, a computed result of a specific function.
@cite_36 @cite_48 @cite_55 @cite_42 @cite_45 @cite_31
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Functional encryption is a new paradigm in public-key encryption that allows users to finely control the amount of information that is revealed by a ciphertext to a given receiver. Recent papers have focused their attention on constructing schemes for general functionalities at expense of efficiency. Our goal, in this paper, is to construct functional encryption schemes for less general functionalities which are still expressive enough for practical scenarios. We propose a functional encryption scheme for the inner-product functionality, meaning that decrypting an encrypted vector ( x ) with a key for a vector ( y ) will reveal only ( x , y ) and nothing else, whose security is based on the DDH assumption. Despite the simplicity of this functionality, it is still useful in many contexts like descriptive statistics. In addition, we generalize our approach and present a generic scheme that can be instantiated, in addition, under the LWE assumption and offers various trade-offs in terms of expressiveness and efficiency. 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. We construct functional encryption schemes for polynomial-time computable functions secure against an a-priori bounded polynomial number of collusions. Our constructions require only semantically secure public-key encryption schemes and pseudorandom generators computable by small-depth circuits known to be implied by most concrete intractability assumptions. For certain special cases such as predicate encryption schemes with public index, the construction requires only semantically secure encryption schemes. Along the way, we show a "bootstrapping theorem" that builds a q-query functional encryption scheme for arbitrary functions starting from a q-query functional encryption scheme for bounded-degree functions. All our constructions rely heavily on techniques from secure multi-party computation and randomized encodings. Our constructions are secure under a strong simulation-based definition of functional encryption. In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages. Given a secret key for a function f, and a ciphertext for a message x, a decryptor learns f(x) and nothing else about x. Inner product encryption is a special case of functional encryption where both secret keys and ciphertext are associated with vectors. The combination of a secret key for a vector ( x ) and a ciphertext for a vector ( y ) reveal ( x , y ) and nothing more about ( y ). An inner product encryption scheme is function-hiding if the keys and ciphertexts reveal no additional information about both ( x ) and ( y ) beyond their inner product.