Machine learning is widely used in practice to produce predictive models for applications such as image processing, speech and text recognition. These models are more accurate when trained on large amount of data collected from different sources. However, the massive data collection raises privacy concerns. In this paper, we present new and efficient protocols for privacy preserving machine learning for linear regression, logistic regression and neural network training using the stochastic gradient descent method. Our protocols fall in the two-server model where data owners distribute their private data among two non-colluding servers who train various models on the joint data using secure two-party computation (2PC). We develop new techniques to support secure arithmetic operations on shared decimal numbers, and propose MPC-friendly alternatives to non-linear functions such as sigmoid and softmax that are superior to prior work. We implement our system in C++. Our experiments validate that our protocols are several orders of magnitude faster than the state of the art implementations for privacy preserving linear and logistic regressions, and scale to millions of data samples with thousands of features. We also implement the first privacy preserving system for training neural networks.

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SecureML: A System for Scalable Privacy-Preserving Machine Learning

from details of underlying secure computation protocol Use only fast symmetric key crypto Code is available on GitHub: http://encrypto.de/code/ABY

/pdf/aby-a-framework-for-efficient-mixed-protocol-secure-two-hozs81ospf.pdf

ABY - A Framework for Efficient Mixed-Protocol Secure Two-Party Computation

/pdf/secureml-a-system-for-scalable-privacy-preserving-machine-3zt40tob0l.pdf

SecureML: A System for Scalable Privacy-Preserving Machine Learning.

Garbled circuits, a classical idea rooted in the work of Yao, have long been understood as a cryptographic technique, not a cryptographic goal. Here we cull out a primitive corresponding to this technique. We call it a garbling scheme. We provide a provable-security treatment for garbling schemes, endowing them with a versatile syntax and multiple security definitions. The most basic of these, privacy, suffices for two-party secure function evaluation (SFE) and private function evaluation (PFE). Starting from a PRF, we provide an efficient garbling scheme achieving privacy and we analyze its concrete security. We next consider obliviousness and authenticity, properties needed for private and verifiable outsourcing of computation. We extend our scheme to achieve these ends. We provide highly efficient blockcipher-based instantiations of both schemes. Our treatment of garbling schemes presages more efficient garbling, more rigorous analyses, and more modularly designed higher-level protocols.

/pdf/foundations-of-garbled-circuits-f3gqwxe1v8.pdf

Foundations of garbled circuits

Garbled circuits, introduced by Yao in the mid 80s, allow computing a function f on an input x without leaking anything about f or x besides f(x). Garbled circuits found numerous applications, but every known construction suffers from one limitation: it offers no security if used on multiple inputs x. In this paper, we construct for the first time reusable garbled circuits. The key building block is a new succinct single-key functional encryption scheme.Functional encryption is an ambitious primitive: given an encryption Enc(x) of a value x, and a secret key sk_f for a function f, anyone can compute f(x) without learning any other information about x. We construct, for the first time, a succinct functional encryption scheme for {\em any} polynomial-time function f where succinctness means that the ciphertext size does not grow with the size of the circuit for f, but only with its depth. The security of our construction is based on the intractability of the Learning with Errors (LWE) problem and holds as long as an adversary has access to a single key sk_f (or even an a priori bounded number of keys for different functions).Building on our succinct single-key functional encryption scheme, we show several new applications in addition to reusable garbled circuits, such as a paradigm for general function obfuscation which we call token-based obfuscation, homomorphic encryption for a class of Turing machines where the evaluation runs in input-specific time rather than worst-case time, and a scheme for delegating computation which is publicly verifiable and maintains the privacy of the computation.

http://people.csail.mit.edu/nickolai/papers/goldwasser-sfe.pdf

Reusable garbled circuits and succinct functional encryption

We advocate schemes based on fixed-key AES as the best route to highly efficient circuit-garbling. We provide such schemes making only one AES call per garbled-gate evaluation. On the theoretical side, we justify the security of these methods in the random-permutation model, where parties have access to a public random permutation. On the practical side, we provide the Just Garble system, which implements our schemes. Just Garble evaluates moderate-sized garbled-circuits at an amortized cost of 23.2 cycles per gate (7.25 nsec), far faster than any prior reported results.

/pdf/efficient-garbling-from-a-fixed-key-blockcipher-2pc03c60uq.pdf

Efficient Garbling from a Fixed-Key Blockcipher

We prove beyond-birthday-bound security for most of the well-known types of generalized Feistel networks: (1) unbalanced Feistel networks, where the n-bit to m-bit round functions may have n ≠ m; (2) alternating Feistel networks, where the round functions alternate between contracting and expanding; (3) type-1, type-2, and type-3 Feistel networks, where n-bit to n-bit round functions are used to encipher kn-bit strings for some k ≥ 2; and (4) numeric variants of any of the above, where one enciphers numbers in some given range rather than strings of some given size. Using a unified analytic framework, we show that, in any of these settings, for any e > 0, with enough rounds, the subject scheme can tolerate CCA attacks of up to q ∼ N1-e adversarial queries, where N is the size of the round functions' domain (the larger domain for alternating Feistel). Prior analyses for most generalized Feistel networks established security to only q ∼ N0.5 queries.

/pdf/on-generalized-feistel-networks-5efwuun977.pdf

On generalized Feistel networks

Standard constructions of garbled circuits provide only static security, meaning the input x is not allowed to depend on the garbled circuit F. But some applications--notably one-time programs (Goldwasser, Kalai, and Rothblum 2008) and secure outsourcing (Gennaro, Gentry, Parno 2010)--need adaptive security, where x may depend on F. We identify gaps in proofs from these papers with regard to adaptive security and suggest the need of a better abstraction boundary. To this end we investigate the adaptive security of garbling schemes, an abstraction of Yao's garbled-circuit technique that we recently introduced (Bellare, Hoang, Rogaway 2012). Building on that framework, we give definitions encompassing privacy, authenticity, and obliviousness, with either coarse-grained or fine-grained adaptivity. We show how adaptively secure garbling schemes support simple solutions for one-time programs and secure outsourcing, with privacy being the goal in the first case and obliviousness and authenticity the goal in the second. We give transforms that promote static-secure garbling schemes to adaptive-secure ones. Our work advances the thesis that conceptualizing garbling schemes as a first-class cryptographic primitive can simplify, unify, or improve treatments for higher-level protocols.

/pdf/adaptively-secure-garbling-with-applications-to-one-time-18obm5drxy.pdf

Adaptively secure garbling with applications to one-time programs and secure outsourcing

With a scheme for robust authenticated-encryption a user can select an arbitrary value \(\lambda \!\ge 0\) and then encrypt a plaintext of any length into a ciphertext that’s \(\lambda \) characters longer. The scheme must provide all the privacy and authenticity possible for the requested \(\lambda \). We formalize and investigate this idea, and construct a well-optimized solution, AEZ, from the AES round function. Our scheme encrypts strings at almost the same rate as OCB-AES or CTR-AES (on Haswell, AEZ has a peak speed of about 0.7 cpb). To accomplish this we employ an approach we call prove-then-prune: prove security and then instantiate with a scaled-down primitive (e.g., reducing rounds for blockcipher calls).

/pdf/robust-authenticated-encryption-aez-and-the-problem-that-it-e11h9mb8j9.pdf

Viet Tung Hoang

Papers

Foundations of garbled circuits

Efficient Garbling from a Fixed-Key Blockcipher

On generalized Feistel networks

Adaptively secure garbling with applications to one-time programs and secure outsourcing

Robust Authenticated-Encryption: AEZ and the Problem that it Solves.