Protecting source code against reverse engineering and theft is an important problem. The goal is to carry out computations using confidential algorithms on an untrusted party while ensuring confidentiality of algorithms. This problem has been addressed for Boolean circuits known as circuit privacy'. Circuits corresponding to real-world programs are impractical. Well-known obfuscation techniques are highly practicable, but provide only limited security, e.g., no piracy protection. In this work, we modify source code yielding programs with adjustable performance and security guarantees ranging from indistinguishability obfuscators to (non-secure) ordinary obfuscation. The idea is to artificially generate misleading' statements. Their results are combined with the outcome of a confidential statement using encrypted . Thus, an attacker must guess' the encrypted selector variables to disguise the confidential source code. We evaluated our method using more than ten programmers as well as pattern mining across open source code repositories to gain insights of (micro-)coding patterns that are relevant for generating misleading statements. The evaluation reveals that our approach is effective in that it successfully preserves source code confidentiality.
In his thesis Gentry @cite_22 gave a fully homomorphic encryption (FHE) scheme. He also discussed how to ensure circuit privacy by adding a large random error vector.
@cite_22
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We present a novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentry's bootstrapping procedure. Specifically, we offer a choice of FHE schemes based on the learning with error (LWE) or ring-LWE (RLWE) problems that have 2λ security against known attacks. For RLWE, we have: • A leveled FHE scheme that can evaluate L-level arithmetic circuits with O(λ · L3) per-gate computation -- i.e., computation quasi-linear in the security parameter. Security is based on RLWE for an approximation factor exponential in L. This construction does not use the bootstrapping procedure. • A leveled FHE scheme that uses bootstrapping as an optimization, where the per-gate computation (which includes the bootstrapping procedure) is O(λ2), independent of L. Security is based on the hardness of RLWE for quasi-polynomial factors (as opposed to the sub-exponential factors needed in previous schemes). We obtain similar results to the above for LWE, but with worse performance. Based on the Ring LWE assumption, we introduce a number of further optimizations to our schemes. As an example, for circuits of large width -- e.g., where a constant fraction of levels have width at least λ -- we can reduce the per-gate computation of the bootstrapped version to O(λ), independent of L, by batching the bootstrapping operation. Previous FHE schemes all required Ω(λ3.5) computation per gate. At the core of our construction is a much more effective approach for managing the noise level of lattice-based ciphertexts as homomorphic operations are performed, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011). In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first. This has many applications, in particular in cloud computing. In all currently known FHE schemes, encryptions are associated to some (non-negative integer) noise level, and at each evaluation of an AND gate, the noise level increases. This is problematic because decryption can only work if the noise level stays below some maximum level @math at every gate of the circuit. To ensure that property, it is possible to perform an operation called to reduce the noise level. However, bootstrapping is time-consuming and has been identified as a critical operation. This motivates a new problem in discrete optimization, that of choosing where in the circuit to perform bootstrapping operations so as to control the noise level; the goal is to minimize the number of bootstrappings in circuits. In this paper, we formally define the , we design a polynomial-time @math -approximation algorithm using a novel method of rounding of a linear program, and we show a matching hardness result: @math -inapproximability for any @math . We propose a method to compute the exact minimal number of bootstrappings required to homomorphically evaluate any circuit. Given a circuit (typically over ( F _2 ) although our method readily extends to circuits over any ring), the maximal noise level supported by the considered fully homomorphic encryption (FHE) scheme and the desired noise level of circuit inputs and outputs, our algorithms return a minimal subset of circuit variables such that boostrapping these variables is enough to perform an evaluation of the whole circuit. We introduce a specific algorithm for 2-level encryption (first generation of FHE schemes) and an extended algorithm for l max -level encryption with arbitrary l max ≥ 2 to cope with more recent FHE schemes. We successfully applied our method to a range of real-world circuits that perform various operations over plaintext bits. Practical results show that some of these circuits benefit from significant improvements over the naive evaluation method where all multiplication outputs are bootstrapped. In particular, we report that a circuit for the AES S-box put forward by Boyar and Peralta admits a solution in 17 bootstrappings instead of 32, thereby leading to a 88 faster homomorphic evaluation of AES for any 2-level FHE scheme. The rise of machine learning as a service multiplies scenarios where one faces a privacy dilemma: either sensitive user data must be revealed to the entity that evaluates the cognitive model (e.g., in the Cloud), or the model itself must be revealed to the user so that the evaluation can take place locally. Fully Homomorphic Encryption (FHE) offers an elegant way to reconcile these conflicting interests in the Cloud-based scenario and also preserve non-interactivity. However, due to the inefficiency of existing FHE schemes, most applications prefer to use Somewhat Homomorphic Encryption (SHE), where the complexity of the computation to be performed has to be known in advance, and the efficiency of the scheme depends on this global complexity.