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The Computer Journal

Indistinguishable Leakage-Resilient Circuit Compiler

Shiyou Xu, Jian Wang, Liangliang Wang

Published Mar 17, 2022• 0 citations
Publisher

Abstract

Abstract Transforming any circuit into a circuit with the same functionality but resilience against well-defined classes of leakage is an essential subject of cryptography. Whereas, according to the relationship between $VBB$ and simulated leakage-resilient circuit compiler, the compiling needs a specific mechanism to guarantee that its input is free of any leakage. Unfortunately, it makes it tough to implement this strategy in the context of actual leaks. In this work, we formally propose the indistinguishable bounded leakage-resilient circuit compiler $\bar{C}$ to solve the problem mentioned above. Specifically, it specifies that any polynomial-time adversary who derives the bound secret information from the circuit compiler can not distinguish an equivalent compiled circuit $\bar{C}^{\prime}$ with the same output. To achieve this goal, first, we utilize the leakage-resilient indistinguishable encoding as its input. Second, it takes advantage of the indistinguishability obfuscation $(IO)$ program to construct an obfuscated circuit that removes the random coins of the input encoding . Its total running time is the original circuit $C$ running time plus $poly(\kappa )$, and the size is independent of the original $C$. As this new compiler overcomes the restriction of the simulated-based leakage resilient circuit compiler,it will bring an independent interest result in leakage-resilient cryptography.

DOI
10.1093/comjnl/bxac036

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Abstract Transforming any circuit into a circuit with the same functionality but resilience against well-defined classes of leakage is an essential subject of cryptography. Whereas, according to the relationship between VBBVBBVBB and simulated leakage-resilient circuit compiler, the compiling needs a specific mechanism to guarantee that its input is free of any leakage. Unfortunately, it makes it tough to implement this strategy in the context of actual leaks. In this work, we formally propose the indistinguishable bounded leakage-resilient circuit compiler Cˉ\bar{C}Cˉ to solve the problem mentioned above. Specifically, it specifies that any polynomial-time adversary who derives the bound secret information from the circuit compiler can not distinguish an equivalent compiled circuit Cˉ′\bar{C}^{\prime}Cˉ′ with the same output. To achieve this goal, first, we utilize the leakage-resilient indistinguishable encoding as its input. Second, it takes advantage of the indistinguishability obfuscation (IO)(IO)(IO) program to construct an obfuscated circuit that removes the random coins of the input encoding . Its total running time is the original circuit CCC running time plus poly(κ)poly(\kappa )poly(κ), and the size is independent of the original CCC. As this new compiler overcomes the restriction of the simulated-based leakage resilient circuit compiler,it will bring an independent interest result in leakage-resilient cryptography.
Physical computational devices leak side-channel information that may, and often does, reveal secret internal states. We present a general transformation that compiles any circuit into a circuit with the same functionality but resilience against well-defined classes of leakage. Our construction requires a small, stateless, and computation-independent leak-proof component that draws random elements from a fixed distribution. In essence, we reduce the problem of shielding arbitrarily complex circuits to the problem of shielding a single, simple component. Our approach is based on modeling the adversary as a powerful observer that inspects the device via a limited measurement apparatus. We allow the apparatus to access all the bits of the computation (except those inside the leak-proof component), and the amount of leaked information to grow unbounded over time. However, we assume that the apparatus is limited in the amount of output bits per iteration and the ability to decode certain linear encodings. While our results apply in general to such leakage classes, in particular, we obtain security against (a) constant-depth circuits leakage, where the leakage function is computed by an AC0\mathsf{AC}^0AC0 circuit (composed of NOT gates and unbounded fan-in AND and OR gates); (b) noisy leakage, where the leakage function reveals all the bits of the internal state of the circuit, but each bit is perturbed by independent binomial noise---i.e., flipped with some probability ppp. Namely, for some number p∈(0,1/2]p\in(0,1/2]p∈(0,1/2], each bit of the computation is flipped with probability ppp, and remains unchanged with probability 1−p1-p1−p.
An indistinguishability obfuscator is a probabilistic polynomial-time algorithm that takes a circuit as input and outputs a new circuit that has the same functionality as the input circuit, such that for any two circuits of the same size that compute the same function, the outputs of the indistinguishability obfuscator are computationally indistinguishable. Here, we study schemes for indistinguishability obfuscation for quantum circuits (qiOqi\mathcal{O}qiO), which consists in a procedure that takes as input a quantum circuit and outputs a quantum state, together with a quantum circuit, which together can be used to evaluate the original quantum circuit on any quantum input; the security guarantee being that for two quantum circuits of the same size that have the same input-output behaviour, the outputs of the obfuscator are computationally indistinguishable. Our main result provides a construction for qiOqi\mathcal{O}qiO, where the size of the output of the obfuscator is exponential in the number of non-Clifford (T gates), which means that the construction is efficient as long as the number of T gates is logarithmic in the circuit size.
We consider the problem of distributing a computation between two parties, such that any bounded-communication leakage function applied to the local views of the two parties reveals essentially nothing about the input. This problem can be motivated by the goal of outsourcing computations on sensitive data to two servers in the cloud, where both servers can be simultaneously corrupted by viruses that have a limited communication bandwidth. We present a simple and efficient reduction of the above problem to that of constructing parity-resilient circuits, namely circuits that map an encoded input to an encoded output so that the parity of any subset of the wires is essentially independent of the input. We then construct parity-resilient circuits from circuits that are resilient to local leakage, which can in turn be obtained from protocols for secure multiparty computation. Our main reduction builds on a novel generalization of the ε-biased masking lemma that applies to interactive protocols. Applying the above, we obtain two-party protocols with resilience to bounded-communication leakage either in the information-theoretic setting, relying on random oblivious transfer correlations, or in the computational setting, relying on non-committing encryption which can be based on a variety of standard cryptographic assumptions.
Abstract Leakage-resilient cryptography aims to protect cryptographic primitives from so-called “side channel attacks” that exploit their physical implementation to learn their input or secret state. Starting from the works of Ishai, Sahai and Wagner (CRYPTO‘03) and Micali and Reyzin (TCC‘04), most works on leakage-resilient cryptography either focus on protecting general computations, such as circuits or multiparty computation protocols, or on specific non-interactive primitives such as storage, encryption, and signatures. This work focuses on leakage resilience for the middle ground, namely for distributed and interactive cryptographic primitives. Our main technical contribution is designing the first secret sharing scheme that is equivocal, resists adaptive probing of a constant fraction of bits from each share, while incurs only a constant blowup in share size. Equivocation is a strong leakage-resilience guarantee, recently introduced by Hazay et al. (ITC, 2021). Our construction is obtained via a general compiler which we introduce, that transforms any secret sharing scheme into an equivocal scheme against adaptive leakage. An attractive feature of our compiler is that it respects additive reconstruction; namely, if the original scheme has additive reconstruction, then the transformed scheme has linear reconstruction. We extend our compiler to a general paradigm for protecting distributed primitives against leakage and show its applicability to various primitives, including secret sharing, verifiable secret sharing, function secret sharing, distributed encryption and signatures, and distributed zero-knowledge proofs. For each of these primitives, our paradigm transforms any construction of the primitive into a scheme that resists adaptive party corruptions, as well as adaptive probing leakage of a constant fraction of bits in each share when the share is stored in memory (but not when it is used in computations). Moreover, the transformation incurs only a constant blowup in the share size and respects additive reconstruction—an important feature for several of these primitives, such as function secret sharing and distributed encryption.
We consider the question of protecting a general computation device, modeled by a stateful Boolean circuit, against leakage of partial information about its internal wires. Goyal et al. (FOCS 2016) obtained a solution for the case of bounded-communication leakage, where the wires are partitioned into two parts and the leakage can be any function computed using t bits of communication between the parts. However, this solution suffers from two major limitations: (1) it only applies to a one-shot (stateless) computation, mapping an encoded input to an encoded output, and (2) the leakage-resilient circuit consumes fresh random bits, whose number scales linearly with the circuit complexity of the computed function. In this work, we eliminate the first limitation and make progress on the second. Concretely: - We present the first construction of stateful circuits that offer information-theoretic protection against continuous bounded-communication leakage. As an application, we extend a two-party “malware-resilient” protocol of Goyal et al. to the continuous-leakage case. - For simple types of bounded-communication leakage, which leak t parities or t disjunctions of circuit wires or their negations, we obtain a deterministic variant that does not require any fresh randomness beyond the randomness in the initial state. Here we get computational security based on a subexponentially secure one-way function. This is the first deterministic leakage-resilient circuit construction for any nontrivial class of global leakage.
In this work, we consider the natural goal of designing secret sharing schemes that ensure security against an adversary who may learn some “leaked'' information about all the shares. We say that a secret sharing scheme is p-party leakage-resilient, if the secret remains statistically hidden even after a computationally unbounded adversary learns a bounded amount of leakage, where each bit of leakage adaptively and jointly depends on the shares of an adaptively chosen subset of p parties. Existing multi-party secret sharing schemes (Dziembowski and Pietrzak FOCS 07), (Goyal and Kumar STOC 18) and (Benhamouda, Degwekar, Ishai and Rabin CRYPTO 18) have focused on handling non-adaptive and individual leakage for (limited special cases of) threshold secret sharing schemes. (1) We give an unconditional compiler that transforms any secret sharing scheme on n parties into a p-party leakage-resilient one for p upto O(log n). This yields the first multi-party secret sharing schemes that are secure against adaptive or joint leakage. (2) As a natural extension, we initiate the study of leakage-resilient non-malleable secret sharing. We empower the adversary to adaptively leak from each of the shares and then use the leakage to tamper with all of them arbitrarily and independently. Leveraging our p-party leakage-resilient schemes, we compile any secret sharing scheme into a non-malleable one ensuring that any such tampering either preserves the secret or completely `destroys' it. This improves upon the non-malleable secret sharing scheme of (Goyal and Kumar CRYPTO 18) where no leakage was permitted. Leakage-resilient non-malleable codes can be seen as 2-out-of-2 schemes satisfying our guarantee and have already found many applications in cryptography. (3) Our constructions rely on a clean connection we draw to communication complexity in the well-studied number-on-forehead (NOF) model and rely on functions that have strong communication-complexity lower bounds in the NOF model (in a black-box way). We get efficient p-party leakage-resilient schemes for p upto O(log n) as our share sizes have exponential dependence on p. We observe that improving this exponential dependence, even for simultaneous, non-adaptive leakage, will lead to progress on longstanding open problems in complexity theory.