International Association
for Cryptologic Research

The Distorted Bounded Distance Decoding Problem (DBDD) was introduced by Dachman-Soled et al. [Crypto ’20] as an intermediate problem between LWE and unique-SVP (uSVP). They presented an approach that reduces an LWE instance to a DBDD instance, integrates side information (or “hints”) into the DBDD instance, and finally reduces it to a uSVP instance, which can be solved via lattice reduction. They showed that this principled approach can lead to algorithms for side-channel attacks that perform better than ad-hoc algorithms that do not rely on lattice reduction. The current work focuses on new methods for integrating hints into a DBDD instance. We view hints from a geometric perspective, as opposed to the distributional perspective from the prior work. Our approach provides the rigorous promise that, as hints are integrated into the DBDD instance, the correct solution remains a lattice point contained in the specified ellipsoid. We instantiate our approach with two new types of hints: (1) Inequality hints, corresponding to the region of intersection of an ellipsoid and a halfspace; (2) Combined hints, corresponding to the region of intersection of two ellipsoids. Since the regions in (1) and (2) are not necessarily ellipsoids, we replace them with ellipsoidal approximations that circumscribe the region of intersection. Perfect hints are reconsidered as the region of intersection of an ellipsoid and a hyperplane, which is itself an ellipsoid. The compatibility of “approximate,” “modular,” and “short vector” hints from the prior work is examined. We apply our techniques to the decryption failure and side-channel attack settings. We show that “inequality hints” can be used to model decryption failures, and that our new approach yields a geometric analogue of the “failure boosting” technique of D’anvers et al. [ePrint, ’18]. We also show that “combined hints” can be used to fuse information from a decryption failure and a side-channel attack, and provide rigorous guarantees despite the data being non-Gaussian. We provide experimental data for both applications. The code that we have developed to implement the integration of hints and hardness estimates extends the Toolkit from prior work and has been released publicly.

We present the first truly explicit constructions of \emph{non-malleable codes} against tampering by bounded polynomial size circuits. These objects imply unproven circuit lower bounds and our construction is secure provided $\Eclass$ requires exponential size nondeterministic circuits, an assumption from the derandomization literature. Prior works on NMC for polysize circuits, either required an untamperable CRS [Cheraghchi, Guruswami ITCS'14; Faust, Mukherjee, Venturi, Wichs EUROCRYPT'14] or very strong cryptographic assumptions [Ball, Dachman-Soled, Kulkarni, Lin, Malkin EUROCRYPT'18; Dachman-Soled, Komargodski, Pass CRYPTO'21]. Both of works in the latter category only achieve non-malleability with respect to efficient distinguishers and, more importantly, utilize cryptographic objects for which no provably secure instantiations are known outside the random oracle model. In this sense, none of the prior yields fully explicit codes from non-heuristic assumptions. Our assumption is not known to imply the existence of one-way functions, which suggests that cryptography is unnecessary for non-malleability against this class. Technically, security is shown by \emph{non-deterministically} reducing polynomial size tampering to split-state tampering. The technique is general enough that it allows us to to construct the first \emph{seedless non-malleable extractors} [Cheraghchi, Guruswami TCC'14] for sources sampled by polynomial size circuits [Trevisan, Vadhan FOCS'00] (resp.~recognized by polynomial size circuits [Shaltiel CC'11]) and tampered by polynomial size circuits. Our construction is secure assuming $\Eclass$ requires exponential size $\Sigma_4$-circuits (resp. $\Sigma_3$-circuits), this assumption is the state-of-the-art for extracting randomness from such sources (without non-malleability). Several additional results are included in the full version of this paper [Eprint 2022/070]. First, we observe that non-malleable codes and non-malleable secret sharing [Goyal, Kumar STOC'18] are essentially equivalent with respect to polynomial size tampering. In more detail, assuming $\Eclass$ is hard for exponential size nondeterministic circuits, any efficient secret sharing scheme can be made non-malleable against polynomial size circuit tampering. Second, we observe that the fact that our constructions only achieve inverse polynomial (statistical) security is inherent. Extending a result from [Applebaum, Artemenko, Shaltiel, Yang CC'16] we show it is impossible to do better using black-box reductions. However, we extend the notion of relative error from [Applebaum, Artemenko, Shaltiel, Yang CC'16] to non-malleable extractors and show that they can be constructed from similar assumptions. Third, we observe that relative-error non-malleable extractors can be utilized to render a broad class of cryptographic primitives tamper and leakage resilient, while preserving negligible security guarantees.

Random sampling from specified distributions is an important tool with wide applications for analysis of large-scale data. In this paper we study how to randomly sample when the distribution is partitioned among two parties' private inputs. Of course, a trivial solution is to have one party send a (possibly encrypted) description of its weights to the other party who can then sample over the entire distribution (possibly using homomorphic encryption). However, this approach requires communication that is linear in the input size which is prohibitively expensive in many settings. In this paper, we investigate secure 2-party sampling with sublinear communication for many standard distributions. We develop protocols for L_1, and L_2 sampling. Additionally, we investigate the feasibility of sublinear product sampling, showing impossibility for the general problem and showing a protocol for a restricted case of the problem. We additionally show how such product sampling can be used to instantiate a sublinear communication 2-party exponential mechanism for differentially-private data release.

Non-malleable codes allow one to encode data in such a way that once a codeword is being tampered with, the modified codeword is either an encoding of the original message, or a completely unrelated one. Since the introduction of this notion by Dziembowski, Pietrzak, and Wichs (ICS '10 and J. ACM '18), there has been a large body of works realizing such coding schemes secure against various classes of tampering functions. It is well known that there is no efficient non-malleable code secure against all polynomial size tampering functions. Nevertheless, no code which is non-malleable for \emph{bounded} polynomial size attackers is known and obtaining such a code has been a major open problem. We present the first construction of a non-malleable code secure against all polynomial size tampering functions that have {bounded} parallel time. This is an even larger class than all bounded polynomial size functions. In particular, this class includes all functions in non-uniform $\mathbf{NC}$ (and much more). Our construction is in the plain model (i.e., no trusted setup) and relies on several cryptographic assumptions such as keyless hash functions, time-lock puzzles, as well as other standard assumptions. Additionally, our construction has several appealing properties: the complexity of encoding is independent of the class of tampering functions and we can obtain (sub-)exponentially small error.

We consider the Learning Parity with Noise (LPN) problem with a sparse secret, where the secret vector $\mathbf{s}$ of dimension $n$ has Hamming weight at most $k$. We are interested in algorithms with asymptotic improvement in the \emph{exponent} beyond the state of the art. Prior work in this setting presented algorithms with runtime $n^{c \cdot k}$ for constant $c < 1$, obtaining a constant factor improvement over brute force search, which runs in time ${n \choose k}$. We obtain the following results: - We first consider the \emph{constant} error rate setting, and in this case present a new algorithm that leverages a subroutine from the acclaimed BKW algorithm [Blum, Kalai, Wasserman, J.~ACM '03] as well as techniques from Fourier analysis for $p$-biased distributions. Our algorithm achieves asymptotic improvement in the exponent compared to prior work, when the sparsity $k = k(n) = \frac{n}{\log^{1+ 1/c}(n)}$, where $c \in o(\log \log(n))$ and $c \in \omega(1)$. The runtime and sample complexity of this algorithm are approximately the same. - We next consider the \emph{low noise} setting, where the error is subconstant. We present a new algorithm in this setting that requires only a \emph{polynomial} number of samples and achieves asymptotic improvement in the exponent compared to prior work, when the sparsity $k = \frac{1}{\eta} \cdot \frac{\log(n)}{\log(f(n))}$ and noise rate of $\eta \neq 1/2$ and $\eta^2 = \left(\frac{\log(n)}{n} \cdot f(n)\right)$, for $f(n) \in \omega(1) \cap n^{o(1)}$. To obtain the improvement in sample complexity, we create subsets of samples using the \emph{design} of Nisan and Wigderson [J.~Comput.~Syst.~Sci. '94], so that any two subsets have a small intersection, while the number of subsets is large. Each of these subsets is used to generate a single $p$-biased sample for the Fourier analysis step. We then show that this allows us to bound the covariance of pairs of samples, which is sufficient for the Fourier analysis. - Finally, we show that our first algorithm extends to the setting where the noise rate is very high $1/2 - o(1)$, and in this case can be used as a subroutine to obtain new algorithms for learning DNFs and Juntas. Our algorithms achieve asymptotic improvement in the exponent for certain regimes. For DNFs of size $s$ with approximation factor $\epsilon$ this regime is when $\log \frac{s}{\epsilon} \in \omega \left( \frac{c}{\log n \log \log c}\right)$, and $\log \frac{s}{\epsilon} \in n^{1 - o(1)}$, for $c \in n^{1 - o(1)}$. For Juntas of $k$ the regime is when $k \in \omega \left( \frac{c}{\log n \log \log c}\right)$, and $k \in n^{1 - o(1)}$, for $c \in n^{1 - o(1)}$.

Non-malleable codes, introduced as a relaxation of error-correcting codes by Dziembowski, Pietrzak, and Wichs (ICS ’10), provide the security guarantee that the message contained in a tampered codeword is either the same as the original message or is set to an unrelated value. Various applications of non-malleable codes have been discovered, and one of the most significant applications among these is the connection with tamper-resilient cryptography. There is a large body of work considering security against various classes of tampering functions, as well as non-malleable codes with enhanced features such as leakage resilience . In this work, we propose combining the concepts of non-malleability , leakage resilience , and locality in a coding scheme. The contribution of this work is threefold: 1. As a conceptual contribution, we define a new notion of locally decodable and updatable non-malleable code that combines the above properties. 2. We present two simple and efficient constructions achieving our new notion with different levels of security. 3. We present an important application of our new tool—securing RAM computation against memory tampering and leakage attacks. This is analogous to the usage of traditional non-malleable codes to secure implementations in the circuit model against memory tampering and leakage attacks.

We propose a framework for cryptanalysis of lattice-based schemes, when side information --in the form of "hints''-- about the secret and/or error is available. Our framework generalizes the so-called primal lattice reduction attack, and allows the progressive integration of hints before running a final lattice reduction step. Our techniques for integrating hints include sparsifying the lattice, projecting onto and intersecting with hyperplanes, and/or altering the distribution of the secret vector. Our main contribution is to propose a toolbox and a methodology to integrate such hints into lattice reduction attacks and to predict the performance of those lattice attacks with side information. While initially designed for side-channel information, our framework can also be used in other cases: exploiting decryption failures, or simply exploiting constraints imposed by certain schemes (LAC, Round5, NTRU), that were previously not known to (slightly) benefit from lattice attacks. We implement a Sage 9.0 toolkit to actually mount such attacks with hints when computationally feasible, and to predict their performances on larger instances. We provide several end-to-end application examples, such as an improvement of a single trace attack on Frodo by Bos et al (SAC 2018). Contrary to ad-hoc practical attacks exploiting side-channel leakage, our work is a generic way to estimate security loss even given very little side-channel information.

We present a transformation from NIZK with inefficient provers in the uniform random string (URS) model to ZAPs (two message witness indistinguishable proofs) with inefficient provers. While such a transformation was known for the case where the prover is efficient, the security proof breaks down if the prover is inefficient. Our transformation is obtained via new applications of Nisan-Wigderson designs, a combinatorial object originally introduced in the derandomization literature. We observe that our transformation is applicable both in the setting of super-polynomial provers/poly-time adversaries, as well as a new fine-grained setting, where the prover is polynomial time and the verifier/simulator/zero knowledge distinguisher are in a lower complexity class, such as $\mathsf{NC}^1$. We also present $\mathsf{NC}^1$-fine-grained NIZK in the URS model for all of NP from the worst-case assumption $\oplus L/\poly \not\subseteq \mathsf{NC}^1$. Our techniques yield the following applications: --ZAPs for $\mathsf{AM}$ from Minicrypt assumptions (with super-polynomial time provers), --$\mathsf{NC}^1$-fine-grained ZAPs for $\mathsf{NP}$ from worst-case assumptions, --Protocols achieving an ``offline'' notion of NIZK (oNIZK) in the standard (no-CRS) model with uniform soundness in both the super-polynomial setting (from Minicrypt assumptions) and the $\mathsf{NC}^1$-fine-grained setting (from worst-case assumptions). The oNIZK notion is sufficient for use in indistinguishability-based proofs.

We investigate fairness in secure multiparty computation when the number of parties n = poly(lambda) grows polynomially in the security parameter, lambda. Prior to this work, efficient protocols achieving fairness with no honest majority and polynomial number of parties were known only for the AND and OR functionalities (Gordon and Katz, TCC'09). We show the following: --We first consider symmetric Boolean functions F : {0,1}^n -> {0,1}, where the underlying function f_{n/2,n/2}: {0, ..., n/2} x {0, ..., n/2} -> {0,1} can be computed fairly and efficiently in the 2-party setting. We present an efficient protocol for any such F tolerating n/2 or fewer corruptions, for n = poly(lambda) number of parties. --We present an efficient protocol for n-party majority tolerating n/2+1 or fewer corruptions, for n = poly(lambda) number of parties. The construction extends to n/2+c or fewer corruptions, for constant c. --We extend both of the above results to more general types of adversarial structures and present instantiations of non-threshold adversarial structures of these types. These instantiations are obtained via constructions of projective planes and combinatorial designs.

Recently, Faust et al. (TCC’14) introduced the notion of continuous non-malleable codes (CNMC), which provides stronger security guarantees than standard non-malleable codes, by allowing an adversary to tamper with the codeword in a continuous way instead of one-time tampering. They also showed that CNMC with information theoretic security cannot be constructed in the 2-split-state tampering model, and presented a construction in the common reference string (CRS) model from collision-resistant hash functions and non-interactive zero-knowledge proofs.In this work, we ask if it is possible to construct CNMC from weaker assumptions. We answer this question by presenting lower as well as upper bounds. We show that it is impossible to construct 2-split-state CNMC, with no CRS, for one-bit messages from any falsifiable assumption, thus establishing the lower bound. We additionally provide an upper bound by constructing 2-split-state CNMC for one-bit messages, assuming only the existence of a family of injective one way functions. We note that in a recent work, Ostrovsky et al. (CRYPTO’18) considered the construction of a relaxed notion of 2-split-state CNMC from minimal assumptions.We also present a construction of 4-split-state CNMC for multi-bit messages in CRS model from the same assumptions. Additionally, we present definitions of the following new primitives: (1) One-to-one commitments, and (2) Continuous Non-Malleable Randomness Encoders, which may be of independent interest.

We construct efficient non-malleable codes (NMC) that are (computationally) secure against tampering by functions computable in any fixed polynomial time. Our construction is in the plain (no-CRS) model and requires the assumptions that (1) $$\mathbf {E}$$E is hard for $$\mathbf {NP}$$NP circuits of some exponential $$2^{\beta n}$$2βn ($$\beta >0$$β>0) size (widely used in the derandomization literature), (2) sub-exponential trapdoor permutations exist, and (3) $$\mathbf {P}$$P-certificates with sub-exponential soundness exist.While it is impossible to construct NMC secure against arbitrary polynomial-time tampering (Dziembowski, Pietrzak, Wichs, ICS ’10), the existence of NMC secure against $$O(n^c)$$O(nc)-time tampering functions (for any fixedc), was shown (Cheraghchi and Guruswami, ITCS ’14) via a probabilistic construction. An explicit construction was given (Faust, Mukherjee, Venturi, Wichs, Eurocrypt ’14) assuming an untamperable CRS with length longer than the runtime of the tampering function. In this work, we show that under computational assumptions, we can bypass these limitations. Specifically, under the assumptions listed above, we obtain non-malleable codes in the plain model against $$O(n^c)$$O(nc)-time tampering functions (for any fixed c), with codeword length independent of the tampering time bound.Our new construction of NMC draws a connection with non-interactive non-malleable commitments. In fact, we show that in the NMC setting, it suffices to have a much weaker notion called quasi non-malleable commitments—these are non-interactive, non-malleable commitments in the plain model, in which the adversary runs in $$O(n^c)$$O(nc)-time, whereas the honest parties may run in longer (polynomial) time. We then construct a 4-tag quasi non-malleable commitment from any sub-exponential OWF and the assumption that $$\mathbf {E}$$E is hard for some exponential size $$\mathbf {NP}$$NP-circuits, and use tag amplification techniques to support an exponential number of tags.

Oblivious RAM (ORAM) is a cryptographic primitive that allows a trusted CPU to securely access untrusted memory, such that the access patterns reveal nothing about sensitive data. ORAM is known to have broad applications in secure processor design and secure multiparty computation for big data. Unfortunately, due to a logarithmic lower bound by Goldreich and Ostrovsky (J ACM 43(3):431–473, 1996 ), ORAM is bound to incur a moderate cost in practice. In particular, with the latest developments in ORAM constructions, we are quickly approaching this limit, and the room for performance improvement is small. In this paper, we consider new models of computation in which the cost of obliviousness can be fundamentally reduced in comparison with the standard ORAM model. We propose the oblivious network RAM model of computation, where a CPU communicates with multiple memory banks, such that the adversary observes only which bank the CPU is communicating with, but not the address offset within each memory bank. In other words, obliviousness within each bank comes for free—either because the architecture prevents a malicious party from observing the address accessed within a bank, or because another solution is used to obfuscate memory accesses within each bank—and hence we only need to obfuscate communication patterns between the CPU and the memory banks. We present new constructions for obliviously simulating general or parallel programs in the network RAM model. We describe applications of our new model in distributed storage applications with a network adversary.

The literature on leakage-resilient cryptography contains various leakage models that provide different levels of security. In the bounded leakage model (Akavia et al.—TCC 2009 ), it is assumed that there is a fixed upper bound L on the number of bits the attacker may leak on the secret key in the entire lifetime of the scheme. Alternatively, in the continual leakage model (Brakerski et al.—FOCS 2010 , Dodis et al.—FOCS 2010 ), the lifetime of a cryptographic scheme is divided into “time periods” between which the scheme’s secret key is updated. Furthermore, in its attack the adversary is allowed to obtain some bounded amount of leakage on the current secret key during each time period. In the continual leakage model, a challenging problem has been to provide security against leakage on key updates , that is, leakage that is a function of not only the current secret key but also the randomness used to update it. We propose a modular approach to overcome this problem based on program obfuscation. Namely, we present a compiler that transforms any public key encryption or signature scheme that achieves a slight strengthening of continual leakage resilience, which we call consecutive continual leakage resilience, to one that is continual leakage resilient with leakage on key updates, assuming indistinguishability obfuscation (Barak et al.—CRYPTO 2001 , Garg et al.—FOCS 2013 ). Under stronger forms of obfuscation, the leakage rate tolerated by our compiled scheme is essentially as good as that of the starting scheme. Our compiler is derived by making a connection between the problems of leakage on key updates and so-called sender-deniable encryption (Canetti et al.—CRYPTO 1997 ), which was recently constructed based on indistinguishability obfuscation by Sahai and Waters (STOC 2014 ). In the bounded leakage model, we give an approach to constructing leakage-resilient public key encryption from program obfuscation based on the public key encryption scheme of Sahai and Waters (STOC 2014 ). In particular, we achieve leakage-resilient public key encryption tolerating L bits of leakage for any L from $${\mathsf {iO}} $$ iO and one-way functions. We build on this to achieve leakage-resilient public key encryption with optimal leakage rate of $$1-o(1)$$ 1 - o ( 1 ) based on stronger forms of obfuscation and collision-resistant hash functions. Such a leakage rate is not known to be achievable in a generic way based on public key encryption alone. We then develop additional techniques to construct public key encryption that is (consecutive) continual leakage resilient under appropriate assumptions, which we believe is of independent interest.

A recent line of work has explored the use of physically unclonable functions (PUFs) for secure computation, with the goals of (1) achieving universal composability without additional setup and/or (2) obtaining unconditional security (i.e., avoiding complexity-theoretic assumptions). Initial work assumed that all PUFs, even those created by an attacker, are honestly generated. Subsequently, researchers have investigated models in which an adversary can create malicious PUFs with arbitrary behavior. Researchers have considered both malicious PUFs that might be stateful , as well as malicious PUFs that can have arbitrary behavior but are guaranteed to be stateless . We settle the main open questions regarding secure computation in the malicious-PUF model: We prove that unconditionally secure oblivious transfer is impossible, even in the stand-alone setting, if the adversary can construct (malicious) stateful PUFs. We show that if the attacker is limited to creating (malicious) stateless PUFs, then universally composable two-party computation is possible, unconditionally.

In a recent result, Dachman-Soled et al. (TCC ’15) proposed a new notion called locally decodable and updatable non-malleable codes, which informally, provides the security guarantees of a non-malleable code while also allowing for efficient random access. They also considered locally decodable and updatable non-malleable codes that are leakage-resilient, allowing for adversaries who continually leak information in addition to tampering.The bounded retrieval model (BRM) (cf. Alwen et al. (CRYPTO ’09) and Alwen et al. (EUROCRYPT ’10)) has been studied extensively in the setting of leakage resilience for cryptographic primitives. This threat model assumes that an attacker can learn information about the secret key, subject only to the constraint that the overall amount of leaked information is upper bounded by some value. The goal is then to construct cryptosystems whose secret key length grows with the amount of leakage, but whose runtime (assuming random access to the secret key) is independent of the leakage amount.In this work, we combine the above two notions and construct local non-malleable codes in the split-state model, that are secure against bounded retrieval adversaries. Specifically, given leakage parameter $$\ell $$ℓ, we show how to construct an efficient, 3-split-state, locally decodable and updatable code (with CRS) that is secure against one-time leakage of any polynomial time, 3-split-state leakage function whose output length is at most $$\ell $$ℓ, and one-time tampering via any polynomial-time 3-split-state tampering function. The locality we achieve is polylogarithmic in the security parameter.