International Association
for Cryptologic Research

We show how to obfuscate a large and expressive class of programs, which we call compute-and-compare programs, under the learning-with-errors (LWE) assumption. Each such program $CC[f,y]$ is parametrized by an arbitrary polynomial-time computable function $f$ along with a target value $y$ and we define $CC[f,y](x)$ to output $1$ if $f(x)=y$ and $0$ otherwise. In other words, the program performs an arbitrary computation $f$ and then compares its output against a target $y$. Our obfuscator satisfies distributional virtual-black-box security, which guarantees that the obfuscated program does not reveal any partial information about the function $f$ or the target value $y$ as long as they are chosen from some distribution where $y$ has sufficient pseudo-entropy given $f$. We also extend our result to multi-bit compute-and-compare programs $MBCC[f,y,z](x)$ which output a message $z$ if $f(x)=y$.

Compute-and-compare programs are powerful enough to capture many interesting obfuscation tasks as special cases. This includes obfuscating conjunctions, and therefore we improve on the prior work of Brakerski et al. (ITCS '16) which constructed a conjunctions obfuscator under a non-standard ``entropic'' ring-LWE assumption, while here we obfuscate a significantly broader class of programs under standard LWE. We show that our obfuscator has several interesting applications. For example, we can take an arbitrary encryption scheme and publish an obfuscated plaintext equality tester that allows users to test whether a ciphertext encrypts some target value $y$; as long as $y$ has sufficient pseudo-entropy this will not harm semantic security. We can also use our obfuscator to generically upgrade attribute-based encryption to predicate encryption as well as witness encryption to indistinguishability obfuscation which is secure for all null circuits. Furthermore, we show that our obfuscator gives new circular-security counter-examples for public-key bit encryption and for unbounded length key cycles.

Our result uses the graph-induced multi-linear maps of Gentry, Gorbunov and Halevi (TCC '15), but only in a carefully restricted manner which is provably secure under LWE. Our technique is inspired by ideas introduced in a recent work of Goyal, Koppula and Waters (EUROCRYPT '17) in a seemingly unrelated context.

We propose simple generic constructions of indistinguishability obfuscator (IO). Our key tool is exponentially-efficient indistinguishability obfuscator (XIO), which is the same as IO except that the size of an obfuscated circuit (or the running-time of an obfuscator) is slightly smaller than that of a brute-force canonicalizer that outputs the entire truth table of a circuit to be obfuscated. A ``compression factor'' of XIO indicates how much XIO compresses the brute-force canonicalizer. In this study, we show that XIO is a powerful enough to achieve cutting-edge cryptography. In particular, we propose the following constructions:

1. A single-key weakly succinct secret-key functional encryption (SKFE) scheme is constructed from XIO (even with a bad compression factor) and one-way function. 2. A single-key weakly succinct public-key functional encryption (PKFE) scheme is constructed from XIO with a good compression factor and public-key encryption scheme. 3. A single-key weakly succinct PKFE scheme is constructed from XIO (even with a bad compression factor) and identity-based encryption scheme.

It is known that sub-exponentially secure single-key weakly succinct PKFE scheme implies IO and that single-key weakly succinct (resp. multi-key non-succinct) SKFE implies XIO with a bad (resp. good) compression factor. Thus, we developed two methods of constructing IO. One uses multi-key SKFE and plain public-key encryption schemes and the other uses single-key weakly succinct SKFE (or XIO) and identity-based encryption schemes. It is not known whether single-key weakly succinct SKFE implies IO (if we use fully black-box reduction in a certain model, it is impossible), but our single-key weakly succinct SKFE scheme gives many interesting by-products.

In this paper we introduce the notion of lockable obfuscation. In a lockable obfuscation scheme there exists an obfuscation algorithm $\mathsf{Obf}$ that takes as input a security parameter $\lambda$, a program $P$, a message $\mathsf{msg}$ and ``lock value'' $\alpha$ and outputs an obfuscated program $\widetilde{P}$. One can evaluate the obfuscated program $\widetilde{P}$ on any input $x$ where the output of evaluation is the message $\mathsf{msg}$ if $P(x) = \alpha$ and otherwise receives a rejecting symbol $\perp$.

We proceed to provide a construction of lockable obfuscation and prove it secure under the Learning with Errors (LWE) assumption. Notably, our proof only requires LWE with polynomial hardness and does not require complexity leveraging.

We follow this by describing multiple applications of lockable obfuscation. First, we show how to transform any attribute-based encryption (ABE) scheme into one in which the attributes used to encrypt the message are hidden from any user that is not authorized to decrypt the message. (Such a system is also know as predicate encryption with one-sided security.) The only previous construction due to Gorbunov, Vaikuntanathan and Wee is based off of a specific ABE scheme of Boneh et al. By enabling the transformation of any ABE scheme we can inherent different forms and features of the underlying scheme such as: multi-authority, adaptive security from polynomial hardness, regular language policies, etc.

We also show applications of lockable obfuscation to separation and uninstantiability results. We first show how to create new separation results in circular encryption that were previously based on indistinguishability obfuscation. This results in new separation results from learning with error including a public key bit encryption scheme that it IND-CPA secure and not circular secure. The tool of lockable obfuscation allows these constructions to be almost immediately realized by translation from previous indistinguishability obfuscation based constructions. In a similar vein we provide random oracle uninstantiability results of the Fujisaki-Okamoto transformation (and related transformations) from the lockable obfuscation combined with fully homomorphic encryption. Again, we take advantage that previous work used indistinguishability obfuscation that obfuscated programs in a form that could easily be translated to lockable obfuscation.

Non-malleable commitment is a fundamental cryptographic tool for preventing man-in-the-middle attacks. Since its proposal by Dolev, Dwork, and Noar in 1991, a rich line of research has steadily reduced the number of communication rounds needed for non-malleable commitment, towards the ultimate goal of constructing non-interactive non-malleable commitment from well-studied hardness assumptions. However, this successful research recently hit a barrier: Pass showed that 2-round non-malleable commitment cannot be based on any, even subexponentially secure, falsifiable assumptions, via black-box security reductions [Pass, STOC 2011], and the only known construction of non-interactive non-malleable commitment is based on a new and non-falsifiable assumption [Pandey, Pass, Vaikuntanathan, Crypto 2008].

In this work, we present a construction of 2-round non-malleable commitment from time-lock puzzles; they are "mechanisms for sending messages to the future" proposed by Rivest, Shamir, and Wagner in 1996, whose original construction has withstood cryptanalysis for two decades. In addition, our construction uses a subexponentially secure injective one-way function and a non-interactive witness indistinguishable proof system. The key to circumventing Pass's impossibility result lies in leveraging the different nature of hardness provided by time-lock puzzles and classical cryptographic primitives. Conventionally, cryptographic hardness is defined against adversaries with bounded time (or equivalently circuit-size); in contrast, the hardness of time-lock puzzles holds against adversaries with bounded parallel-time (or circuit-depth). This difference allows us to construct commitment schemes that are simultaneously harder than each other according to different complexity measures, which imply a weak form of non-malleability. It is then strengthened through a new 2-round non-malleability amplification technique, and the final protocol is non-malleable even in the fully concurrent setting.

To the best of our knowledge, this is the first time that time-lock puzzles are used constructively outside time-released cryptography, and opens an interesting direction of combining hardness w.r.t. different complexity measures for achieving cryptographic goals.

In leakage-resilient symmetric cryptography, two important concepts have been proposed in order to decrease the success rate of differential side-channel attacks. The first one is to limit the attacker’s data complexity by restricting the number of observable inputs; the second one is to create correlated algorithmic noise by using parallel S-boxes with equal inputs. The latter hinders the typical divide and conquer approach of differential side-channel attacks and makes key recovery much more difficult in practice. The use of localized electromagnetic (EM) measurements has already been shown to limit the effectiveness of such measures in previous works based on PRESENT S-boxes and 90nm FPGAs. However, it has been left for future investigation in recent publications based on AES S-boxes. We aim at providing helpful results and insights from LDA-preprocessed, multivariate, localized EM attacks against a 45nm FPGA implementation using AES S-boxes. We show, that even in the case of densely placed S-boxes (with identical routing constraints), and even when limiting the data complexity to the minimum of only two inputs, the guessing entropy of the key is reduced to only 2^48 , which remains well within the key enumeration capabilities of today’s adversaries. Relaxing the S-box placement constraints further reduces the guessing entropy. Also, increasing the data complexity for efficiency, decreases it down to a direct key recovery. While our results are empirical and reflective of one device and implementation, they emphasize the threat of multivariate localized EM attacks to such AES-based leakage-resilient constructions, more than currently believed.

Masking is an effective countermeasure against side-channel attacks. In this paper, we improve the efficiency of the high-order masking of look-up tables countermeasure introduced at Eurocrypt 2014, based on a combination of three techniques, and still with a proof of security in the Ishai-Sahai-Wagner (ISW) probing model. The first technique consists in proving security under the stronger t-SNI definition, which enables to use n=t+1 shares instead of n=2t+1 against t-th order attacks. The second technique consists in progressively incrementing the number of shares within the countermeasure, from a single share to n, thereby reducing the complexity of the countermeasure. The third technique consists in adapting the common shares approach introduced by Coron et al. at CHES 2016, so that half of a randomized look-up table can be pre-computed for multiple SBoxes. When combined, our three techniques lead to a factor 10.7 improvement in efficiency, asymptotically for a large number of shares n. For a practical implementation with a reasonable number of shares, we get a 4.8 speed-up factor compared to the initial countermeasure for AES.

Rational proofs, introduced by Azar and Micali (STOC 2012), are a variant of interactive proofs in which the prover is rational, and may deviate from the protocol for increasing his reward. Guo et al.\ (ITCS 2014) demonstrated that rational proofs are relevant to delegation of computation. By restricting the prover to be computationally bounded, they presented a one-round delegation scheme with sublinear verification for functions computable by log-space uniform circuits with logarithmic depth. In this work, we study rational proofs in which the verifier is also rational, and may deviate from the protocol for decreasing the prover's reward. We construct a three-message delegation scheme with sublinear verification for functions computable by log-space uniform circuits with polylogarithmic depth in the random oracle model.

Side channel analysis and fault attacks are two powerful methods to analyze and break cryptographic implementations. Recently, secure multiparty computation has been applied to prevent side channel attacks. While multiparty computation is known to be fault resistant as well, the particular schemes popular for side channel protection do not currently offer this feature. In this paper we introduce a new secure multiparty circuit to prevent both fault attacks and side channel analysis. The new scheme builds on an existing side channel countermeasure and extends it to preserve errors and propagate them until the end of the circuit. A new recombination operation ensures randomization of the output in the case of an error, ensuring that nothing can be learned from the faulty output. After introducing the new secure multiparty circuit, we show how it can be applied to AES and present the performance and security analysis.

Sanitizable signatures, introduced by Ateniese et al. (ESORICS '05), allow the signer to delegate the sanitization right of signed messages. The sanitizer can modify the message and update the signature accordingly, so that the sanitized part of the message is kept private. For a stronger protection of sensitive information, it is desirable that no one can link sanitized message-signature pairs of the same document. This idea was formalized by Brzuska et al. (PKC '10) as unlinkability, which was followed up recently by Fleischhacker et al. (PKC '16). Unfortunately, the existing generic constructions of sanitizable signatures, unlinkable or not, are based on building blocks with specially crafted features of which efficient (standard model) instantiations are absent. Basing on existing primitives or a conceptually simple primitive is more desirable.

In this work, we present two such generic constructions, leading to efficient instantiations in the standard model. The first one is based on rerandomizable tagging, a new primitive which may find independent interests. It captures the core accountability mechanism of sanitizable signatures. The second one is based on accountable ring signatures (CARDIS '04, ESORICS '15). As an intermediate result, we propose the first accountable ring signature scheme in the standard model.

Recently, gray-box attacks on white-box cryptographic implementations have succeeded. These attacks are more efficient than white-box attacks because they can be performed without detailed knowledge of the target implementation. The success of the gray-box attack is due to the unbalanced encoding used to generate the white-box lookup table. In this paper, we propose a method to protect the gray-box attack against white-box implementations. The basic idea is to use Boolean masking before encoding intermediate values during the white-box lookup table generation. Compared to the existing white-box AES implementation, the lookup table size and the table lookups increase by about 1.5- and 1.6 times, respectively.

Polytopic cryptanalysis was introduced at EUROCRYPT 2016 as a cryptanalytic technique for low-data-complexity attacks on block ciphers. In this paper, we give an account of how the technique was developed, quickly go over the basic ideas and techniques of polytopic cryptanalysis, look into how the technique differs from previously existing cryptographic techniques, and discuss whether the attack angle can be useful for developing improved cryptanalytic techniques.

This paper puts forward an efficient broadcast encryption in public key setting employing ternary tree subset difference method for revocation. It provides outsider anonymity disabling the revoked users from getting any information of message and concealing the set of subscribed users from the revoked users. Our approach utilizes composite order bilinear group setting and exhibits significant improvement in the broadcast efficiency. The proposed scheme compares favourably over the existing similar schemes in standard model. The public key and secret key sizes are poly-logarithmic while the ciphertext size is sub linear in total number of users. Our scheme achieves selective security against chosen plaintext attack in the standard model under reasonable assumptions.

In the RFC 7748 memorandum, the Internet Research Task Force specified a Montgomery ladder scalar multiplication function based on two recently proposed prime elliptic curves. The purpose of this function is to support the Diffie-Hellman key exchange algorithm included in the coming version of the Transport Layer Security cryptographic protocol. In this paper, we introduce a Montgomery-ladder variant that permits to accelerate the fixed-point multiplication function when applied in the Diffie-Hellman key pair generation step. Our function combines a right-to-left variant of the Montgomery ladder with the pre-computation of multiples of the base point, and by requiring very modest memory resources and a small implementation effort with respect to the RFC 7748 programming code, it obtains significant performance improvements on desktop architectures. To our knowledge, this is the first proposal of a Montgomery ladder procedure for prime elliptic curves that admits the extensive use of pre-computation.

We solve the problem of finding the success rate of an optimal side-channel attack targeting at once the first and the last round of a block cipher. We relate the results to the properties of the direct and inverse substitution boxes (when they are bijective), in terms of confusion coefficients.

Most modern actively secure multiparty computation protocols make use of a function and input independent pre-processing phase. This pre-processing phase is tasked with producing some form of correlated randomness and distributing it to the parties. Whilst the “online” phase of such protocols is exceedingly fast, the bottleneck comes in the pre-processing phase. In this paper we examine situations where the computing parties in the online phase may want to outsource the pre-processing phase to another set of parties, or to a sub-committee. We examine how this can be done, and also describe situations where this may be a benefit.

Side-channel attacks represent a powerful category of attacks against cryptographic devices. Still, side-channel analysis for lightweight ciphers is much less investigated than for instance for AES. Although intuition may lead to the conclusion that lightweight ciphers are weaker in terms of side-channel resistance, that remains to be confirmed and quantified. In this paper, we consider various side-channel analysis metrics which should provide an insight on the resistance of lightweight ciphers against side-channel attacks. In particular, for the non-profiled scenario we use the theoretical confusion coefficient and empirical correlation power analysis. Furthermore, we conduct a profiled side-channel analysis using various machine learning attacks on PRESENT and AES. Our results show that the difference between AES and lightweight ciphers is smaller than one would expect. Interestingly, we observe that the studied 4-bit S-boxes have a different side-channel resilience, while the difference in the 8-bit ones is only theoretically present.

This paper explores a new type of MACs called message-recovery MACs (MRMACs). MRMACs have an additional input $R$ that gets recovered upon verification. Receivers must execute verification in order to recover $R$, making the verification process unskippable. Such a feature helps avoid mis-implementing verification algorithms. The syntax and security notions of MRMACs are rigorously formulated. In particular, we formalize the notion of unskippability and present a construction of an unskippable MRMAC from a tweakable cipher and a universal hash function. Our construction is provided with formal security proofs. We extend the idea of MRMACs to a new type of authenticated encryption called verification-unskippable AE (VUAE). We propose a generic Enc-then-MRMAC composition which realizes VUAE. The encryption part needs to satisfy a new security notion called one-time undecipherability. We provide three constructions that are one-time undecipherable, and they are proven secure under various security models.

Sampling integers with Gaussian distribution is a fundamental problem that arises in almost every application of lattice cryptography, and it can be both time consuming and challenging to implement. Most previous work has focused on the optimization and implementation of integer Gaussian sampling in the context of specific applications, with fixed sets of parameters. We present new algorithms for discrete Gaussian sampling that are both generic (application independent), efficient, and more easily implemented in constant time without incurring a substantial slow-down, making them more resilient to side-channel (e.g., timing) attacks. As an additional contribution, we present new analytical techniques that can be used to simplify the precision/security evaluation of floating point cryptographic algorithms, and an experimental comparison of our algorithms with previous algorithms from the literature.

We give a polynomial-time quantum reduction from worst-case (ideal) lattice problems directly to the decision version of (Ring-)LWE. This extends to decision all the worst-case hardness results that were previously known for the search version, for the same or even better parameters and with no algebraic restrictions on the modulus or number field. Indeed, our reduction is the first that works for decision Ring-LWE with any number field and any modulus.

We formally define and give the first construction of (leveled) threshold fully homomorphic encryption for any access structure induced by a monotone boolean formula and in particular for the threshold access structure. Our construction is based on the learning with errors assumption and can be instantiated with any existing homomorphic encryption scheme that satisfies fairly general conditions, such as Gentry, Sahai, Waters (CRYPTO 2013) and Brakerski, Gentry, Vaikuntanathan (ITCS 2012).

From threshold homomorphic encryption, we construct function secret sharing and distributed pseudorandom functions for the aforementioned access structures. No such constructions were known prior to this work.