In this article we present the BB84 quantum key distribution scheme from two perspectives. First, we provide a theoretical discussion of the steps Alice and Bob take to reach a shared secret using this protocol, while an eavesdropper Eve is either involved or not. Then, we offer and discuss two distinct implementations that simulate BB84 using IBM’s Qiskit framework, the first being an exercise solved during the “IBM Quantum Challenge” event in early May 2020, while the other was developed independently to showcase the intercept-resend attack strategy in detail. We note the latter’s scalability and increased output verbosity, which allow for a statistical analysis to determine the probability of detecting the act of eavesdropping.

The tight security bound of the Key-Alternating Cipher (KAC) construction whose round permutations are independent from each other has been well studied. Then a natural question is how the security bound will change when we use fewer permutations in a KAC construction. In CRYPTO 2014, Chen et al. proved that 2-round KAC with a single permutation (2KACSP) has the same security level as the classic one (i.e., 2-round KAC). But we still know little about the security bound of incompletely-independent KAC constructions with more than 2 rounds. In this paper,we will show that a similar result also holds for 3-round case. More concretely, we prove that 3-round KAC with a single permutation (3KACSP) is secure up to $\varTheta(2^{\frac{3n}{4}})$ queries, which also caps the security of 3-round KAC. To avoid the cumbersome graphical illustration used in Chen et al.'s work, a new representation is introduced to characterize the underlying combinatorial problem. Benefited from it, we can handle the knotty dependence in a modular way, and also show a plausible way to study the security of $r$KACSP. Technically, we abstract a type of problems capturing the intrinsic randomness of $r$KACSP construction, and then propose a high-level framework to handle such problems. Furthermore, our proof techniques show some evidence that for any $r$, $r$KACSP has the same security level as the classic $r$-round KAC in random permutation model.

In this paper we present an analysis of the SpoC cipher, a second round candidate of the NIST Lightweight Crypto Standardization process. First we present a differential analysis on the sLiSCP-light permutation, a core element of SpoC. Then we propose a series of attacks on both versions of SpoC, namely round-reduced differential tag forgery and message recovery attacks, as well as a time-memory trade-off key-recovery attack on the full round version of Spoc-64. Finally, we present an observation regarding the constants used in the sLiSCP-light permutation. To the best of our knowledge, this paper represents the first third-party analysis on both SpoC cipher and the sLiSCP-light permutation.

Studying the security and efficiency of blind signatures is an important goal for privacy sensitive applications. In particular, for large-scale settings (e.g., cryptocurrency tumblers), it is important for schemes to scale well with the number of users in the system. Unfortunately, all practical schemes either 1) rely on (very strong) number theoretic hardness assumptions and/or computationally expensive pairing operations over bilinear groups, or 2) support only a polylogarithmic number of concurrent (i.e., arbitrarily interleaved) signing sessions per public key. In this work, we revisit the security of two pairing-free blind signature schemes in the Algebraic Group Model (AGM) + Random Oracle Model (ROM). Concretely, 1. We consider the security of Abe’s scheme (EUROCRYPT ‘01), which is known to have a flawed proof in the plain ROM. We adapt the scheme to allow a partially blind variant and give a proof of the new scheme under the discrete logarithm assumption in the AGM+ROM, even for (polynomially many) concurrent signing sessions. 2. We then prove that the popular blind Schnorr scheme is secure under the one-more discrete logarithm assumption if the signatures are issued sequentially. While the work of Fuchsbauer et al. (EUROCRYPT ‘20) proves the security of the blind Schnorr scheme for concurrent signing sessions in the AGM+ROM, its underlying assumption, ROS, is proven false by Benhamouda et al. (EUROCRYPT‘21) when more than polylogarithmically many signatures are issued. Given the recent progress, we present the first security analysis of the blind Schnorr scheme in the slightly weaker sequential setting. We also show that our security proof reduces from the weakest possible assumption, with respect to known reduction techniques.

Let $\mathbb{F}_{\!q}$ be a finite field and $E_b\!: y^2 = x^3 + b$ be an ordinary elliptic $\mathbb{F}_{\!q}$-curve of $j$-invariant $0$ such that $\sqrt{b} \in \mathbb{F}_{\!q}$. In particular, this condition is fulfilled for the curve BLS12-381 and for one of sextic twists of the curve BW6-761 (in both cases $b=4$). These curves are very popular in pairing-based cryptography. The article provides an efficient constant-time encoding $h\!: \mathbb{F}_{\!q} \to E_b(\mathbb{F}_{\!q})$ of an absolutely new type for which $q/6 \leqslant \#\mathrm{Im}(h)$. We prove that at least for $q \equiv 4 \ (\mathrm{mod} \ 9)$ the hash function $H\!: \{0,1\}^* \to E_b(\mathbb{F}_{\!q})$ induced by $h$ is indifferentiable from a random oracle. The main idea of our encoding consists in extracting in $\mathbb{F}_{\!q}$ (for $q \equiv 1 \ (\mathrm{mod} \ 3)$) a cubic root instead of a square root as in the well known (universal) SWU encoding and in its simplified analogue. Besides, the new hashing can be implemented without quadratic and cubic residuosity tests (as well as without inversions) in $\mathbb{F}_{\!q}$. Thus in addition to the protection against timing attacks, $H$ is much more efficient than the SWU hash function, which generally requires to perform $4$ quadratic residuosity tests in $\mathbb{F}_{\!q}$. For instance, in the case of BW6-761 this allows to avoid approximately $4 \!\cdot\! 761 \approx 3000$ field multiplications.

We address the problem of constructing zkSNARKs whose SRS is $\mathit{universal}$ – valid for all relations within a size-bound – and $\mathit{updatable}$ – a dynamic set of participants can add secret randomness to it indefinitely thus increasing confidence in the setup. We investigate formal frameworks and techniques to design efficient universal updatable zkSNARKs with linear-size SRS and their commit-and-prove variants. We achieve a collection of zkSNARKs with different tradeoffs. One of our constructions achieves the smallest proof size and proving time compared to the state of art for proofs for arithmetic circuits. The language supported by this scheme is a variant of R1CS, called R1CS-lite, introduced by this work. Another of our constructions supports directly standard R1CS and improves on previous work achieving the fastest proving time for this type of constraint systems. We achieve this result via the combination of different contributions: (1) a new algebraically-flavored variant of IOPs that we call $\mathit{Polynomial}$ $\mathit{Holographic}$ $\mathit{IOPs}$ (PHPs), (2) a new compiler that combines our PHPs with $\mathit{commit}$-$\mathit{and}$-$\mathit{prove}$ $\mathit{\ zkSNARKs}$ for committed polynomials, (3) pairing-based realizations of these CP-SNARKs for polynomials, (4) constructions of PHPs for R1CS and R1CS-lite, (5) a variant of the compiler that yields a commit-and-prove universal zkSNARK.

Private Information Retrieval (PIR) is one of the promising techniques to preserve user privacy in the presence of trusted-but- curious servers. The information-theoretically private query construction assures the highest user privacy over curious and unbounded computation servers. Therefore, the need for information-theoretic private retrieval was fulfilled by various schemes in a variety of PIR settings. To augment previous work, we propose a combination of new bit connection methods called rail-shape and signal-shape and new quadratic residuosity assumption based family of trapdoor functions for generic single database Private Block Retrieval (PBR). The main goal of this work is to show that the possibility of mapping from computationally bounded privacy to information-theoretic privacy or vice-versa in a single database setting using newly constructed bit connection and trapdoor function combinations. The proposed bit connection and trapdoor function combinations have achieved the following results. • Single Database information-theoretic PBR (SitPBR): The proposed combinations are used to construct SitPBR in which the user privacy is preserved through the generation of information-theoretic queries and data privacy is preserved using quadratic residuosity assumption. • Single Database computationally bounded PBR (ScPBR): The proposed combinations are used to construct ScPBR in which both user privacy and data privacy are preserved using a well-known intractability assumption called quadratic residuosity assumption. • Map(SitPBR)→ScPBR: The proposed combinations can be used to transform (or map) SitPBR into ScPBR scheme by choosing appropriate function parameters. • Map(ScPBR)→SitPBR: The proposed combinations can be used to transform (or map) ScPBR into SitPBR scheme by choosing appropriate function parameters. All the proposed schemes are single round, memoryless and plain database schemes (at their basic constructions).

This paper presents a constant time hardware implementation of the NIST round 2 post-quantum cryptographic algorithm Streamlined NTRU Prime. We implement the entire KEM algorithm, including all steps for key generation, encapsulation and decapsulation, and all en- and decoding. We focus on optimizing the resources used, as well as applying optimization and parallelism available due to the hardware design. We show the core en- and decapsulation requires only a fraction of the total FPGA fabric resource cost, which is dominated by that of the hash function, and the en- and decoding algorithm. For the NIST Security Level 3, our implementation uses a total of 1841 slices on a Xilinx Zynq Ultrascale+ FPGA, together with 14 BRAMs and 19 DSPs. The maximum achieved frequency is 271 MHz, at which the key generation, encapsulation and decapsulation take 4808 μs, 524 μs and 958 μs respectively. To our knowledge, this work is the first full hardware implementation where the entire algorithm is implemented.

In this work, we propose different techniques that can be used to implement the ROLLO, and partially RQC, family of algorithms in a standalone, efficient and constant time library. For simplicity, we focus our attention on one specific instance of this family, ROLLO-I-128. For each of these techniques, we present explicit code (with intrinsics when required), or pseudo-code and performance measures to show their impact. More precisely, we use a combination of original and known results and describe procedures for Gaussian reduction of binary matrices, generation of vectors of given rank, multiplication with lazy reduction and inversion of polynomials in a composite Galois field. We also carry out a global performance analysis to show the impact of these improvements on ROLLO-I-128. Through the SUPERCOP framework, we compare it to other 128-bit secure KEMs in the NIST competition. To our knowledge, this is the first optimized full constant time implementation of ROLLO-I-128.

Side-channel attacks based on machine learning have recently been introduced to recover the secret information from software and hardware implementations of mathematically secure algorithms. Convolutional Neural Networks (CNNs) have proven to outperform the template attacks due to their ability of handling misalignment in the symmetric algorithms leakage data traces. However, one of the limitations of deep learning algorithms is the requirement of huge datasets for model training. For evaluation scenarios, where limited leakage trace instances are available, simple machine learning with the selection of proper feature engineering, data splitting, and validation techniques, can be more effective. Moreover, limited analysis exists for public-key algorithms, especially on non-traditional implementations like those using Residue Number System (RNS). Template attacks are successful on RNS-based Elliptic Curve Cryptography (ECC), only if the aligned portion is used in templates. In this study, we present a systematic methodology for the evaluation of ECC cryptosystems with and without countermeasures against machine learning side-channel attacks using two attack models. RNS-based ECC datasets have been evaluated using four machine learning classifiers and comparison is provided with existing state-of-the-art template attacks. Moreover, we analyze the impact of raw features and advanced hybrid feature engineering techniques, along with the effect of splitting ratio. We discuss the metrics and procedures that can be used for accurate classification on the imbalance datasets. The experimental results demonstrate that, for ECC RNS datasets, the efficiency of simple machine learning algorithms is better than the complex deep learning techniques when such datasets are not so huge.

I describe a non-interactive transaction scheme for Mimblewimble protocol, so as to overcome the usability issue of the Mimblewimble wallet. With the Diffie–Hellman, we can use an Ephemeral Key shared between the sender and the receiver, a public nonce R is added to the output for that, removing the interactive cooperation procedure. And an additional one-time public key P' is used to lock the output to make it only spendable for the receiver, i.e. the owner of P'. Furtherly, to keep Mimblewimble privacy character, the Stealth Address is used in this new transaction scheme.

This paper constructs unbounded simulation sound proofs for boolean circuit satisfiability under standard assumptions with proof size O(n+d) bilinear group elements, where d is the depth and n is the input size of the circuit. Our technical contribution is to add unbounded simulation soundness to a recent NIZK of González and Ràfols (ASIACRYPT'19) with very small overhead. We give two different constructions: the first one is more efficient but not tight, and the second one is tight. Our new scheme can be used to construct Signatures of Knowledge based on standard assumptions that also can be composed universally with other cryptographic protocols/primitives. As an independent contribution we also detail a simple formula to encode Boolean circuits as Quadratic Arithmetic Programs.

We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our implementation provides the means to assess with precision the scaling of the number of gates and depth of a full-fledged quantum circuit designed to find the preimages of a given hash digest. The detailed construction of the quantum oracle shows that the presence of AND gates, OR gates, shifts of bits and the reuse of the initial state along the computation, require extra quantum resources as compared with other hash functions based on modular additions, XOR gates and rotations. We also track the entanglement entropy present in the quantum register at every step along the computation, showing that it becomes maximal at the inner core of the first action of the quantum oracle, which implies that no classical simulation based on Tensor Networks would be of relevance. Finally, we show that strategies that suggest a shortcut based on sampling the quantum register after a few steps of Grover's algorithm can only provide some marginal practical advantage in terms of error mitigation.

In the conference “Fast Software Encryption 2015”, a new line of research was proposed by introducing the first small-state stream cipher (SSC). The goal was to design lightweight stream ciphers for hardware application by going beyond the rule that the internal state size must be at least twice the intended security level. Time-memory-data trade-off (TMDTO) attacks and fast correlation attacks (FCA) were successfully applied to all proposed SSCs which can be implemented by less than 1000 gate equivalents in hardware. It is possible to increase the security of stream ciphers against FCA by exploiting more complicated functions for the nonlinear feedback shift register and the output function, but we use lightweight functions to design the lightest SSC in the world while providing more security against FCA. Our proposed cipher provides 80-bit security against TMDTO distinguishing attacks, while Lizard and Plantlet provide only 60-bit and 58-bit security against distinguishing attacks, respectively. Our main contribution is to propose a lightweight round key function with a very long period that increases the security of SSCs against FCA.

Circular security is the most elementary form of key-dependent message (KDM) security, which allows us to securely encrypt only a copy of secret key bits. In this work, we show that circular security is complete for KDM security in the sense that an encryption scheme satisfying this security notion can be transformed into one satisfying KDM security with respect to all functions computable by a-priori bounded-size circuits (bounded-KDM security). This result holds in the presence of any number of keys and in any of secret-key/public-key and CPA/CCA settings. Such a completeness result was previously shown by Applebaum (EUROCRYPT 2011) for KDM security with respect to projection functions (projection-KDM security) that allows us to securely encrypt both a copy and a negation of secret key bits. Besides amplifying the strength of KDM security, our transformation in fact can start from an encryption scheme satisfying circular security against CPA attacks and results in one satisfying bounded-KDM security against CCA attacks. This result improves the recent result by Kitagawa and Matsuda (TCC 2019) showing a CPA-to-CCA transformation for KDM secure public-key encryption schemes.

When generating primes $p$ and $q$ for an RSA key, the algorithm specifies that they should be checked to see that $p-1$ and $q-1$ are relatively prime to the public exponent $e$, and regenerated if this is not the case. If this is not done, then the calculation of the decrypt exponent will fail. However, what if a software bug allows the generation of public parameters $N$ and $e$ of an RSA key with this property and then it is subsequently used for encryption? Though this may seem like a purely academic question, a software bug in the RSA key generation implementation in the CNG API of a preview release of the Windows 10 operating system makes this question of more than purely hypothetical value. Without a well defined decrypt exponent, plaintexts encrypted to such keys will be undecryptable thus potentially losing user data, a serious software defect. Though the decrypt exponent is no longer well defined, it is in fact possible to recover the plaintext, or a small number of potential plaintexts if the prime factors $p$ and $q$ of the public modulus $N$ are known. This paper presents an analysis of what steps fail in the RSA algorithm and use this to give a plaintext recovery algorithm. The runtime of the algorithm scales linearly in the magnitude of the public exponent, in practice this is manageable as there are only a few small public exponents that are used. This algorithm has been implemented in a publicly available python script. We further discuss the software bug that lead to this and derive lessons that can be used while testing randomized functions in cryptographic software. Specifically, we derive an explicit formula that describes the trade off between number of iterations of tests of a randomized cryptographic functions and the potential number of users affected by a bug dependent on the random values.

The Joux-Vitse Crossbred algorithm's aim is to efficiently solve a system of semi-regular multivariate polynomials. For random polynomials, this is thought to be at least hard for a classical computer to solve. In this work, the algorithm is described in detail, a bivariate generating series to test the admissibility of parameters in F_2 is investigated and from this, a new series for F_q, q > 2 is presented. In addition, a complexity estimate is given for both F_2 and F_q, q > 2, which is compared to an estimate presented by Samardijska et al. Their estimate is shown to be an upper bound for the Crossbred algorithm. By obtaining optimal parameters using the previous results, the cost of theoretically applying Crossbred, FES and Hybrid-F5 to polynomial systems of various sizes of various numbers of variables and q was plotted. Overall, it was determined that for larger fields, the Crossbred algorithm provides an improved asymptotic complexity over FES. However, it does not provide any improvement over Hybrid-F5.

MuSig is a multi-signature scheme for Schnorr signatures, which supports key aggregation and is secure in the plain public key model. Standard derandomization techniques for discrete logarithm-based signatures such as RFC 6979, which make the signing procedure immune to catastrophic failures in the randomness generation, are not applicable to multi-signatures as an attacker could trick an honest user into producing two different partial signatures with the same randomness, which would reveal the user's secret key. In this paper, we propose a variant of MuSig in which signers generate their nonce deterministically as a pseudorandom function of the message and all signers' public keys and prove that they did so by providing a non-interactive zero-knowledge proof to their cosigners. The resulting scheme, which we call MuSig-DN, is the first Schnorr multi-signature scheme with deterministic signing. Therefore its signing protocol is robust against failures in the randomness generation as well as attacks trying to exploit the statefulness of the signing procedure, e.g., virtual machine rewinding attacks. As an additional benefit, a signing session in MuSig-DN requires only two rounds instead of three as required by all previous Schnorr multi-signatures including MuSig. To instantiate our construction, we identify a suitable algebraic pseudorandom function and provide an efficient implementation of this function as an arithmetic circuit. This makes it possible to realize MuSig-DN efficiently using zero-knowledge proof frameworks for arithmetic circuits which support inputs given in Pedersen commitments, e.g., Bulletproofs. We demonstrate the practicality of our technique by implementing it for the secp256k1 elliptic curve used in Bitcoin.

Block ciphers are prevalent in various security protocols used daily such as TLS, OpenPGP, and SSH. Their primary purpose is the protection of user data, both in transit and at rest. One of the de facto methods to evaluate block cipher security is differential cryptanalysis. Differential cryptanalysis observes the propagation of input patterns (input differences) through the cipher to produce output patterns (output differences). This probabilistic propagation is known as a differential; the identification of which is a measure of a block cipher’s security margins. This paper introduces an optimized GPU-based branch-and-bound framework for differential search. We optimize search efficiency by parallelizing all branch-and-bound operations, completing the entire search on the GPU without communicating with the CPU. The meet-in-the-middle (MITM) approach is also adopted for further performance gains. We analyze the financial and computational costs of the proposed framework using Google Cloud VM to showcase its practicality. When optimized for performance, we can attain up to 90x speedup while saving up to 47% of the running cost as compared to a single CPU core. When optimized for cost, the proposed framework can save up to 83% of financial costs while retaining a speedup of up to 40x. As a proof of concept, the proposed framework was then applied on 128-bit TRIFLE-BC, 64-bit PRESENT, and 64-bit GIFT. Notably, we identified the best differentials for PRESENT (16 rounds) and 64-bit GIFT (13 rounds) to date, with estimated probabilities of $2^{-61.7964}$ and $2^{-60.66}$ respectively. Although the differential results for TRIFLE-BC were incremental, the proposed framework was able to construct differentials for 43 rounds that consisted of approximately 5.8x more individual trails than previous work, making it one of the most efficient approaches for larger block ciphers.

A new post-quantum, hash-based signature (HBS) scheme is introduced. In known HBS, the size and cost of each signature increase as the total number of messages one wishes to authenticate increase. In real-world applications, requiring large volumes of signatures, they can become impractical. This paper studies HBS in a blockchain: a public, decentralized database. The proposed HBS scheme shows that, when all signatures are known, quite the opposite is possible: the signatures can become more efficient as the number of signatures grows. Authenticating large volumes of messages results less costly on average than authenticating only a few.

We show that verifiable voting systems require a security notion beyond individual- and universal-verifiability plus cast-as-intended.

At CRYPTO 2018, Cascudo et al. introduced Reverse Multiplication Friendly Embeddings (RMFEs). These are a mechanism to compute $\delta$ parallel evaluations of the same arithmetic circuit over a field $\mathbb{F}_q$ at the cost of a single evaluation of that circuit in $\mathbb{F}_{q^d}$, where $\delta < d$. Due to this inequality, RMFEs are a useful tool when protocols require to work over $\mathbb{F}_{q^d}$ but one is only interested in computing over $\mathbb{F}_q$. In this work we introduce Circuit Amortization Friendly Encodings (CAFEs), which generalize RMFEs while having concrete efficiency in mind. For a Galois Ring $R = GR(2^{k}, d)$, CAFEs allow to compute certain circuits over $\mathbb{Z}_{2^k}$ at the cost of a single secure multiplication in $R$. We present three CAFE instantiations, which we apply to the protocol for MPC over $\mathbb{Z}_{2^k}$ via Galois Rings by Abspoel et al. (TCC 2019). Our protocols allow for efficient switching between the different CAFEs, as well as between computation over $GR(2^{k}, d)$ and $\mathbb{F}_{2^{d}}$ in a way that preserves the CAFE in both rings. This adaptability leads to efficiency gains for e.g. Machine Learning applications, which can be represented as highly parallel circuits over $\mathbb{Z}_{2^k}$ followed by bit-wise operations. From an implementation of our techniques, we estimate that an SVM can be evaluated on 250 images in parallel up to $\times 7$ more efficiently using our techniques, compared to the protocol from Abspoel et al. (TCC 2019).

Threshold wallets leverage threshold signature schemes (TSS) to distribute signing rights across multiple parties when issuing blockchain transactions. These provide greater assurance against insider fraud, and are sometimes seen as an alternative to methods using a trusted execution environment to issue the signature. This new class of applications motivated researchers to discover better protocols, entrepreneurs to create start-up companies, and large organizations to deploy TSS-based solutions. For example, the leading cryptocurrency exchange (in transaction volume) adopted TSS to protect some of its wallets. Although the TSS concept is not new, this is the first time that so many TSS implementations are written and deployed in such a critical context, where all liquidity reserves could be lost in a minute if the crypto fails. Furthermore, TSS schemes are sometimes extended or tweaked to best adapt to their target use case---what could go wrong? This paper, based on the authors' experience with building and analyzing TSS technology, describes three different attacks on TSS implementations used by leading organizations. Unlike security analyses of on-paper protocols, this work targets TSS as deployed in real applications, and exploits logical vulnerabilities enabled by the extra layers of complexity added by TSS software. The attacks have concrete applications, and could for example have been exploited to empty an organization's cold wallet (typically worth at least an 8-digit dollar figure). Indeed, one of our targets is the cold wallet system of the biggest cryptocurrency exchange (which has been fixed after our disclosure).

Only the method to estimate the upper bound of the algebraic degree on block ciphers is known so far, but it is not useful for the designer to guarantee the security. In this paper we provide meaningful lower bounds on the algebraic degree of modern block ciphers.

The two traditional streams of multiparty computation (MPC) protocols consist of-- (a) protocols achieving guaranteed output delivery (god) or fairness (fn) in the honest-majority setting and (b) protocols achieving unanimous or selective abort (ua, sa) in the dishonest-majority setting. The favorable presence of honest majority amongst the participants is necessary to achieve the stronger notions of god or fn. While the constructions of each type are abound in the literature, one class of protocols does not seem to withstand the threat model of the other. For instance, the honest-majority protocols do not guarantee privacy of the inputs of the honest parties in the face of dishonest majority and likewise the dishonest-majority protocols cannot achieve god and fn, tolerating even a single corruption, let alone dishonest minority. The promise of the unconventional yet much sought-after species of MPC, termed as `Best-of-Both-Worlds' (BoBW), is to offer the best possible security depending on the actual corruption scenario. This work nearly settles the exact round complexity of two classes of BoBW protocols differing on the security achieved in the honest-majority setting, namely god and fn respectively, under the assumption of no setup (plain model), public setup (CRS) and private setup (CRS + PKI or simply PKI). The former class necessarily requires the number of parties to be strictly more than the sum of the bounds of corruptions in the honest-majority and dishonest-majority setting, for a feasible solution to exist. Demoting the goal to the second-best attainable security in the honest-majority setting, the latter class needs no such restriction. Assuming a network with pair-wise private channels and a broadcast channel, we show that 5 and 3 rounds are necessary and sufficient for the class of BoBW MPC with fn under the assumption of `no setup' and `public and private setup' respectively. For the class of BoBW MPC with god, we show necessity and sufficiency of 3 rounds for the public setup case and 2 rounds for the private setup case. In the no setup setting, we show the sufficiency of 5 rounds, while the known lower bound is 4. All our upper bounds are based on polynomial-time assumptions and assume black-box simulation. With distinct feasibility conditions, the classes differ in terms of the round requirement. The bounds are in some cases different and on a positive note at most one more, compared to the maximum of the needs of the honest-majority and dishonest-majority setting. Our results remain unaffected when security with abort and fairness are upgraded to their identifiable counterparts.

We show that the underlying permutation of ChaCha20 stream cipher does not behave as a random permutation for up to 17 rounds with respect to rotational cryptanalysis. In particular, we derive a lower and an upper bound for the rotational probability through ChaCha quarter round, we show how to extend the bound to a full round and then to the full permutation. The obtained bounds show that the probability to find what we call a parallel rotational collision is, for example, less than $2^{-488}$ for 17 rounds of ChaCha permutation, while for a random permutation of the same input size, this probability is $2^{-511}$. We remark that our distinguisher is not an attack to ChaCha20 stream cipher, but rather a theoretical analysis of its internal permutation from the point of view of rotational cryptanalysis.

Since it was proposed in 2015 as a generalization of integral properties, the division property has evolved into a powerful tool for probing the structures of Boolean functions whose algebraic normal forms are not available. We capture the most essential elements for the detection of division properties from a pure algebraic perspective, proposing a technique named as monomial prediction, which can be employed to determine the presence or absence of a monomial in any product of the coordinate functions of a vectorial Boolean function $\boldsymbol f$ by counting the number of the so-called monomial trails across a sequence of simpler functions whose composition is $\boldsymbol f$. Under the framework of the monomial prediction, we formally prove that most algorithms for detecting division properties in literature raise no false alarms but may miss. We also establish the equivalence between the monomial prediction and the three-subset bit-based division property without unknown subset presented at EUROCRYPT 2020, and show that these two techniques are perfectly accurate. The monomial prediction technique can be regarded as a purification of the definitions of the division properties without resorting to external multisets. This algebraic formulation gives more insights into division properties and inspires new search strategies. With the monomial prediction, we obtain the exact algebraic degrees of TRIVIUM up to 834 rounds for the first time. In the context of cube attacks, we are able to explore a larger search space in limited time and recover the exact algebraic normal forms of complex superpolies with the help of a divide-and-conquer strategy. As a result, we identify more cubes with smaller dimensions, leading to improvements of some near-optimal attacks against 840-, 841- and 842-round TRIVIUM.

Side-channel attacks are one of the greatest practical threats to security-related applications, because they are capable of breaking ciphers that are assumed to be mathematically secure. Lots of studies have been devoted to power or electro-magnetic (EM) analysis against desktop CPUs, mobile CPUs (including ARM, MSP, AVR, etc) and FPGAs, but rarely targeted modern GPUs. Modern GPUs feature their special and specific single instruction multiple threads (SIMT) execution fashion, which makes their power/EM leakage more sophisticated in practical scenarios. In this paper, we study side-channel attacks with leakage from SIMT systems, and propose leakage models suited to any SIMT systems and specifically to CUDA-enabled GPUs. Afterwards, we instantiate the models with a GPU AES implementation, which is also used for performance evaluations. In addition to the models, we provide optimizations on the attacks that are based on the models. To evaluate the models and optimizations, we run the GPU AES implementation on a CUDA-enabled GPU and, at the same time, collect its EM leakage. The experimental results show that the proposed models are more efficient and the optimizations are effective as well. Our study suggests that GPU-based cryptographic implementations may be much vulnerable to microarchitecture-based side-channel attacks. Therefore, GPU-specific countermeasures should be considered for GPU-based cryptographic implementations in practical applications.

At FSE 2020, a linear distinguishing attack is presented against the ZUC-256 stream cipher based on the $32$-bit word with a data/time complexity of about $2^{236.38}$. In this paper, we re-evaluate the complexity of this attack and discuss the applicability of such a distinguishing attack in 5G application scenarios, where each keystream frame is limited to $20000$, and up to $2^{32}$ bits. To assure a high success probability close to $1$, it is shown that the precise time complexity of the distinguishing attack is $2^{253.93}$ basic operations with a data complexity of $2^{241.38}$ bits keystream, which is far beyond the keystream length limit in 5G application settings in the single-frame setting. Besides, we also consider the multiple-frame scenario where a long keystream could be formed by concatenating many short keystream frames generated from different (Key, IV) pairs. We show that even in such a strong model of distinguishing attacks, the reported bias will not exist in 5G application scenarios and the linear distinguishing attack will not work due to the fact that the long linear combination relation derived from the polynomial multiple of the LFSR in ZUC-256 over $\mbox{GF}(2^{31}-1)$, which has been verified in experiments. It is concluded that the ZUC-256 stream cipher offers the full $256$-bit security in 5G application scenarios.

This paper presents the first third-party security analysis of \tinyjambu, which is one of 32 second-round candidates in NIST's lightweight cryptography standardization process. TinyJAMBU adopts an NLFSR based keyed-permutation that computes only a single NAND gate as a non-linear component per round. The designers evaluated the minimum number of active AND gates, however such a counting method neglects the dependency between multiple AND gates. There also exist previous works considering such dependencies with stricter models, however those are known to be too slow. In this paper, we present a new model that provides a good balance of efficiency and accuracy by only taking into account the first-order correlation of AND gates that frequently occurs in TinyJAMBU. With the refined model, we show a 338-round differential with probability $2^{-62.68}$ that leads to a forgery attack breaking 64-bit security. This implies that the security margin of TinyJAMBU with respect to the number of unattacked rounds is approximately 12%. We also show a differential on full 384 rounds with probability $2^{-70.64}$, thus the security margin of full rounds with respect to the data complexity, namely the gap between the claimed security bits and the attack complexity, is less than 8 bits. Our attacks also point out structural weaknesses of the mode that essentially come from the minimal state size to be lightweight.

We analyze the handshake protocol of the Transport Layer Security (TLS) protocol, version 1.3. We address both the full TLS 1.3 handshake (the one round-trip time mode, with signatures for authentication and (elliptic curve) Diffie–Hellman ephemeral ((EC)DHE) key exchange), and the abbreviated resumption/"PSK" mode which uses a pre-shared key for authentication (with optional (EC)DHE key exchange and zero round-trip time key establishment). Our analysis in the reductionist security framework uses a multi-stage key exchange security model, where each of the many session keys derived in a single TLS 1.3 handshake is tagged with various properties (such as unauthenticated versus unilaterally authenticated versus mutually authenticated, whether it is intended to provide forward security, how it is used in the protocol, and whether the key is protected against replay attacks). We show that these TLS 1.3 handshake protocol modes establish session keys with their desired security properties under standard cryptographic assumptions.

Symmetric password-authenticated key exchange (sPAKE) can be seen as an extension of traditional key exchange where two parties agree on a shared key if and only if they share a common secret (possibly low-entropy) password. We present the first sPAKE protocol to simultaneously achieve the following properties: - only two exponentiations per party, the same as plain unauthenticated Diffie-Hellman key agreement (and likely optimal); - optimal round complexity: a single flow (one message from each party that can be sent in parallel) to achieve implicit authentication, or two flows to achieve explicit mutual authentication; - security in the random oracle model, rather than ideal cipher or generic group model; - UC security, rather than game-based. Our protocol is a generalization of the seminal EKE protocol of Bellovin & Merritt (S&P 1992). We also present a UC-secure 1-out-of-$N$ oblivious transfer (OT) protocol, for random payloads. Its communication complexity is independent of $N$, meaning that $N$ can even be exponential in the security parameter. Such a protocol can also be considered a kind of oblivious PRF (OPRF). Our protocol improves over the leading UC-secure 1-out-of-$N$ OT construction of Masny & Rindal (CCS 2019) for all $N>2$, and has essentially the same cost for $N=2$. The new technique underlying these results is a primitive we call programmable-once public function (POPF). Intuitively, a POPF is a function whose output can be programmed by one party on exactly one point. All other outputs of the function are outside of any party's control, in a provable sense. Update: dos Santos et al. (Eurocrypt 2023) showed that our POPF definition is not strong enough to prove security of EKE against a man-in-the-middle. See Januzelli et al. (Eurocrypt 2025) for a fixed POPF abstraction and EKE security proof.

We present a new, simple candidate construction of indistinguishability obfuscation (iO). Our scheme is inspired by lattices and learning-with-errors (LWE) techniques, but we are unable to prove security under a standard assumption. Instead, we formulate a new falsifiable assumption under which the scheme is secure. Furthermore, the scheme plausibly achieves post-quantum security. Our construction is based on the recent "split FHE" framework of Brakerski, Döttling, Garg, and Malavolta (EUROCRYPT '20), and we provide a new instantiation of this framework. As a first step, we construct an iO scheme that is provably secure assuming that LWE holds \emph{and} that it is possible to obliviously generate LWE samples without knowing the corresponding secrets. We define a precise notion of oblivious LWE sampling that suffices for the construction. It is known how to obliviously sample from any distribution (in a very strong sense) using iO, and our result provides a converse, showing that the ability to obliviously sample from the specific LWE distribution (in a much weaker sense) already also implies iO. As a second step, we give a heuristic contraction of oblivious LWE sampling. On a very high level, we do this by homomorphically generating pseudoradnom LWE samples using an encrypted pseudorandom function.

Often in cryptography one needs to make a consistent choice of square root in a finite field. We show that such a choice is equivalent to providing a reasonable sign function. Then we show that for $\mathbb{F}_{p^k}$ (with odd prime $p \neq 1$ and $k\neq 0$) such a sign function exists if and only if $k$ is odd.

Applied cryptographic protocols have to meet a rich set of security requirements under diverse environments and against diverse adversaries. However, currently used security specifications, based on either simulation (e.g., `ideal functionality' in UC) or games, are monolithic, combining together different aspects of protocol requirements, environment and assumptions. Such security specifications are complex, error-prone, and foil reusability, modular analysis and incremental design. We present the Modular Security Specifications (MoSS) framework, which cleanly separates the security requirements (goals) which a protocol should achieve, from the models (assumptions) under which each requirement should be ensured. This modularity allows us to reuse individual models and requirements across different protocols and tasks, and to compare protocols for the same task, either under different assumptions or satisfying different sets of requirements. MoSS is flexible and extendable, e.g., it can support both asymptotic and concrete definitions for security. So far, we confirmed the applicability of MoSS to two applications: secure broadcast protocols and PKI schemes.

Blockchain is a multiparty protocol to reach agreement on the order of events, and to record them consistently and immutably without centralized trust. In some cases, however, the blockchain can benefit from some controlled mutability. Examples include removing private information or unlawful content, and correcting protocol vulnerabilities which would otherwise require a hard fork. Two approaches to control the mutability are: moderation, where one or more designated administrators can use their private keys to approve a redaction, and voting, where miners can vote to endorse a suggested redaction. In this paper, we first present several attacks against existing redactable blockchain solutions. Next, we provide a definitional framework for moderated redactable blockchains. Finally, we propose a provable and efficient construct, which applies a single digital signature per redaction, achieving a much simpler and secure result compared to the prior art in the moderated setting.

The Number Theoretic Transform (NTT) is a critical sub-block used in several structured lattice-based schemes, including Kyber and Dilithium, which are finalist candidates in the NIST's standardization process for post-quantum cryptography. The NTT was shown to be susceptible to single trace side-channel attacks by Primas et al. in CHES 2017 and Pessl et al. in Latincrypt 2019 who demonstrated full key recovery from single traces on the ARM Cortex-M4 microcontroller. However, the cost of deploying suitable countermeasures to protect the NTT from these attacks on the same target platform has not yet been studied. In this work, we propose novel shuffling and masking countermeasures to protect the NTT from such single trace attacks. Firstly, we exploit arithmetic properties of twiddle constants used within the NTT computation to propose efficient and generic masking strategies for the NTT with configurable SCA resistance. Secondly, we also propose new variants of the shuffling countermeasure with varying granularity for the NTT. We perform a detailed comparative evaluation of the runtime performances for our proposed countermeasures within open source implementations of Kyber and Dilithium from the pqm4 library on the ARM Cortex-M4 microcontroller. Our proposed countermeasures yield a reasonable overhead in the range of 7%-78% across all procedures of Kyber, while the overheads are much more pronounced for Dilithium, ranging from 12%-197% for the key generation procedure and 32%-490% for the signing procedure.

Although large numbers of hardware and software implementations have been proposed to accelerate lattice-based cryptography, Saber, a module-LWR-based algorithm, which has advanced to second round of the NIST standardization process, has not been adequately supported by the current solutions. Based on these motivations, a high-performance crypto-processor is proposed based on an algorithm-hardware co-design in this paper. First, a hierarchical Karatsuba calculating framework, a hardware-efficient Karatsuba scheduling strategy and an optimized circuit structure are utilized to enable high-throughput polynomial multiplication. Furthermore, a task-level pipeline and truncated multipliers are proposed to enable algorithm-specific fine-grained processing. Enabled by all of the above optimizations, Avalon takes 943, 1156, and 408 clock cycles for key generation, encryption, and decryption, respectively. Enabled by these optimizations, our processor takes 943, 1156 and 408 clock cycles for key generation, encryption, and decryption of Saber768, achieving 5.4x, 5.2x and 4.2x reductions compared with the state-of-the-art FPGA solutions, respectively. The post-layout simulation of our design is implemented with TSMC 40nm CMOS process within 0.35 mm2. The throughput for Saber768 is up to 346k encryption operations per second and the energy efficiency is 0.12uJ/encryption while operating at 400MHz, achieving nearly 52x improvement and 30x improvement, respectively compared with current PQC hardware solutions.

We examine the security of the Australian card payment system by analysing existing cryptographic protocols. In this analysis, we examine TDES and DES-V key derivation and the use of secure cryptographic devices, then contrast this with alternative mechanisms to enable secure card payments. We compare current Australian cryptographic methods with their international counterparts, such as the ANSI methods, and then motivate alternative methods for authenticated encryption in card payment systems.

Komargodski et.al. introduced {\em Evolving Secret Sharing} which allows an imaprtial participant, called \emph{dealer}, to share a secret among unbounded number of participants over any given access structure. In their construction for evolving secret sharing over general access structure, the size of share of the $i^{th}$ participant happens to be exponential $(\mathcal{O}(2^{i-1}))$. They also provided constructions for $(k,\infty)$ threshold secret sharing. We consider the problem of evolving secret sharing with $t$ essential participants, namely, over $t$-$(k,\infty)$ access structure, a generalization of $(k,\infty)$ secret sharing $(t=0)$. We further generalize this access structure to a possible case of unbounded number of essential participants and provide a construction for secret sharing on it. Both the constructions are information theoretically secure and reduce the share size of the construction due to Komargodski et.al. over general access structure, exponentially. Moreover, the essential participants receive ideal (and hence, optimal) shares in the first construction.

In this paper, we revisit the difference enumeration technique for LowMC and develop new algebraic techniques to achieve efficient key-recovery attacks. In the original difference enumeration attack framework, an inevitable step is to precompute and store a set of intermediate state differences for efficient checking via the binary search. Our first observation is that Bar-On et al.'s general algebraic technique developed for SPNs with partial nonlinear layers can be utilized to fulfill the same task, which can make the memory complexity negligible as there is no need to store a huge set of state differences any more. Benefiting from this technique, we could significantly improve the attacks on LowMC when the block size is much larger than the key size and even break LowMC with such a kind of parameter. On the other hand, with our new key-recovery technique, we could significantly improve the time to retrieve the full key if given only a single pair of input and output messages together with the difference trail that they take, which was stated as an interesting question by Rechberger et al. at ToSC 2018. Combining both techniques, with only 2 chosen plaintexts, we could break 4 rounds of LowMC adopting a full S-Box layer with block size of 129, 192 and 255 bits, respectively, which are the 3 recommended parameters for Picnic3, an alternative third-round candidate in NIST's Post-Quantum Cryptography competition. We have to emphasize that our attacks do not indicate that Picnic3 is broken as the Picnic use-case is very different and an attacker cannot even freely choose 2 plaintexts to encrypt for a concrete LowMC instance. However, such parameters are deemed as secure in the latest LowMC. Moreover, much more rounds of seven instances of the backdoor cipher LowMC-M as proposed by Peyrin and Wang in CRYPTO 2020 can be broken without finding the backdoor by making full use of the allowed $2^{64}$ data. The above mentioned attacks are all achieved with negligible memory.

We propose RANDCHAIN, a Decentralised Randomness Beacon (DRB) that is the first to achieve both scalability (i.e., a large number of participants can join) and fairness (i.e., each participant controls comparable power on deciding random outputs). Unlike existing DRBs where participants are collaborative, i.e., aggregating their local entropy into a single output, participants in RANDCHAIN are competitive, i.e., competing with each other to generate the next output. The competitive design reduces the communication complexity from at least O(n2) to O(n) without trusted party, breaking the scalability limit in existing DRBs. To build RANDCHAIN, we introduce Sequential Proof-of-Work (SeqPoW), a cryptographic puzzle that takes a random and unpredictable number of sequential steps to solve. We implement RANDCHAIN and evaluate its performance on up to 1024 nodes, demonstrating its superiority (1.3 seconds per output with a constant bandwidth of 200KB/s per node) compared to state-of-the-art DRBs RandHerd (S&P’18) and HydRand (S&P’20).

This note describes several attacks on the MALICIOUS framework for creating backdoored tweakable block ciphers. It is shown that, although the embedded malicious tweak pair itself is hard to recover, it is feasible to find additional weak tweak pairs that can be used to mount key-recovery attacks. Full-round attacks on most instances of LowMC-M are given. Our attacks are far from optimized and significant future improvements are to be expected. We focus on low-data attacks, since these are the most relevant for typical use-cases of LowMC. In addition, this implies that our attacks can not be prevented by limiting the amount of data that can be encrypted using the weak tweak pair. Despite our findings, we believe that the MALICIOUS framework can be used to create backdoored variants of LowMC provided that the parameters are modified.

In this paper we show that deep learning can be used to identify the shape of power traces corresponding to the responses of a protected arbiter PUF implemented in FPGAs. To achieve that, we combine power analysis with bitstream modification. We train a CNN classifier on two 28nm XC7 FPGAs implementing 128-stage arbiter PUFs and then classify the responses of PUFs from two other FPGAs. We demonstrate that it is possible to reduce the number of traces required for a successful attack to a single trace by modifying the bitstream to replicate PUF responses.

At EUROCRYPT 2020, Hosoyamada and Sasaki proposed the first dedicated quantum attack on hash functions --- a quantum version of the rebound attack exploiting differentials whose probabilities are too low to be useful in the classical setting. This work opens up a new perspective toward the security of hash functions against quantum attacks. In particular, it tells us that the search for differentials should not stop at the classical birthday bound. Despite these interesting and promising implications, the concrete attacks described by Hosoyamada and Sasaki make use of large quantum random access memories (qRAMs), a resource whose availability in the foreseeable future is controversial even in the quantum computation community. Without large qRAMs, these attacks incur significant increases in time complexities. In this work, we reduce or even avoid the use of qRAMs by performing a quantum rebound attack based on differentials with non-full-active super S-boxes. Along the way, an MILP-based method is proposed to systematically explore the search space of useful truncated differentials with respect to rebound attacks. As a result, we obtain improved attacks on AES-MMO, AES-MP, and the first classical collision attacks on 4- and 5-round Grostl-512. Interestingly, the use of non-full-active super S-box differentials in the analysis of AES-MMO gives rise to new difficulties in collecting enough starting points. To overcome this issue, we consider attacks involving two message blocks to gain more degrees of freedom, and we successfully compress the qRAM demand of the collision attacks on AES-MMO and AES-MP (EUROCRYPT 2020) from $2^{48}$ to a range from $2^{16}$ to $0$, while still maintaining a comparable time complexity. To the best of our knowledge, these are the first dedicated quantum attacks on hash functions that slightly outperform Chailloux, Naya-Plasencia, and Schrottenloher's generic quantum collision attack (ASIACRYPT 2017) in a model where large qRAMs are not available. This work demonstrates again how a clever combination of classical cryptanalytic technique and quantum computation leads to improved attacks, and shows that the direction pointed out by Hosoyamada and Sasaki deserves further investigation.

We give new, fully-quantitative and concrete bounds that justify the SIGMA and TLS 1.3 key exchange protocols not just in principle, but in practice. By this we mean that, for standardized elliptic curve group sizes, the overall protocol actually achieves the intended security level. Prior work gave reductions of both protocols' security to the underlying building blocks that were loose (in the number of users and/or sessions), so loose that they gave no guarantees for practical parameters. Adapting techniques by Cohn-Gordon et al. (Crypto 2019), we give reductions for SIGMA and TLS 1.3 to the strong Diffie-Hellman problem which are tight. Leveraging our tighter bounds, we meet the protocols' targeted security levels when instantiated with standardized curves and improve over prior bounds by up to over 90 bits of security across a range of real-world parameters.

Contact tracing is an effective tool in controlling the spread of infectious diseases such as COVID-19. It involves digital monitoring and recording of physical proximity between people over time with a central and trusted authority, so that when one user reports infection, it is possible to identify all other users who have been in close proximity to that person during a relevant time period in the past and alert them. One way to achieve this involves recording on the server the locations, e.g. by reading and reporting the GPS coordinates of a smartphone, of all users over time. Despite its simplicity, privacy concerns have prevented widespread adoption of this method. Technology that would enable the "hiding" of data could go a long way towards alleviating privacy concerns and enable contact tracing at a very large scale. In this article we describe a general method to hide data. By hiding, we mean that instead of disclosing a data value x, we would disclose an "encoded" version of x, namely E(x), where E(x) is easy to compute but very difficult, from a computational point of view, to invert. We propose a general construction of such a function E and show that it guarantees perfect recall, namely, all individuals who have potentially been exposed to infection are alerted, at the price of an infinitesimal number of false alarms, namely, only a negligible number of individuals who have not actually been exposed will be wrongly informed that they have.

With the emergence of the Industrial Internet of Things (IIoT), numerous operations based on smart devices contribute to producing convenience and comfortable applications for individuals and organizations. Considering the untrusted feature of the communication channels in IIoT, it is essential to ensure the authentication and incontestableness of the messages transmitted in the IIoT. In this paper, we firstly proposed a certificate-based parallel key-insulated aggregate signature (CB-PKIAS), which can resist the fully chosen-key attacks. Concretely, the adversary who can obtain the private keys of all signers in the system is able to forge a valid aggregate signature by using the invalid single signature. Furthermore, our scheme inherits the merits of certificate-based and key-insulated to avoid the certificate management problem, key escrow problems as well as the key exposures simultaneously. In addition, the rigorous analysis and the concrete simulation experiment demonstrated that our proposed scheme is secure under the random oracle and more suitable for the IIoT environment.

This paper presents the first functional encryption schemes for quadratic functions (or degree-2 polynomials) achieving simulation-based security in the semi-adaptive model with constant-size secret key. The unique prior construction with the same security guarantee by Gay [PKC 20] has secret keys of size linear in the message size. They also enjoy shorter ciphertexts: - our first scheme is based on bilateral DLIN (decisional linear) assumption as Gay's scheme and the ciphertext is 15% shorter; - our second scheme based on SXDH assumption and bilateral DLIN assumption is more efficient; it has 67% shorter ciphertext than previous SXDH-based scheme with selective indistinguishability security by Baltico et al. [CRYPTO 17]; the efficiency is comparable to their second scheme in the generic group model. Technically, we roughly combine Wee's ``secret-key-to-public-key'' compiler [TCC 17] with Gay's paradigm [PKC 20]. We avoid (partial) function-hiding inner-product functional encryption used in Gay's work and make our schemes conceptually simpler.

ARX algorithms are a class of symmetric-key algorithms constructed by Addition, Rotation, and XOR, which achieve the best software performances in low-end microcontrollers. To evaluate the resistance of an ARX cipher against differential cryptanalysis and its variants, the recent automated methods employ constraint satisfaction solvers, such as SMT solvers, to search for optimal characteristics. The main difficulty to formulate this search as a constraint satisfaction problem is obtaining the differential models of the non-linear operations, that is, the constraints describing the differential probability of each non-linear operation of the cipher. While an efficient bit-vector differential model was obtained for the modular addition with two variable inputs, no differential model for the modular addition by a constant has been proposed so far, preventing ARX ciphers including this operation from being evaluated with automated methods. In this paper, we present the first bit-vector differential model for the n-bit modular addition by a constant input. Our model contains O(log_2(n)) basic bit-vector constraints and describes the binary logarithm of the differential probability. We also represent an SMT-based automated method to look for differential characteristics of ARX, including constant additions, and we provide an open-source tool ArxPy to find ARX differential characteristics in a fully automated way. To provide some examples, we have searched for related-key differential characteristics of TEA, XTEA, HIGHT, and LEA, obtaining better results than previous works. Our differential model and our automated tool allow cipher designers to select the best constant inputs for modular additions and cryptanalysts to evaluate the resistance of ARX ciphers against differential attacks.

We construct indistinguishability obfuscation (iO) solely under circular-security properties of encryption schemes based on the Learning with Errors (LWE) problem. Circular-security assumptions were used before to construct (non-leveled) fully-homomorphic encryption (FHE), but our assumption is stronger and requires circular randomness-leakage-resilience. In contrast with prior works, this assumption can be conjectured to be post-quantum secure; yielding the first provably secure iO construction that is (plausibly) post-quantum secure. Our work follows the high-level outline of the recent work of Gay and Pass [ePrint 2020], who showed a way to remove the heuristic step from the homomorphic-encryption based iO approach of Brakerski, Döttling, Garg, and Malavolta [EUROCRYPT 2020]. They thus obtain a construction proved secure under circular security assumption of natural homomorphic encryption schemes --- specifically, they use homomorphic encryption schemes based on LWE and DCR, respectively. In this work we show how to remove the DCR assumption and remain with a scheme based on the circular security of LWE alone. Along the way we relax some of the requirements in the Gay-Pass blueprint and thus obtain a scheme that is secure under a relaxed assumption. Specifically, we do not require security in the presence of a key-cycle, but rather only in the presence of a key-randomness cycle.

Anonymous veto networks (AV-nets), originally proposed by Hao and Zielinski (2006), are particularly lightweight protocols for evaluating a veto function in a peer-to-peer network such that anonymity of all protocol participants is preserved. Prior to this work, anonymity in all AV-nets from the literature relied on the decisional Diffie-Hellman (DDH) assumption and can thus be broken by (scalable) quantum computers. In order to defend against this threat, we propose two practical and completely lattice-based AV-nets. The first one is secure against passive and the second one is secure against active adversaries. We prove that anonymity of our AV-nets reduces to the ring learning with errors (RLWE) assumption. As such, our AV-nets are the first ones with post-quantum anonymity. We also provide performance benchmarks to demonstrate their practicality.

This paper proposes new Polynomial IOPs for arithmetic circuits. They rely on the monomial coefficient basis to represent the matrices and vectors arising from the arithmetic constraint satisfaction system, and build on new protocols for establishing the correct computation of linear algebra relations such as matrix-vector products and Hadamard products. Our protocols give rise to concrete proof systems with succinct verification when compiled down with a cryptographic compiler whose role is abstracted away in this paper. Depending only on the compiler, the resulting SNARKs are either transparent or rely on a trusted setup.

Permissionless distributed ledgers, such as those arising from blockchain protocols, have been touted as the centerpiece of an upcoming security-critical information technology infrastructure. Their basic properties---consistency and liveness---can be guaranteed under specific constraints on the resources available to an adversary relative to the resources of the participants that follow the protocol. Given their permissionless participation convention and their intended long-livedness, a critical open security question is their behavior---and potential resilience---to temporary spikes in adversarial resources. In this work we give the first thorough treatment of the self-healing properties of Nakamoto ledgers, addressing both proof-of-work (PoW) and proof-of-stake (PoS) protocols. First, we present a unified model that allows us to define self-healing for both of these protocol classes. Then we provide a formal analysis establishing self-healing with respect to both consistency and liveness in both classes, quantifying the resulting vulnerability period as a function of the magnitude of the spike. Finally, we provide numerical simulations giving explicit quantitative bounds relevant for practice.

We prove that the module learning with errors (M-LWE) problem with arbitrary polynomial-sized modulus p is classically at least as hard as standard worst-case lattice problems, as long as the module rank d is not smaller than the number field degree n. Previous publications only showed the hardness under quantum reductions. We achieve this result in an analogous manner as in the case of the learning with errors (LWE) problem. First, we show the classical hardness of M-LWE with an exponential-sized modulus. In a second step, we prove the hardness of M-LWE using a binary secret. And finally, we provide a modulus reduction technique. The complete result applies to the class of power-of-two cyclotomic fields. However, several tools hold for more general classes of number fields and may be of independent interest.

We analyze the multi-user security of the streaming encryption in Google's Tink library via an extended version of the framework of nonce-based online authenticated encryption of Hoang et al. (CRYPTO'15) to support random-access decryption. We show that Tink's design choice of using random nonces and a nonce-based key-derivation function indeed improves the concrete security bound. We then give two better alternatives that are more robust against randomness failure. In addition, we show how to efficiently instantiate the key-derivation function via AES, instead of relying on HMAC-SHA256 like the current design in Tink. To accomplish this we give a multi-user analysis of the XOR-of-permutation construction of Bellare, Krovetz, and Rogaway (EUROCRYPT'98).

Let S = {1,...,n} be a set of integers and X be a subset of S. We study the boolean function f_X(Y) which outputs 1 if and only if Y is a small enough superset (resp., big enough subset) of X. Our purpose is to protect X from being known when the function is evasive, yet allow evaluations of f_X on any input Y \subseteq S. The corresponding research area is called function obfuscation. The two kinds of functions are called small superset functions (SSF) and big subset functions (BSF), respectively. In this paper, we obfuscate SSF and BSF in a very simple and efficient way. We prove both input-hiding security and virtual black-box (VBB) security based on the subset product problem. We also give a proof of input-hiding based on the discrete logarithm problem (DLP) for the conjunction obfuscation by Bartusek et al. [4] (see Appendix A) and propose a new conjunction obfuscation based on SSF and BSF obfuscation (see Appendix B). The security of our conjunction obfuscation is from our new computational problem called the twin subset product problem.

This paper contains an analysis of decentralized exchange governance as an effective framework for voting, profit sharing baking and partially updating the system with a possibility to create new pairs for decentralized exchange with automatic market-making. It will also review 2 alternative baker election and rotation mechanisms such as “Simple first-place voting protocol” and “First-place with veto protocol” and will provide a more in-depth look on these mechanisms. It will examine a proposed architectural software solution for monitoring the decentralized network to mediate deviant baker behavior - the watchtower.

The protection of intellectual property (IP) rights of well-trained deep learning (DL) models has become a matter of major concern, especially with the growing trend of deployment of Machine Learning as a Service (MLaaS). In this work, we demonstrate the utilization of a hardware root-of-trust to safeguard the IPs of such DL models which potential attackers have access to. We propose an obfuscation framework called Hardware Protected Neural Network (HPNN) in which a deep neural network is trained as a function of a secret key and then, the obfuscated DL model is hosted on a public model sharing platform. This framework ensures that only an authorized end-user who possesses a trustworthy hardware device (with the secret key embedded on-chip) is able to run intended DL applications using the published model. Extensive experimental evaluations show that any unauthorized usage of such obfuscated DL models result in significant accuracy drops ranging from 73.22 to 80.17% across different neural network architectures and benchmark datasets. In addition, we also demonstrate the robustness of proposed HPNN framework against a model fine-tuning type of attack.

Multivariate cryptography studies applications of endomorphisms of K[x_1, x_2, …, x_n] where K is a finite commutative ring. The importance of this direction for the construction of multivariate digital signature systems is well known. We suggest modification of the known digital signature systems for which some of cryptanalytic instruments were found . This modification prevents possibility to use recently developed attacks on classical schemes such as rainbow oil and vinegar system, and LUOV. Modification does not change the size of hashed messages and size of signatures. Basic idea is the usage of multivariate messages of unbounded degree and polynomial density for the construction of public rules. Modified algorithms are presented for standardization and certification studies.

In recent years, deep neural networks (DNN) have become an important type of intellectual property due to their high performance on various classification tasks. As a result, DNN stealing attacks have emerged. Many attack surfaces have been exploited, among which cache timing side-channel attacks are hugely problematic because they do not need physical probing or direct interaction with the victim to estimate the DNN model. However, existing cache-side-channel-based DNN reverse engineering attacks rely on analyzing the binary code of the DNN library that must be shared between the attacker and the victim in the main memory. In reality, the DNN library code is often inaccessible because 1) the code is proprietary, or 2) memory sharing has been disabled by the operating system. In our work, we propose GANRED, an attack approach based on the generative adversarial nets (GAN) framework which utilizes cache timing side-channel information to accurately recover the structure of DNNs without memory sharing or code access. The benefit of GANRED is four-fold. 1) There is no need for DNN library code analysis. 2) No shared main memory segment between the victim and the attacker is needed. 3) Our attack locates the exact structure of the victim model, unlike existing attacks which only narrow down the structure search space. 4) Our attack efficiently scales to deeper DNNs, exhibiting only linear growth in the number of layers in the victim DNN.

Gated Recurrent Unit (GRU) has broad application fields, such as sentiment analysis, speech recognition, malware analysis, and other sequential data processing. For low-cost deployment and efficient machine learning services, a growing number of model owners choose to deploy the trained GRU models through Machine-learning-as-a-service (MLaaS). However, privacy has become a significant concern for both model owners and prediction clients, including model weights privacy, input data privacy, and output results privacy. The privacy leakage may be caused by either external intrusion or insider attacks. To address the above issues, this research designs a framework for privacy-preserving GRU models, which aims for privacy scenarios such as predicting on textual data, network packets, heart rate data, and so on. In consideration of accuracy and efficiency, this research uses additive secret sharing to design the basic operations and gating mechanisms of GRU. The protocols can meet the security requirements of privacy and correctness under the Universal Composability framework with the semi-honest adversary. Additionally, the framework and protocols are realized with a proof-of-concept implementation. The experiment results are presented with respect to time consumption and inference accuracy.

Oblivious transfer (OT) is an essential cryptographic tool that can serve as a building block for almost all secure multiparty functionalities. The strongest security notion against malicious adversaries is universal composability (UC-secure). An important goal is to have post-quantum OT protocols. One area of interest for post-quantum cryptography is isogeny-based crypto. Isogeny-based cryptography has some similarities to Diffie-Hellman, but lacks some algebraic properties that are needed for discrete-log-based OT protocols. Hence it is not always possible to directly adapt existing protocols to the isogeny setting. We propose the first practical isogeny-based UC-secure oblivious transfer protocol in the presence of malicious adversaries. Our scheme uses the CSIDH framework and does not have an analogue in the Diffie-Hellman setting. The scheme consists of a constant number of isogeny computations. The underlying computational assumption is a problem that we call the computational reciprocal CSIDH problem, and that we prove polynomial-time equivalent to the computational CSIDH problem.

The private join and compute (PJC) functionality enables secure computation over data distributed across different databases, which is a functionality with a wide range of applications, many of which address settings where the input databases are of significantly different sizes. We introduce the notion of private information retrieval (PIR) with default, which enables two-party PJC functionalities in a way that hides the size of the intersection of the two databases and incurs sublinear communication cost in the size of the bigger database. We provide two constructions for this functionality, one of which requires offline linear communication, which can be amortized across queries, and one that provides sublinear cost for each query but relies on more computationally expensive tools. We construct inner-product PJC, which has applications to ads conversion measurement and contact tracing, relying on an extension of PIR with default. We evaluate the efficiency of our constructions, which can enable $\mathbf{2^{12}}$ PIR with default lookups on a database of size $\mathbf{2^{30}}$ (or inner-product PJC on databases with such sizes) with the communication of $\mathbf{945}$MB, which costs less than $\mathbf{\$0.04}$ for the client and $\mathbf{\$5.22}$ for the server.

We show the existence of indistinguishability obfuscators (iO) for general circuits assuming subexponential security of: - the Learning with Error (LWE) assumption (with subexponential modulus-to-noise ratio); - a circular security conjecture regarding the Gentry-Sahai-Water's (GSW) encryption scheme and a Packed version of Regev's encryption scheme. The circular security conjecture states that a notion of leakage-resilient security, that we prove is satisfied by GSW assuming LWE, is retained in the presence of an encrypted key-cycle involving GSW and Packed Regev. Our work thus places iO on qualitatively similar assumptions as (unlevelled) FHE, for which known constructions also rely on a circular security conjecture.

We construct a VBB and perfect circuit-hiding obfuscator for evasive deterministic finite automata using a matrix encoding scheme with a limited zero-testing algorithm. We construct the matrix encoding scheme by extending an existing matrix FHE scheme. Using obfuscated DFAs we can for example evaluate secret regular expressions or disjunctive normal forms on public inputs. In particular, the possibility of evaluating regular expressions solves the open problem of obfuscated substring matching.

Side-channel attacks exploit information that is leaked from hardware. The differential power analysis (DPA) attack aims at extracting sensitive information that is processed by the operations in a cryptographic primitive. Power traces are collected and subsequently processed using statistical methods. The ChipWhisperer Nano is a low-cost, open-source device that can be used to implement and study side-channel attacks. This paper describes how the DPA attack with the difference of means method can be used to extract the secret key from both an 8-bit and a 32-bit implementation of AES using the ChipWhisperer Nano. The results show that although it is possible to carry out the attack on both implementations, the attack on the 32-bit implementation requires more traces than the 8-bit implementation.

In 2019, Gu Chunsheng introduced Integer-RLWE, a variant of RLWE devoid of some of its efficiency flaws. Most notably, he proposes a setting where $n$ can be an arbitrary positive integer, contrarily to the typical construction $n = 2^k$. In this paper, we analyze the new problem and implement the classical meet-in-the-middle and lattice-based attacks. We then use the peculiarity of the construction of $n$ to build an improved lattice-based attack in cases where $n$ is composite with an odd divisor. For example, for parameters $n = 2000$ and $q = 2^{33}$, we reduce the estimated complexity of the attack from $2^{288}$ to $2^{164}$. We also present reproducible experiments confirming our theoretical results.

CSIDH is an isogeny-based post-quantum key establishment protocol proposed in 2018. In this work, we analyze attacking implementations of CSIDH which use dummy isogeny operations using fault injections from a mathematical perspective. We detail an attack by which the private key can be learned by the attacker up to sign with absolute certainty using $\sum \lceil \log_2(b_i) + 1 \rceil$ fault attacks on pairwise distinct group action evaluations under the same private key under ideal conditions using a binary search approach, where $\vec{b}$ is the bound vector defining the keyspace. As a countermeasure to this attack, we propose randomly mixing the real degree $\ell_j$ isogenies together with the dummy ones by means of a binary decision vector. To evaluate the efficacy of this countermeasure, we formulate a probability-based attack on this randomized scheme using a maximum likelihood approach and simulate the attack using 6 bound vectors used in previous CSIDH implementations. We found that the number of attacks required under our model to reach just 1% certainty about the key increased by a factor between 8--12 over the standard approach in the setting of signed private keys and a factor between 28--45 using non-negative private keys, depending on $\vec{b}$. We derive theoretical upper bounds on the number of attacks required to reach a specified certainty threshold about the key under our model. Based on our data and the minimal additional overhead required, we recommend all future implementations of CSIDH to employ a randomized decision vector approach. Finally since our model assumes fault attacks provide no information on the sign of the key, we use a technique based on Gray codes to optimize the standard meet-in-the-middle attack for learning the sign of the key values once their magnitudes have been learned through fault attacks. We estimate that, on average, this optimized technique uses approximately 88% fewer field-multiplication-equivalent operations over the standard approach.

The isogeny-based scheme CSIDH is a promising candidate for quantum-resistant static-static key exchanges with very small public keys, but is inherently difficult to implement in constant time. In the current literature, there are two directions for constant-time implementations: algorithms containing dummy computations and dummy-free algorithms. While the dummy-free implementations come with a 2x slowdown, they offer by design more resistance against fault attacks. In this work, we evaluate how practical fault injection attacks are on the constant-time implementations containing dummy calculations. We present three different fault attacker models. We evaluate our fault models both in simulations and in practical attacks. We then present novel countermeasures to protect the dummy isogeny computations against fault injections. The implemented countermeasures result in an overhead of 7% on the Cortex-M4 target, falling well short of the 2x slowdown for dummy-less variants.

WebAuthn, forming part of FIDO2, is a W3C standard for strong authentication, which employs digital signatures to authenticate web users whilst preserving their privacy. Owned by users, WebAuthn authenticators generate attested and unlinkable public-key credentials for each web service to authenticate users. Since the loss of authenticators prevents users from accessing web services, usable recovery solutions preserving the original WebAuthn design choices and security objectives are urgently needed. We examine Yubico's recent proposal for recovering from the loss of a WebAuthn authenticator by using a secondary backup authenticator. We analyse the cryptographic core of their proposal by modelling a new primitive, called Asynchronous Remote Key Generation (ARKG), which allows some primary authenticator to generate unlinkable public keys for which the backup authenticator may later recover corresponding private keys. Both processes occur asynchronously without the need for authenticators to export or share secrets, adhering to WebAuthn's attestation requirements. We prove that Yubico's proposal achieves our ARKG security properties under the discrete logarithm and PRF-ODH assumptions in the random oracle model. To prove that recovered private keys can be used securely by other cryptographic schemes, such as digital signatures or encryption schemes, we model compositional security of ARKG using composable games by Brzuska et al. (ACM CCS 2011), extended to the case of arbitrary public-key protocols. As well as being more general, our results show that private keys generated by ARKG may be used securely to produce unforgeable signatures for challenge-response protocols, as used in WebAuthn. We conclude our analysis by discussing concrete instantiations behind Yubico's ARKG protocol, its integration with the WebAuthn standard, performance, and usability aspects.

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto’2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Theorem: Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $\lambda$ is a security parameter, $p$ is a $\lambda$-bit prime, and the parameters $\ell,k,n$ are large enough polynomials in $\lambda$: - the Learning With Errors ($\mathsf{LWE}$) assumption over $\mathbb{Z}_p$ with subexponential modulus-to-noise ratio $2^{k^\epsilon}$, where $k$ is the dimension of the $\mathsf{LWE}$ secret, - the Learning Parity with Noise ($\mathsf{LPN}$) assumption over $\mathbb{Z}_p$ with polynomially many $\mathsf{LPN}$ samples and error rate $1/\ell^\delta$, where $\ell$ is the dimension of the $\mathsf{LPN}$ secret, - the existence of a Boolean Pseudo-Random Generator ($\mathsf{PRG}$) in $\mathsf{NC}^0$ with stretch $n^{1+\tau}$, where $n$ is the length of the $\mathsf{PRG}$ seed, - the Symmetric eXternal Diffie-Hellman ($\mathsf{SXDH}$) assumption on asymmetric bilinear groups of order $p$. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists. Further, assuming only polynomial security of the aforementioned assumptions, there exists collusion resistant public-key functional encryption for all polynomial-size circuits.

We present CrypTFlow2, a cryptographic framework for secure inference over realistic Deep Neural Networks (DNNs) using secure 2-party computation. CrypTFlow2 protocols are both correct -- i.e., their outputs are bitwise equivalent to the cleartext execution -- and efficient -- they outperform the state-of-the-art protocols in both latency and scale. At the core of CrypTFlow2, we have new 2PC protocols for secure comparison and division, designed carefully to balance round and communication complexity for secure inference tasks. Using CrypTFlow2, we present the first secure inference over ImageNet-scale DNNs like ResNet50 and DenseNet121. These DNNs are at least an order of magnitude larger than those considered in the prior work of 2-party DNN inference. Even on the benchmarks considered by prior work, CrypTFlow2 requires an order of magnitude less communication and 20x-30x less time than the state-of-the-art.

In distributed symmetric-key encryption (DiSE), a set of n distributed servers share a key (or key set) and any t, t <= n, servers can collectively use the shared key (or key set) in a DiSE transaction to encrypt a message or decrypt a ciphertext without reconstructing the shared key (or key set). Each participating server contributes one or more partial results and one participating server called the initiator combines all partial results into a final result. An adversary who has compromised up to (t-1) servers will not be able to access the shared key (or key set). Due to the distributed nature of DiSE, a DiSE server that has been compromised by an adversary may return wrong partial results to the initiator. Worse, multiple DiSE servers compromised by the same adversary may collude to send back wrong partial results. In this article we developed a robust DiSE that allows an honest initiator to detect wrong partial results by an adversary. The robustness of our DiSE is built through redundant computation. Our robust DiSE can detect wrong partial results by an adversary who has compromised up to min(t-1, n-t) servers. Next, the honest-initiator assumption is removed by rotating the initiator role among active servers across multiple DiSE transactions. A scalable, industry-level implementation for the robust DiSE has been developed and two cases, (t=3, n=5) and (t=16, n=24), have been tested to show the feasibility of robust DiSE. Our robust DiSE can be used to build intrusion-tolerant applications, such as intrusion-tolerant database encryption.

In relay attacks, a man-in-the-middle adversary impersonates a legitimate party and makes it this party appear to be of an authenticator, when in fact they are not. In order to counteract relay attacks, distance-bounding protocols provide a means for a verifier (e.g., an payment terminal) to estimate his relative distance to a prover (e.g., a bankcard). We propose FlexiDB, a new cryptographic model for distance bounding, parameterised by different types of fine-grained corruptions. FlexiDB allows to consider classical cases but also new, generalised corruption settings. In these settings, we exhibit new attack strategies on existing protocols. Finally, we propose a proof-of-concept mechanisation of FlexiDB in the interactive cryptographic prover EasyCrypt. We use this to exhibit a flavour of man-in-the-middle security on a variant of MasterCard's contactless-payment protocol.

Symmetric Searchable Encryption (SSE) is an encryption technique that allows users to search directly on their outsourced encrypted data while preserving the privacy of both the files and the queries. Unfortunately, majority of the SSE schemes allows users to either decrypt the whole ciphertext or nothing at all. In this paper, we propose a novel scheme based on traditional symmetric primitives, that allows data owners to bind parts of their ciphertexts with specific policies. Inspired by the concept of Attribute-Based Encryption (ABE) in the public setting, we design a scheme through which users can recover only certain parts of an encrypted document if and only if they retain a set of attributes that satisfy a policy. Our construction satisfies the important notion of forward privacy while at the same time supports the multi-client model by leveraging SGX functionality for the synchronization of users. To prove the correctness of our approach, we provide a detailed simulation-based security analysis coupled with an extensive experimental evaluation that shows the effectiveness of our scheme.

Blockchain systems have severe scalability limitations e.g., long confirmation delays. Layer-2 protocols are designed to address such limitations. The most prominent class of such protocols are payment channel networks e.g., the Lightning Network for Bitcoin where pairs of participants create channels that can be concatenated into networks. These allow payments across the network without interaction with the blockchain. A drawback is that all intermediary nodes within a payment path must be online. Virtual Channels, as recently proposed by Dziembowski et al. (CCS'18), allow payments without this limitation. However, these can only be implemented on blockchains with smart contract capability therefore limiting its applicability. Our work proposes the notion of --Lightweight-- Virtual Payment Channels, i.e. only requiring timelocks and multisignatures, enabling Virtual Channels on a larger range of blockchain systems of which a prime example is Bitcoin. More concretely, other contributions of this work are (1) to introduce a fully-fledged formalization of our construction, and (2) to present a simulation based proof of security in Canetti's UC Framework.

There once was a table of hashes That held extra items in stashes It all seemed like bliss But things went amiss When the stashes were stored in the caches The first Oblivious RAM protocols introduced the ``hierarchical solution,'' (STOC '90) where the servers store a series of hash tables of geometrically increasing capacities. Each ORAM query would read a small number of locations from each level of the hierarchy, and each level of the hierarchy would be reshuffled and rebuilt at geometrically increasing intervals to ensure that no single query was ever repeated twice at the same level. This yielded an ORAM protocol with polylogarithmic overhead. Future works extended and improved the hierarchical solution, replacing traditional hashing with cuckoo hashing (ICALP '11) and cuckoo hashing with a combined stash (Goodrich et al. SODA '12). In this work, we identify a subtle flaw in the protocol of Goodrich et al. (SODA '12) that uses cuckoo hashing with a stash in the hierarchical ORAM solution. We give a concrete distinguishing attack against this type of hierarchical ORAM that uses cuckoo hashing with a combined stash. This security flaw has propagated to at least 5 subsequent hierarchical ORAM protocols, including the recent optimal ORAM scheme, OptORAMa (Eurocrypt '20). In addition to our attack, we identify a simple fix that does not increase the asymptotic complexity. We note, however, that our attack only affects more recent hierarchical ORAMs, but does not affect the early protocols that predate the use of cuckoo hashing, or other types of ORAM solutions (e.g. Path ORAM or Circuit ORAM).

To prove computational complexity lower bounds in cryp- tography, one often resorts to so-called generic models of computation. For example, a generic algorithm for the discrete logarithm is one which works independently from the group representation—and thus works generically for all group representations. There are a multitude of different models in the literature making comparing different results—and even matching lower and upper bounds proven in different models— rather difficult. In this work we view a model as a set of games with the same type of interactions. Using a standard notion of reduction between two games, we establish a hierarchy between models. Different models may now be classified as weaker and stronger if a reduction between them exists. We propose different extensions of the generic group model with different queries, explicitly capturing different information that an algorithm may need to exploit. Finally, we use the hierarchy between these models to systematically compare and improve the results in the literature. First we strengthen the model in which the baby-step giant-step algorithm is proven and weaken the model in which the matching lower bound is proven. We then analyse the discrete logarithm with preprocessing. Upper and lower bounds have been proven in the literature in mismatching models. We weaken the model of the lower bound and strengthen the model of the upper bound to close the gap between the two.

One can bootstrap LWE-based fully homomorphic encryption (FHE) schemes in less than one second, but bootstrapping AGCD-based FHE schemes, also known as FHE over the integers, is still very slow. In this work we propose a fast bootstrapping method for FHE over the integers, closing thus this gap between these two types of schemes. We use a variant of the AGCD problem to construct a new GSW-like scheme that can natively encrypt polynomials, then, we show how the single-gate bootstrapping method proposed by Ducas and Micciancio (EUROCRYPT 2015) can be adapted to FHE over the integers using our scheme, and we implement a bootstrapping that, using around 400 MB of key material, runs in less than one second in a common personal computer.

We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument of knowledge with the following three efficiency properties for computing and proving a (non-deterministic, polynomial time) parallel RAM computation that can be computed in parallel time T with at most p processors: (1) The prover’s (parallel) running time is T + polylog(T * p). (In other words, the prover’s running time is essentially T for large computation times!) (2) The prover uses at most p * polylog(T * p) processors, and (3) the communication and verifier complexity are both polylog(T * p). The combination of all three is desirable as it gives a way to leverage a moderate increase in parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover’s parallel running time is not allowed. Our main contribution is a generic construction of SPARKs from any succinct argument of knowledge where the prover’s parallel running time is T * polylog(T * p) when using p processors, assuming collision-resistant hash functions. When suitably instantiating our construction, we achieve a four-round SPARK for any parallel RAM computation assuming only collision resistance. Additionally assuming the existence of a succinct non-interactive argument of knowledge (SNARK), we construct a non-interactive SPARK that also preserves the space complexity of the underlying computation up to polylog(T * p) factors. We also show the following applications of non-interactive SPARKs. First, they immediately imply delegation protocols with near optimal prover (parallel) running time. This, in turn, gives a way to construct verifiable delay functions (VDFs) from any sequential function. When the sequential function is also memory-hard, this yields the first construction of a memory-hard VDF.

A new approach to the security analysis of hardware-oriented masked ciphers against second-order side-channel attacks is developed. By relying on techniques from symmetric-key cryptanalysis, concrete security bounds are obtained in a variant of the probing model that allows the adversary to make only a bounded, but possibly very large, number of measurements. Specifically, it is formally shown how a bounded-query variant of robust probing security can be reduced to the linear cryptanalysis of masked ciphers. As a result, the compositional issues of higher-order threshold implementations can be overcome without relying on fresh randomness. From a practical point of view, the aforementioned approach makes it possible to transfer many of the desirable properties of first-order threshold implementations, such as their low randomness usage, to the second-order setting. For example, a straightforward application to the block cipher LED results in a masking using less than 700 random bits including the initial sharing. In addition, the cryptanalytic approach introduced in this paper provides additional insight into the design of masked ciphers and allows for a quantifiable trade-off between security and performance.

We propose single-trace side-channel attacks against lattice-based KEMs, the current candidates of the NIST's standardization project. More specifically, we analyze the message encoding in the encapsulation of lattice-based KEMs to obtain the ephemeral session keys, concluding that a single trace leakage allows a whole key recovery: our implementation on a ChipWhisperer UFO STM32F3 target board shows 100% success rates for Crystals-Kyber and Saber regardless of optimization level, and more than a 79% success rate for FrodoKEM. We further show that our attack methodologies are not restricted to the above algorithms but widely applicable to other NIST PQC candidates, including LAC, NewHope, NTRU Prime, and NTRU.

Hash functions serve as the fingerprint of a message. They also serve as an authentication mechanism in many applications. Nowadays, hash functions are widely used in blockchain technology and bitcoins. Today, most of the work concentrates on the design of lightweight hash functions which needs minimal hardware and software resources. This paper proposes a lightweight hash function which makes use of Cellular Automata (CA) and sponge functions. This hash function accepts arbitrary length message and produces fixed size hash digest. An additional property of this function is that the size of the hash digest may be adjusted based on the application because of the inherent property of varying length output of sponge function. The proposed hash function can be efficiently used in resource constraint environments in a secure and efficient manner. In addition, the function is resistant to all known generic attacks against hash functions and is also preimage resistant, second preimage resistant and collision resistant.

Post-QuantumCryptography(PQC)isregardedasaneffectivewaytoresistattackswithquantum computers. Since National Institute of Standards and Technology (NIST) proposed its PQC standardiza- tion project in 2016, many candidates have been submitted and their quantum-resistant capability has been measuring by researchers. Besides this research, this Migration issues of Post-Quantum Cryptography (PQC) has been attracting more and more at- tentions ever since the National Institute of Standards and Technology (NIST) published round 3 candidates of its PQC standardization project in July, 2020. Many candidates’ quantum-resistant capability had been measured by researchers. Meanwhile, it is also indispensable to point out limitations and give proposals to those candidates’ migration issues, especially for migrating PQC to constrained environments. In this paper, we assume the cases of using PQC on hardware security module (HSM), which is designed to provide a trusted environment to perform cryptographic operations. Our comparisons includes the cases of not only small data (e.g. less than Kilobytes data) which is often used for key encryption or authentication, but also large data (e.g. several Gigabytes data) which is often used for document signing or code signing. We focus on and evaluate hashing and asymmetric operations of three lattice-based cryptosystems which are strong candidates of NIST’s PQC standardization project. Then we construct two kinds of cryptographic bound- aries for those cryptosystems that make their hashing operations inside or outside of a HSM. We compare their performances with several data sizes under different cryptographic boundary constructions, and discuss how much efficiency versus security we gain or lose with internal or external hashing. This problem already exists today with RSA/ECC and our result indicates that it is also acute with the new lattice-based schemes from the NIST round 3 finalists.

SIS problem has numerous applications in cryptography. The known algorithms for solving that problem are exponential in complexity. A new algorithm is suggested in this note, its complexity is sub-exponential for a range of parameters.

In this work, we investigate a practical consideration for Electromagnetic (EM) side-channel analysis, namely, positioning EM probe at the best location for an efficient attack, requiring fewer traces to reveal the secret key of cryptographic engines. We present Multi-Layer Perceptron (MLP) based probe positioning and EM analysis method, defining it as a classification problem by dividing the chip surface scanned by the EM probe into virtual grids, and identifying each grid location by a class label. The MLP, trained to identify the location given a single EM trace, achieves $99.55\%$ accuracy on average for traces captured during different acquisition campaigns.

Password-Authenticated Key Exchange (PAKE) lets users with passwords exchange a cryptographic key. There have been two variants of PAKE which make it more applicable to real-world scenarios: - Asymmetric PAKE (aPAKE), which aims at protecting a client's password even if the authentication server is untrusted, and - Fuzzy PAKE (fPAKE), which enables key agreement even if passwords of users are noisy, but ``close enough''. Supporting fuzzy password matches eases the use of higher entropy passwords and enables using biometrics and environmental readings (both of which are naturally noisy). Until now, both variants of PAKE have been considered only in separation. In this paper, we consider both of them simultaneously. We introduce the notion of Fuzzy Asymmetric PAKE (fuzzy aPAKE), which protects against untrusted servers and supports noisy passwords. We formulate our new notion in the Universal Composability framework of Canetti (FOCS'01), which is the preferred model for password-based primitives. We then show that fuzzy aPAKE can be obtained from oblivious transfer and some variant of robust secret sharing (Cramer et al, EC'15). We achieve security against malicious parties while avoiding expensive tools such as non-interactive zero-knowledge proofs. Our construction is round-optimal, with message and password file sizes that are independent of the schemes error tolerance.

Inserting backdoors in encryption algorithms has long seemed like a very interesting, yet difficult problem. Most attempts have been unsuccessful for symmetric-key primitives so far and it remains an open problem how to build such ciphers. In this work, we propose the MALICIOUS framework, a new method to build tweakable block ciphers that have backdoors hidden which allows to retrieve the secret key. Our backdoor is differential in nature: a specific related-tweak differential path with high probability is hidden during the design phase of the cipher. We explain how any entity knowing the backdoor can practically recover the secret key of a user and we also argue why even knowing the presence of the backdoor and the workings of the cipher will not permit to retrieve the backdoor for an external user. We analyze the security of our construction in the classical black-box model and we show that retrieving the backdoor (the hidden high-probability differential path) is very difficult. We instantiate our framework by proposing the LowMC-M construction, a new family of tweakable block ciphers based on instances of the LowMC cipher, which allow such backdoor embedding. Generating LowMC-M instances is trivial and the LowMC-M family has basically the same efficiency as the LowMC instances it is based on.

We introduce a category of O-oriented supersingular elliptic curves and derive properties of the associated oriented and nonoriented $\ell$-isogeny supersingular isogeny graphs. As an application we introduce an oriented supersingular isogeny Diffie-Hellman protocol (OSIDH), analogous to the supersingular isogeny Diffie-Hellman (SIDH) protocol and generalizing the commutative supersingular isogeny Diffie-Hellman (CSIDH) protocol.

The intersection of Non-commutative and Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K with the unit. We consider special subsemigroups (platforms) in a semigroup of all endomorphisms of K[x_1, x_2, …, x_n]. Efficiently computed homomorphisms between such platforms can be used in Post Quantum key exchange protocols when correspondents elaborate common transformation of (K*)^n. The security of these schemes is based on a complexity of decomposition problem for an element of a semigroup into a product of given generators. We suggest three such protocols (with a group and with two semigroups as platforms) for their usage with multivariate digital signatures systems. The usage of protocols allows to convert public maps of these systems into private mode, i.e. one correspondent uses the collision map for safe transfer of selected multivariate rule to his/her partner. The ‘’ privatisation’’ of former publicly given map allows the usage of digital signature system for which some of cryptanalytic instruments were found ( estimation of different attacks on rainbow oil and vinegar system, cryptanalytic studies LUOV) with the essentially smaller size of hashed messages. Transition of basic multivariate map to safe El Gamal type mode does not allow the usage of cryptanalytic algorithms for already broken Imai - Matsumoto cryptosystem or Original Oil and Vinegar signature schemes proposed by J.Patarin. So even broken digital signatures schemes can be used in the combination with protocol execution during some restricted ‘’trust interval’’ of polynomial size. Minimal trust interval can be chosen as a dimension n of the space of hashed messages, i. e. transported safely multivariate map has to be used at most n times. Before the end of this interval correspondents have to start the session of multivariate protocol with modified multivariate map. The security of such algorithms rests not on properties of quadratic multivariate maps but on the security of the protocol for the map delivery and corresponding NP hard problem.

We report the successful recovery of the key to a Zip archive containing only two encrypted files. The attack improves on our 2001 ciphertext-only attack, which required five encrypted files. The main innovations are a new differential meet-in-the-middle attack for the initial stages and the use of lattice reduction to recover the internal state of the truncated linear congruential generator.

Election verifiability aims to ensure that the outcome produced by electronic voting systems correctly reflects the intentions of eligible voters, even in the presence of an adversary that may corrupt various parts of the voting infrastructure. Protecting such systems from manipulation is challenging because of their distributed nature involving voters, election authorities, voting servers and voting platforms. An adversary corrupting any of these can make changes that, individually, would go unnoticed, yet in the end will affect the outcome of the election. It is, therefore, important to rigorously evaluate whether the measures prescribed by election verifiability achieve their goals. We propose a formal framework that allows such an evaluation in a systematic and automated way. We demonstrate its application to the verification of various scenarios in Helios and Belenios, two prominent internet voting systems, for which we capture features and corruption models previously outside the scope of formal verification. Relying on the Tamarin protocol prover for automation, we derive new security proofs and attacks on deployed versions of these protocols, illustrating trade-offs between usability and security.

The lightweight block cipher PRESENT has become viable for areas like IoT (Internet of Things) and RFID tags, due to its compact design and low power consumption, while providing a sufficient level of security for the aforementioned applications. However, the key scheduling algorithm of a cipher plays a major role in deciding how secure it is. In this paper we test the strength of the key scheduling algorithm (KSA) of the 80-bit key length variant of PRESENT by attempting to retrieve the main key register from the final round key register, using deep learning.

We construct a succinct non-interactive publicly-verifiable delegation scheme for any log-space uniform circuit under the sub-exponential Learning With Errors ($\mathsf{LWE}$) assumption. For a circuit $C:\{0,1\}^N\rightarrow\{0,1\}$ of size $S$ and depth $D$, the prover runs in time $\mathsf{poly}(S)$, the communication complexity is $D \cdot \mathsf{polylog} (S)$, and the verifier runs in time $(D+N) \cdot \mathsf{polylog} (S)$. To obtain this result, we introduce a new cryptographic primitive: lossy correlation-intractable hash functions. We use this primitive to soundly instantiate the Fiat-Shamir transform for a large class of interactive proofs, including the interactive sum-check protocol and the $\mathsf{GKR}$ protocol, assuming the sub-exponential hardness of $\mathsf{LWE}$. By relying on the result of Choudhuri et al. (STOC 2019), we also establish the sub-exponential average-case hardness of $\mathsf{PPAD}$, assuming the sub-exponential hardness of $\mathsf{LWE}$.

Mercurial signatures are a useful building block for privacy-preserving schemes, such as anonymous credentials, delegatable anonymous credentials, and related applications. They allow a signature $\sigma$ on a message $m$ under a public key $\mathsf{pk}$ to be transformed into a signature $\sigma'$ on an equivalent message $m'$ under an equivalent public key $\mathsf{pk}'$ for an appropriate notion of equivalence. For example, $\mathsf{pk}$ and $\mathsf{pk}'$ may be unlinkable pseudonyms of the same user, and $m$ and $m'$ may be unlinkable pseudonyms of a user to whom some capability is delegated. The only previously known construction of mercurial signatures suffers a severe limitation: in order to sign messages of length $n$, the signer's public key must also be of length $n$. In this paper, we eliminate this restriction and provide a signing protocol that admits messages of any length. This significantly improves the applicability of mercurial signatures to chains of anonymous credentials.

We propose a new cryptanalytic technique and key recovery attack for the Sparx cipher, Partly-Pseudo-Linear Cryptanalysis, a meet-in-the-middle attack combining linear and pseudo-linear approximations. We observe improvements over the linear hull attacks in the literature for Sparx 128/128 and 128/256. Additionally, we generate another attack for comparison purposes, using the Cho-Pieprzyk property for a fully-linear approximation and a corresponding key recovery attack. We observe improvements on the data complexity, bias, and number of recovered key bits, over all variants of Sparx, when compared to the use of only the Cho-Pieprzyk approximation.

The deep learning-based side-channel analysis represents a powerful and easy to deploy option for profiled side-channel attacks. A detailed tuning phase is often required to reach a good performance where one first needs to select relevant hyperparameters and then tune them. A common selection for the tuning phase are hyperparameters connected with the neural network architecture, while those influencing the training process are less explored. In this work, we concentrate on the optimizer hyperparameter, and we show that this hyperparameter has a significant role in the attack performance. Our results show that common choices of optimizers (Adam and RMSprop) indeed work well, but they easily overfit, which means that we must use short training phases, small profiled models, and explicit regularization. On the other hand, SGD type of optimizers works well on average (slower convergence and less overfit), but only if momentum is used. Finally, our results show that Adagrad represents a strong option to use in scenarios with longer training phases or larger profiled models.

Fitzi, Garay, Maurer, and Ostrovsky (Journal of Cryptology 2005) showed that in the presence of a dishonest majority, no primitive of cardinality $n - 1$ is complete for realizing an arbitrary $n$-party functionality with guaranteed output delivery. In this work, we introduce a new $2$-party primitive $\mathcal{F}_{\mathsf{SyX}}$ (``synchronizable fair exchange'') and show that it is complete for realizing any $n$-party functionality with fairness in a setting where all $n$ parties are pairwise connected by independent instances of $\mathcal{F}_{\mathsf{SyX}}$. In the $\mathcal{F}_{\mathsf{SyX}}$-hybrid model, the two parties load $\mathcal{F}_{\mathsf{SyX}}$ with some input, and following this, either party can trigger $\mathcal{F}_{\mathsf{SyX}}$ with a suitable ``witness'' at a later time to receive the output from $\mathcal{F}_{\mathsf{SyX}}$. Crucially the other party also receives output from $\mathcal{F}_{\mathsf{SyX}}$ when $\mathcal{F}_{\mathsf{SyX}}$ is triggered. The trigger witnesses allow us to synchronize the trigger phases of multiple instances of $\mathcal{F}_{\mathsf{SyX}}$, thereby aiding in the design of fair multiparty protocols. Additionally, a pair of parties may reuse a single a priori loaded instance of $\mathcal{F}_{\mathsf{SyX}}$ in any number of multiparty protocols (possibly involving different sets of parties).

We design Aardvark, a novel authenticated dictionary with short proofs of correctness for lookups and modifications. Our design reduces storage requirements for transaction validation in cryptocurrencies by outsourcing data from validators to untrusted servers, which supply proofs of correctness of this data as needed. In this setting, short proofs are particularly important because proofs are distributed to many validators, and the transmission of long proofs can easily dominate costs. A proof for a piece of data in an authenticated dictionary may change whenever any (even unrelated) data changes. This presents a problem for concurrent issuance of cryptocurrency transactions, as proofs become stale. To solve this problem, Aardvark employs a versioning mechanism to safely accept stale proofs for a limited time. On a dictionary with 100 million keys, operation proof sizes are about 1KB in a Merkle Tree versus 100–200B in Aardvark. Our evaluation shows that a 32-core validator processes 1492– 2941 operations per second, saving about 800× in storage costs relative to maintaining the entire state.