This work introduce a new approach called Max bias analysis for the entropy computation of structures of Free Ring Oscillator-based Physical Random Number Generator. It employs the stochastic model based on the well-established Wiener process, specifically adapted to only capture thermal noise contributions while accounting for potential non-zero bias in the duty cycle. Our analysis is versatile, applicable to combinations of multiple sampled Ring Oscillator (RO) filtering by any function....

The nonlinear filter model is an old and well understood approach to the design of secure stream ciphers. Extensive research over several decades has shown how to attack stream ciphers based on this model and has identified the security properties required of the Boolean function used as the filtering function to resist such attacks. This led to the problem of constructing Boolean functions which provide adequate security and at the same time are efficient to implement. Unfortunately, over...

The increasing number of blockchain projects introduced annually has led to a pressing need for secure and efficient interoperability solutions. Currently, the lack of such solutions forces end-users to rely on centralized intermediaries, contradicting the core principle of decentralization and trust minimization in blockchain technology. In this paper, we propose a decentralized and efficient interoperability solution (aka Bridge Protocol) that operates without additional trust assumptions,...

Zero-knowledge proofs of training (zkPoT) allow a party to prove that a model is trained correctly on a committed dataset without revealing any additional information about the model or the dataset. Existing zkPoT protocols prove the entire training process in zero knowledge; i.e., they prove that the final model was obtained in an iterative fashion starting from the training data and a random seed (and potentially other parameters) and applying the correct algorithm at each iteration. This...

We consider the problem of electing a leader among $n$ parties with the guarantee that each (honest) party has a reasonable probability of being elected, even in the presence of a coalition that controls a subset of parties, trying to bias the output. This notion is called ``game-theoretic fairness'' because such protocols ensure that following the honest behavior is an equilibrium and also the best response for every party and coalition. In the two-party case, Blum's commit-and-reveal...

We introduce a powerful attack, termed the bit-fixing correlation attack, on Goldreich's pseudorandom generators (PRGs), specifically focusing on those based on the $\mathsf{XOR}\text{-}\mathsf{THR}$ predicate. By exploiting the bit-fixing correlation property, we derive correlation equations with high bias by fixing certain bits. Utilizing two solvers to handle these high-bias correlation equations, we present inverse attacks on $\mathsf{XOR}\text{-}\mathsf{THR}$ based PRGs within the...

We present a key-recovery attack on a variant of the Seasign signature scheme presented by [Kim24], which attempts to avoid rejection sampling by presampling vectors $\mathbf{f}$ such that the $\mathbf{f}-\mathbf{e}$ is contained in an acceptable bound, where $\mathbf{e}$ is the secret key. We show that this choice leads to a bias of these vectors such that, in a small number of signatures, the secret key can either be completely recovered or its keyspace substantially reduced. In...

In the *Distributed Secret Sharing Generation* (DSG) problem $n$ parties wish to obliviously sample a secret-sharing of a random value $s$ taken from some finite field, without letting any of the parties learn $s$. *Distributed Key Generation* (DKG) is a closely related variant of the problem in which, in addition to their private shares, the parties also generate a public ``commitment'' $g^s$ to the secret. Both DSG and DKG are central primitives in the domain of secure multiparty...

Differential-linear cryptanalysis was introduced by Langford and Hellman in 1994 and has been extensively studied since then. In 2019, Bar-On et al. presented the Differential-Linear Connectivity Table (DLCT), which connects the differential part and the linear part, thus an attacked cipher is divided to 3 subciphers: the differential part, the DLCT part, and the linear part. In this paper, we firstly present an accurate mathematical formula which establishes a relation between...

This paper presents a framework for evaluating the differential cryptanalysis resistance of a Feistel cipher that uses Ajtai SIS hash function as its S-box. We derive an upper bound on the maximum differential probability and analyze the S-box output bias using a generalized extreme value (GEV) model. Simulation results indicate that practical security is achieved with 16 rounds for a 32-bit block and six for a 128-bit block.

FuLeeca is a signature scheme submitted to the recent NIST call for additional signatures. It is an efficient hash-and-sign scheme based on quasi-cyclic codes in the Lee metric and resembles the lattice-based signature Falcon. FuLeeca proposes a so-called concentration step within the signing procedure to avoid leakage of secret-key information from the signatures. However, FuLeeca is still vulnerable to learning attacks, which were first observed for lattice-based schemes. We present three...

Statistical Fault Attacks (SFA), introduced by Fuhr et al., exploit the statistical bias resulting from injected faults. Unlike prior fault analysis attacks, which require both faulty and correct ciphertexts under the same key, SFA leverages only faulty ciphertexts. In CHES 2018, more powerful attacks called Statistical Ineffective Fault Attacks (SIFA) have been proposed. In contrast to the previous fault attacks that utilize faulty ciphertexts, SIFA exploits the distribution of the...

Regular access to unpredictable and bias-resistant randomness is important for applications such as blockchains, voting, and secure distributed computing. Distributed random beacon protocols address this need by distributing trust across multiple nodes, with the majority of them assumed to be honest. Numerous applications across the blockchain space have led to the proposal of several distributed random beacon protocols, with some already implemented. However, many current random beacon...

We present a set of physical profiled attacks against CRYSTALS-Dilithium that accumulate noisy knowledge on secret keys over multiple signatures, finally leading to a full recovery attack. The methodology is composed of two steps. The first step consists of observing or inserting a bias in the posterior distribution of sensitive variables. The second step of an information processing phase which is based on belief propagation, which allows effectively exploiting that bias. The proposed...

A revealable functional commitment allows a prover to commit to a secret polynomial size function $f$. Later, the prover has the ability to (1) prove that $y = f(x)$ for public $x, y$ and (2) open a small window into $f$'s machinery, via an encoded set of constraints - all without divulging any other information about $f$. In this way, revealable functional commitments allow the operator of a proprietary function to prove desired predicate about the function. For example, a government can...

Protocols for distributed (threshold) key generation (DKG) in the discrete-logarithm setting have received a tremendous amount of attention in the past few years. Several synchronous DKG protocols have been proposed, but most such protocols are not fully secure: they either allow corrupted parties to bias the key, or are not robust and allow malicious parties to prevent successful generation of a key. We explore the round complexity of fully secure DKG in the honest-majority setting where...

Abstract—Corporate sexual harassment policies often prioritize liability mitigation over the creation of a corporate culture free of harassment. Victims of sexual harassment are often required to report claims individually to HR. This can create an environment of self-censorship when employees feel that they cannot trust HR to act as an unbiased mediator. This problem is compounded when corporations have a culture that is tolerant of certain types of harassment. Forcing employees to report...

A central problem in cryptanalysis is to find all the significant deviations from randomness in a given $n$-bit cryptographic primitive. When $n$ is small (e.g., an $8$-bit S-box), this is easy to do, but for large $n$, the only practical way to find such statistical properties was to exploit the internal structure of the primitive and to speed up the search with a variety of heuristic rules of thumb. However, such bottom-up techniques can miss many properties, especially in cryptosystems...

The Mixed Integer Linear Programming (MILP) technique has been widely applied in the realm of symmetric-key cryptanalysis. In this paper, we propose a new bitwise breakdown MILP modeling strategy for describing the linear propagation rules of modular addition-based operations. We apply such new techniques to cryptanalysis of the SNOW stream cipher family and find new linear masks: we use the MILP model to find many linear mask candidates among which the best ones are identified with...

We construct the first actively-secure threshold version of the cryptosystem based on class groups from the so-called CL~framework (Castagnos and Laguillaumie, 2015). We show how to use our threshold scheme to achieve general universally composable (UC) secure multiparty computation (MPC) with only transparent set-up, i.e., with no secret trapdoors involved. On the way to our goal, we design new zero-knowledge (ZK) protocols with constant communication complexity for proving...

Random Allocation -the random assignment of the data to the parties- is a well-studied topic in the analysis of medical or judicial data, and the context of resource distribution. Random allocation reduces the chance of bias or corruption in the relevant applications, which makes the results more reliable. This is done by preventing a special or pre-planned assignment of the data to accommodate the assessment toward the desired results. This paper provides the first formal syntax and...

Numerous fault models have been developed, each with distinct characteristics and effects. These models should be evaluated in light of their costs, repeatability, and practicability. Moreover, there must be effective ways to use the injected fault to retrieve the secret key, especially if there are some countermeasures in the implementation. In this paper, we introduce a new fault analysis technique called ``linked fault analysis'' (LFA), which can be viewed as a more powerful version of...

We introduce a notion of round-robin secure sampling that captures several protocols in the literature, such as the "powers-of-tau" setup protocol for pairing-based polynomial commitments and zk-SNARKs, and certain verifiable mixnets. Due to their round-robin structure, protocols of this class inherently require $n$ sequential broadcast rounds, where $n$ is the number of participants. We describe how to compile them generically into protocols that require only $O(\sqrt{n})$ broadcast...

Public random beacons publish random numbers at regular intervals, which anyone can obtain and verify. The design of public distributed random beacons has been an exciting research direction with significant implications for blockchains, voting, and beyond. Distributed random beacons, in addition to being bias-resistant and unpredictable, also need to have low communication overhead and latency, high resilience to faults, and ease of reconfigurability. Existing synchronous random beacon...

The topic of this contribution is the cryptanalytic use of spurious keys, i.e. non-target keys returned by exhaustive key search. We show that the counting of spurious keys allows the construction of distinguishing attacks against block ciphers that are generically expected to start working at (marginally) lower computational cost than is required to find the target key by exhaustive search. We further show that if a brute force distinguisher does return a strong distinguishing signal,...

This study focuses on differential cryptanalysis of the ChaCha stream cipher. In the conventional approach, an adversary first searches for an input/output differential pair with the highest differential bias and then analyzes the probabilistic neutral bits (PNB) based on the obtained input/output differential pair. However, although the time and data complexities for the attack can be estimated by the differential bias and PNB obtained by this approach, the combination of the differential...

Using secure multiparty computation (MPC), organizations which own sensitive data (e.g., in healthcare, finance or law enforcement) can train machine learning models over their joint dataset without revealing their data to each other. At the same time, secure computation restricts operations on the joint dataset, which impedes computation to assess its quality. Without such an assessment, deploying a jointly trained model is potentially illegal. Regulations, such as the European Union's...

Consider an $n$-message coin-tossing protocol between $n$ parties $P_1,\dots,P_n$, in which $P_i$ broadcasts a single message $w_i$ in round $i$ (possibly based on the previously shared messages) and at the end they agree on bit $b$. A $k$-replacing adversary $A_k$ can change up to $k$ of the messages as follows. In every round $i$, the adversary who knows all the messages broadcast so far, as well as a message $w_i$ that is prepared by $P_i$ to be just sent, can can to replace the prepared...

Thermal jitter (phase noise) from a free-running ring oscillator is a common, easily implementable physical randomness source in True Random Number Generators (TRNGs). We show how to evaluate entropy, autocorrelation, and bit pattern distributions of ring oscillator noise sources, even with low jitter levels or some bias. Entropy justification is required in NIST 800-90B and AIS-31 testing and for applications such as the RISC-V entropy source extension. Our numerical evaluation algorithms...

Arbiter based Physical Unclonable Function (sometimes called Physically Unclonable Function, or in short PUF) is a hardware based pseudorandom bit generator. The pseudorandomness in the output bits depends on device specific parameters. For example, based on the delay parameters, an $n$-length Arbiter PUF can be considered as an n-variable Boolean function. We note that the random variation of the delay parameters cannot exhaust all the Boolean functions and the class is significantly...

We present the LP-PUF, a novel, Arbiter PUF-based, CMOS-compatible strong PUF design. We explain the motivation behind the design choices for LP-PUF and show evaluation results to demonstrate that LP-PUF has good uniqueness, low bias, and fair bit sensitivity and reliability values. Furthermore, based on analyses and discussion of the LR and splitting attacks, the reliability attacks, and MLP attack, we argue that the LP-PUF has potential to be secure against known PUF modeling attacks,...

Cleve’s celebrated lower bound (STOC’86) showed that a de facto strong fairness notion is impossible in 2-party coin toss, i.e., the corrupt party always has a strategy of biasing the honest party’s outcome by a noticeable amount. Nonetheless, Blum’s famous coin-tossing protocol(CRYPTO’81) achieves a strictly weaker “game-theoretic” notion of fairness — specifically, it is a 2-party coin toss protocol in which neither party can bias the outcome towards its own preference; and thus the...

The developments in the areas of strong Physical Unclonable Functions (PUFs) predicate an ongoing struggle between designers and attackers. Such a combat motivated the atmosphere of open research, hence enhancing PUF designs in the presence of Machine Learning (ML) attacks. As an example of this controversy, at CHES 2019, a novel delay-based PUF (iPUF) has been introduced and claimed to be resistant against various ML and reliability attacks. At CHES 2020, a new divide-and-conquer modeling...

Reliable and verifiable public randomness is not only an essential building block in various cryptographic primitives, but also is a critical component in many distributed and decentralized protocols, e.g., blockchain sharding. A 'good' randomness generator should preserve several distinctive properties, such as public-verifiability, bias-resistance, unpredictability, and availability. However, it is a challenging task to generate such good randomness. For instance, a dishonest party may...

This note solves the open problem of finding a closed formula for the bias of a rotational differential-linear distinguisher proposed in IACR ePrint 2021/189 (EUROCRYPT 2021), completely generalizing the results on ordinary differential-linear distinguishers due to Blondeau, Leander, and Nyberg (JoC 2017) to the case of rotational differential-linear distinguishers.

The introduction of the automatic search boosts the cryptanalysis of symmetric-key primitives to some degree. However, the performance of the automatic search is not always satisfactory for the search of long trails or ciphers with large state sizes. Compared with the extensive attention on the enhancement for the search with the mixed integer linear programming (MILP) method, few works care for the acceleration of the automatic search with the Boolean satisfiability problem (SAT) or...

This paper presents three attack vectors of bit-wise cryptanalysis including rotational, bit-wise differential, and zero-sum distinguishing attacks on the AND-RX permutation Friet-PC, which is implemented in a lightweight authenticated encryption scheme Friet. First, we propose a generic procedure for a rotational attack on AND-RX cipher with round constants. By applying the proposed attack to Friet-PC, we can construct an 8-round rotational distinguisher with a time complexity of 2^{102}....

The differential-linear attack, combining the power of the two most effective techniques for symmetric-key cryptanalysis, was proposed by Langford and Hellman at CRYPTO 1994. From the exact formula for evaluating the bias of a differential-linear distinguisher (JoC 2017), to the differential-linear connectivity table (DLCT) technique for dealing with the dependencies in the switch between the differential and linear parts (EUROCRYPT 2019), and to the improvements in the context of...

Having shared access to high-quality random numbers is essential in many important applications. Yet, existing constructions of distributed random beacons still have limitations such as imperfect security guarantees, strong setup or network assumptions, or high costs. In this paper, we present SPURT, an efficient distributed randomness beacon protocol that does not require any trusted or expensive setup and is secure against a malicious adversary that controls up to one-third of the nodes in...

Random beacon protocols provide a continuous public source of randomness and their applications range from public lotteries to zero-knowledge proofs. Existing random beacon protocols in the bounded synchronous model sacrifice either the fault tolerance or the communication complexity for security, or ease of reconfigurability. This work overcomes the challenges with the existing works through a novel communication efficient combination of state machine replication and (publicly) verifiable...

The Statistical Ineffective Fault Analysis, SIFA, is a recent addition to the family of fault based cryptanalysis techniques. SIFA based attack is shown to be formidable and is able to bypass virtually all the conventional fault attack countermeasures. Reported countermeasures to SIFA incur overheads of the order of at least thrice the unprotected cipher. We propose a novel countermeasure that reduces the overhead (compared to all existing countermeasures) as we rely on a simple duplication...

Fully secure multiparty computation (MPC) allows a set of parties to compute some function of their inputs, while guaranteeing correctness, privacy, fairness, and output delivery. Understanding the necessary and sufficient assumptions that allow for fully secure MPC is an important goal. Cleve (STOC'86) showed that full security cannot be obtained in general without an honest majority. Conversely, by Rabin and Ben-Or (STOC'89), assuming a broadcast channel and an honest majority enables a...

Subterranean 2.0 is a cipher suite that can be used for hashing, authenticated encryption, MAC computation, etc. It was designed by Daemen, Massolino, Mehrdad, and Rotella, and has been selected as a candidate in the second round of NIST's lightweight cryptography standardization process. Subterranean 2.0 is a duplex-based construction and utilizes a single-round permutation in the duplex. It is the simplicity of the round function that makes it an attractive target of cryptanalysis. In...

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...

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...

Differential analysis is an important cryptanalytic technique on block ciphers. In one form, this measures the probability of occurrence of the differences between certain inputs vectors and the corresponding outputs vectors. For this analysis, the constituent S-boxes of Block cipher need to be studied carefully. In this direction, we derive further cryptographic properties of inverse function, especially higher-order differential properties here. This improves certain results of Boukerrou...

In this paper, we extend the concept of bias amplifiers and show how they can be used to detect badly broken noise sources both in the design and production phases of a true random number generator. We also develop a theoretical framework that supports the experimental results obtained in this paper.

Although it is one of the most popular signature schemes today, ECDSA presents a number of implementation pitfalls, in particular due to the very sensitive nature of the random value (known as the nonce) generated as part of the signing algorithm. It is known that any small amount of nonce exposure or nonce bias can in principle lead to a full key recovery: the key recovery is then a particular instance of Boneh and Venkatesan's hidden number problem (HNP). That observation has been...

The Gimli permutation proposed in CHES 2017 was designed for cross-platform performance. One main strategy to achieve such a goal is to utilize a sparse linear layer (Small-Swap and Big-Swap), which occurs every two rounds. In addition, the round constant addition occurs every four rounds and only one 32-bit word is affected by it. The above two facts have been recently exploited to construct a distinguisher for the full Gimli permutation with time complexity $2^{64}$. By utilizing a new...

In their seminal work, Ben-Or and Linial (1985) introduced the full information model for collective coin-tossing protocols involving $n$ processors with unbounded computational power using a common broadcast channel for all their communications. The design and analysis of coin-tossing protocols in the full information model have close connections to diverse fields like extremal graph theory, randomness extraction, cryptographic protocol design, game theory, distributed protocols, and...

In this paper we exploit elementary combinatorial techniques to settle different cryptanalytic observations on RC4 that remained unproved for more than two decades. At the same time, we present new observations with theoretical proofs. We first prove the biases (non-randomness) presented by Fluhrer and McGrew (FSE 2000) two decades ago. It is surprising that though the biases have been published long back, and there are many applications of them in cryptanalysis till recent days as well, the...

The $k$-nearest neighbors ($k$NN) classifier predicts a class of a query, $q$, by taking the majority class of its $k$ neighbors in an existing (already classified) database, $S$. In secure $k$NN, $q$ and $S$ are owned by two different parties and $q$ is classified without sharing data. In this work we present a classifier based on $k$NN, that is more efficient to implement with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make to consider $\kappa$...

There is a significant interest in securely computing functionalities with guaranteed output delivery, \aka, fair computation. For example, consider a 2-party $n$-round coin-tossing protocol in the information-theoretic setting. Even if one party aborts during the protocol execution, the other party has to receive her outcome. Towards this objective, every round, the sender of that round's message, preemptively prepares a defense coin, which is her output if the other party aborts...

In this paper we provide a theoretical argument towards an unsolved question related to Mantin's ``Digraph Repetition Bias" (Eurocrypt 2005) that is observed in the key-stream of RC4. The open question, that depends on the observation that arrival of four consecutive same bytes (of the form $AAAA$) in RC4 key-stream is slightly negatively biased, was posed by Bricout et al [Des. Codes Cryptogr. (2018) 86:743-770] in 2016. Moreover, for the first time, we consider the ``Reverse Digraph...

In the setting of secure multiparty computation (MPC), a set of mutually distrusting parties wish to jointly compute a function, while guaranteeing the privacy of their inputs and the correctness of the output. An MPC protocol is called fully secure if no adversary can prevent the honest parties from obtaining their outputs. A protocol is called fair if an adversary can prematurely abort the computation, however, only before learning any new information. We present highly efficient...

We consider the problem of amplifying two-party coin-tossing protocols: given a protocol where it is possible to bias the common output by at most $\rho$, we aim to obtain a new protocol where the output can be biased by at most $\rho^\star<\rho$. We rule out the existence of a natural type of amplifiers called oblivious amplifiers for every $\rho^\star<\rho$. Such amplifiers ignore the way that the underlying $\rho$-bias protocol works and can only invoke an oracle that provides $\rho$-bias...

Distributed randomness is very useful for many applications, such as smart contract, proof-of-stake-based blockchain, elliptic curve generation and lottery. Randomness beacon protocols are proposed, which are aimed at continuously distributed randomness generation. However, a reliable source of distributed randomness is gained with difficulty because of Byzantine behavior, which may lead to bias for distributed randomness. These Byzantine behaviors include, but not limited to, the “last...

We demonstrate that XOR Arbiter PUFs with an even number of arbiter chains have inherently biased responses, even if all arbiter chains are perfectly unbiased. This rebukes the believe that XOR Arbiter PUFs are, like Arbiter PUFs, unbiased when ideally implemented and proves that independently manufactured Arbiter PUFs are not statistically independent. As an immediate result of this work, we suggest to use XOR Arbiter PUFs with odd numbers of arbiter chains whenever possible. Furthermore,...

SNOW 3G is a stream cipher designed in 2006 by ETSI/SAGE, serving in 3GPP as one of the standard algorithms for data confidentiality and integrity protection. It is also included in the 4G LTE standard. In this paper we derive vectorized linear approximations of the finite state machine in SNOW 3G. In particular, we show one 24-bit approximation with a bias around $2^{-37}$ and one byte-oriented approximation with a bias around $2^{-40}$. We then use the approximations to launch attacks on...

In this paper, we provide a notable step towards filling the gap between theory (estimates of running-time) and practice (a discrete logarithm record computation) for the Tower Number Field Sieve (TNFS) algorithm. We propose a generalisation of ranking formula for selecting the polynomials used in the very first step of TNFS algorithm. For this we provide a definition and an exact implementation (Magma and SageMath) of the alpha function. This function measures the bias in the smoothness...

SipHash is a family of ARX-based MAC algorithms optimized for short inputs. Already, a lot of implementations and applications for SipHash have been proposed, whereas the cryptanalysis of SipHash still lags behind. In this paper, we study the property of truncated differential in SipHash and find out the output bits with the most imbalanced differential biases. Making use of these results, we construct distinguishers with practical complexity $2^{10}$ for SipHash-2-1 and $2^{36}$ for...

Machine learning is nowadays supplanting or extending human expertise in many domains ranging from board games to text translation. Correspondingly, the use of such tools is also on the rise in computer security. Alongside CHES 2018, a side channel challenge was organised under the theme of ’Deep Learning vs Classical SCA’ to test whether Deep Learning is presently widely used in the SCA community and whether it yields competitive results. The competition had 58 participants, it ran for...

We design an efficient method for sampling a large batch of $d$ independent coins with a given bias $p \in [0,1]$. The folklore secure computation method for doing so requires $O(\lambda + \log d)$ communication and computation per coin to achieve total statistical difference $2^{-\lambda}$. We present an exponential improvement over the folklore method that uses just $O(\log(\lambda+\log d))$ gates per coin when sampling $d$ coins with total statistical difference $2^{-\lambda}$. We...

The fast correlation attack (FCA) is one of the most important cryptanalytic techniques against LFSR-based stream ciphers. In CRYPTO 2018, Todo et al. found a new property for the FCA and proposed a novel algorithm which was successfully applied to the Grain family of stream ciphers. Nevertheless, these techniques can not be directly applied to Grain-like small state stream ciphers with keyed update, such as Plantlet, Fruit-v2, and Fruit80. In this paper, we study the security of Grain-like...

Machine learning techniques represent a powerful option in profiling side-channel analysis. Still, there are many settings where their performance is far from expected. In such occasions, it is very important to understand the difficulty of the problem and the behavior of the machine learning algorithm. To that end, one needs to investigate not only the performance of machine learning but also to provide insights into its explainability. One tool enabling us to do this is the bias-variance...

One of Bitcoin’s core security guarantees is that, for an attacker to be able to successfully interfere with the Bitcoin network and reverse transactions, they need to control 51% of total hash power. Eyal et al., however, significantly reduces Bitcoin’s security guarantee by introducing another type of attack, called "Selfish Mining". The key idea behind selfish mining is for a miner to keep its discovered blocks private, thereby intentionally forking the chain. As a result of a selfish...

Statistical saturation attack takes advantage of a set of plaintext with some bits fixed while the others vary randomly, and then track the evolution of a non-uniform plaintext distribution through the cipher. Previous statistical saturation attacks are all implemented under single-key setting, and there is no public attack models under related-key/tweak setting. In this paper, we propose a new cryptanalytic method which can be seen as related-key/tweak statistical saturation attack by...

We propose an authenticated encryption scheme for the VMPC-R stream cipher. VMPC-R is an RC4-like algorithm proposed in 2013. It was created in a challenge to find a bias-free cipher within the RC4 design scope and to the best of our knowledge no security weakness in it has been published to date. The contribution of this paper is an algorithm to compute Message Authentication Codes (MACs) along with VMPC-R encryption. We also propose a simple method of transforming the MAC computation...

In this paper, we compute hundreds of Bitcoin private keys and dozens of Ethereum, Ripple, SSH, and HTTPS private keys by carrying out cryptanalytic attacks against digital signatures contained in public blockchains and Internet-wide scans. The ECDSA signature algorithm requires the generation of a per-message secret nonce. If this nonce is not generated uniformly at random, an attacker can potentially exploit this bias to compute the long-term signing key. We use a lattice-based...

Coin toss has been extensively studied in the cryptography literature, and the well-accepted notion of fairness (henceforth called strong fairness) requires that a corrupt coalition cannot cause non-negligible bias. It is well-understood that two-party coin toss is impossible if one of the parties can prematurely abort; further, this impossibility generalizes to multiple parties with a corrupt majority (even if the adversary is computationally bounded and fail-stop only). Interestingly, the...

We investigate sampling procedures that certify that an arbitrary quantum state on $n$ subsystems is close to an ideal mixed state $\varphi^{\otimes n}$ for a given reference state $\varphi$, up to errors on a few positions. This task makes no sense classically: it would correspond to certifying that a given bitstring was generated according to some desired probability distribution. However, in the quantum case, this is possible if one has access to a prover who can supply a purification of...

A two-party coin-flipping protocol is $\epsilon$-fair if no efficient adversary can bias the output of the honest party (who always outputs a bit, even if the other party aborts) by more than $\epsilon$. Cleve [STOC '86] showed that $r$-round $o(1/r)$-fair coin-flipping protocols do not exist. Awerbuch et al. [Manuscript '85] constructed a $\Theta(1/\sqrt{r})$-fair coin-flipping protocol, assuming the existence of one-way functions. Moran et al. [Journal of Cryptology '16] constructed an...

Like any other cryptanalytic attack, the success rate of a linear attack is expected to improve as more data becomes available. Bogdanov and Tischhauser (FSE 2013) made the rather surprising claim that the success rate of a linear attack may go down with increasing plaintext amount, after an optimal point. They supported this claim with experimental evidence by an attack on SmallPresent-20. Different explanations have been given to explain this surprising phenomenon. In this note, we give...

Most secure computation protocols can be effortlessly adapted to offload a significant fraction of their computationally and cryptographically expensive components to an offline phase so that the parties can run a fast online phase and perform their intended computation securely. During this offline phase, parties generate private shares of a sample generated from a particular joint distribution, referred to as the correlation. These shares, however, are susceptible to leakage attacks by...

A reliable source of randomness is not only an essential building block in various cryptographic, security, and distributed systems protocols, but also plays an integral part in the design of many new blockchain proposals. Consequently, the topic of publicly-verifiable, bias-resistant and unpredictable randomness has recently enjoyed increased attention. In particular random beacon protocols, aimed at continuous operation, can be a vital component for current Proof-of-Stake based distributed...

AEGIS is an authenticated cipher introduced at SAC 2013, which takes advantage of AES-NI instructions to reach outstanding speed in software. Like LEX, Fides, as well as many sponge-based designs, AEGIS leaks part of its inner state each round to form a keystream. In this paper, we investigate the existence of linear biases in this keystream. Our main result is a linear mask with bias $2^{-89}$ on the AEGIS-256 keystream. The resulting distinguisher can be exploited to recover bits of a...

In 2013, Misoczki, Tillich, Sendrier and Barreto proposed a variant of the McEliece cryptosystem based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes. This proposal uses an iterative bit-flipping algorithm in its decryption procedure. Such algorithms fail with a small probability. At Asiacrypt 2016, Guo, Johansson and Stankovski (GJS) exploited these failures to perform a key recovery attack. They introduced the notion of the distance spectrum of a sparse vector and showed...

In this paper, using probability transition matrix, at first we revisit the work of Mantin on finding the probability distribution of RC4 permutation after the completion of KSA. After that, we extend the same idea to analyse the probabilities during any iteration of Pseudo Random Generation Algorithm. Next, we study the bias $Z_r=r$ (where $Z_r$ is the $r$-th output keystream bit), which is one of the significant biases observed in RC4 output keystream. This bias has played an important...

Austrin, Chung, Mahmoody, Pass and Seth (Crypto'14) studied the notion of bitwise $p$-tampering attacks over randomized algorithms in which an efficient `virus' gets to control each bit of the randomness with independent probability $p$ in an online way. The work of Austrin et al. showed how to break certain `privacy primitives' (e.g., encryption, commitments, etc.) through bitwise $p$-tampering, by giving a bitwise $p$-tampering biasing attack for increasing the average $E[f(U_n)]$ of...

Device-specific physical characteristics provide the foundation for PUFs, a hardware primitive for secure storage of cryptographic keys. So far, they have been implemented by either directly evaluating a binary output or by mapping outputs from a higher-order alphabet to a fixed-length bit sequence. However, the latter causes a significant bias in the derived key when combined with an equidistant quantization. To overcome this limitation, we propose a variable-length bit mapping that...

Random number generation is critical to many security protocols, a basic building block on which it rests the robustness of many security solutions. Quantum physics, on the other hand, offers a very attractive approach to True Random Number Generation, based on the inherent randomness of some physical phenomena. Naturally, there are a number of quantum random number generators in the market. In this work, we present the first analysis of a popular commercial family called Quantis, designed...

Defined in the standard GOST 28147-89, GOST is a Soviet and Russian government standard symmetric-key block cipher. GOST has the 64-bit block size and a key length of 256 bits. It is a Feistel network of 32 rounds. In 2010, GOST was submitted to ISO 18033 to become a worldwide industrial encryption standard. GOST 28147-89 has also been published as informational RFC 5830 with IETF. In this paper, we study linear attacks on GOST 28147-89. Prior to us, [Shorin-Jelezniakov-Gabidulin'2001]...

Designing a secure permissionless distributed ledger that performs on par with centralized payment processors such as Visa is challenging. Most existing distributed ledgers are unable to "scale-out'' -- growing total processing capacity with number of participants -- and those that do compromise security or decentralization. This work presents OmniLedger, the first scale-out distributed ledger that can preserve long-term security under permissionless operation. OmniLedger ensures strong...

This paper deals with linear approximations having absolute bias smaller than $2^{-\frac{n}{2}}$ which were previously believed to be unusable for a linear attack. We show how a series of observations which are individually not statistically significant can be used to create a $\chi^2$ distinguisher. This is different from previous works which combined a series of significant observations to reduce the data complexity of a linear attack. We test the distinguisher on a real-world cipher and...

The internal state of RC4 stream cipher is a permutation over ${\mathbb Z}_N$ and its state transition is effectively a transposition or swapping of two elements. How the randomness of RC4 state evolves due to its state transitions has been studied for many years. As the number of swaps increases, the state comes closer to a uniform random permutation. We call the burn-in period of RC4 state transition as the number of swaps required to make the state very close to uniform random permutation...

Bias-resistant public randomness is a critical component in many (distributed) protocols. Existing solutions do not scale to hundreds or thousands of participants, as is needed in many decentralized systems. We propose two large-scale distributed protocols, RandHound and RandHerd, which provide publicly-verifiable, unpredictable, and unbiasable randomness against Byzantine adversaries. RandHound relies on an untrusted client to divide a set of randomness servers into groups for scalability,...

ChaCha and Salsa are two software oriented stream ciphers that have attracted serious attention in academic as well as commercial domain. The most important cryptanalysis of reduced versions of these ciphers was presented by Aumasson et al. in FSE 2008. One part of their attack was to apply input difference(s) to investigate biases after a few rounds. So far there have been certain kind of limited exhaustive searches to obtain such biases. For the first time, in this paper, we show how to...

Linear cryptanalysis is considered to be one of the strongest techniques in the cryptanalyst’s arsenal. In most cases, Matsui’s Algorithm 2 is used for the key recovery part of the attack. The success rate analysis of this algorithm is based on an assumption regarding the bias of a linear approximation for a wrong key, known as the wrong-key-randomization hypothesis. This hypothesis was refined by Bogdanov and Tischhauser to take into account the stochastic nature of the bias for a wrong...

An $\alpha$-fair coin-tossing protocol allows a set of mutually distrustful parties to generate a uniform bit, such that no efficient adversary can bias the output bit by more than $\alpha$. Cleve [STOC 1986] has shown that if half of the parties can be corrupted, then, no $r$-round coin-tossing protocol is $o(1/r)$-fair. For over two decades the best known $m$-party protocols, tolerating up to $t\geq m/2$ corrupted parties, were only $O(t/\sqrt{r})$-fair. In a surprising result, Moran,...

We introduce “thrifty” zero-knowledge protocols, or TZK. These protocols are constructed by introducing a bias in the challenge send by the prover. This bias is chosen so as to maximize the security versus effort trade-off. We illustrate the benefits of this approach on several well-known zero-knowledge protocols.

Walsh-Hadamard transform is used in a wide variety of scientific and engineering applications, including bent functions and cryptanalytic optimization techniques in cryptography. In linear cryptanalysis, it is a key question to find a good linear approximation, which holds with probability $(1+d)/2$ and the bias $d$ is large in absolute value. Lu and Desmedt (2011) take a step toward answering this key question in a more generalized setting and initiate the work on the generalized bias...

At Crypto 2015, Blondeau et al. showed a known-key analysis on the full PRESENT lightweight block cipher. Based on some of the best differential distinguishers, they introduced a meet in the middle (MitM) layer to pre-add the differential distinguisher, which extends the number of attacked rounds on PRESENT from 26 rounds to full rounds without reducing differential probability. In this paper, we generalize their method and present a distinguisher on a kind of permutations called...

Spritz is a stream cipher proposed by Rivest and Schuldt at the rump session of CRYPTO 2014. It is intended to be a replacement of the popular RC4 stream cipher. In this paper we propose distinguishing attacks on the full Spritz, based on {\it a short-term bias} in the first two bytes of a keystream and {\it a long-term bias} in the first two bytes of every cycle of $N$ keystream bytes, where $N$ is the size of the internal permutation. Our attacks are able to distinguish a keystream of...

The Arbiter Physically Unclonable Function (APUF) is a widely used strong delay PUF design. There are two FPGA variants of this design, namely, Programmable Delay Line APUF (PAPUF) and Double APUF (DAPUF) to mitigate the FPGA platform specific implementation issues. In this paper, we introduce the idea of Architectural Bias to compare the impact of the architecture of these APUF designs on their design bias. The biased challenge-response behavior of a delay PUF implies the non-uniform...

Instead of simply using two-dimensional $User \times Item$ features, advanced recommender systems rely on more additional dimensions (e.g. time, location, social network) in order to provide better recommendation services. In the first part of this paper, we will survey a variety of dimension features and show how they are integrated into the recommendation process. When the service providers collect more and more personal information, it brings great privacy concerns to the public. On...

The device-unique response of a physically unclonable function (PUF) can serve as the root of trust in an embedded cryptographic system. Fuzzy extractors transform this noisy non-uniformly distributed secret into a stable high-entropy key. The overall efficiency thereof, typically depending on error-correction with a binary [n,k,d] block code, is determined by the universal and well-known (n-k) bound on the min-entropy loss. We derive new considerably tighter bounds for PUF-induced...

In a celebrated paper published in 1951, von Neumann presented a simple procedure allowing to correct the bias of random sources. This device outputs bits at irregular intervals. However, cryptographic hardware is usually synchronous. This paper proposes a new building block called Pace Regulator, inserted between the randomness consumer and the von Neumann regulator to streamline the pace of random bits.

At CRYPTO 2014 Bellare, Paterson, and Rogaway (BPR) presented a formal treatment of symmetric encryption in the light of algorithm substitution attacks (ASAs), which may be employed by `big brother' entities for the scope of mass surveillance. Roughly speaking, in ASAs big brother may bias ciphertexts to establish a covert channel to leak vital cryptographic information. In this work, we identify a seemingly benign assumption implicit in BPR's treatment and argue that it artificially (and...

PUF-based key generators have been widely considered as a root-of-trust in digital systems. They typically require an error-correcting mechanism (e.g. based on the code-offset method) for dealing with bit errors between the enrollment and reconstruction of keys. When the used PUF does not have full entropy, entropy leakage between the helper data and the device-unique key material can occur. If the entropy level of the PUF becomes too low, the PUF-derived key can be attacked through the...

In this article, we analyse the known-key security of the standardized PRESENT lightweight block cipher. Namely, we propose a known-key distinguisher on the full PRESENT, both 80- and 128-bit key versions. We first leverage the very latest advances in differential cryptanalysis on PRESENT, which are as strong as the best linear cryptanalysis in terms of number of attacked rounds. Differential properties are much easier to handle for a known-key distinguisher than linear properties, and we...