Bitcoin’s security relies on its Proof-of-Work consensus, where miners solve puzzles to propose blocks. The puzzle’s difficulty is set by the difficulty adjustment mechanism (DAM), based on the network’s available mining power. Attacks that destroy some portion of mining power can exploit the DAM to lower difficulty, making such attacks profitable. In this paper, we analyze three types of mining power destruction attacks in the presence of petty-compliant mining pools: selfish mining, bribery, and mining power distraction attacks. We analyze selfish mining while accounting for the distribution of mining power among pools, a factor often overlooked in the literature. Our findings indicate that selfish mining can be more destructive when the non-adversarial mining share is well distributed among pools. We also introduce a novel bribery attack, where the adversarial pool bribes petty-compliant pools to orphan others’ blocks. For small pools, we demonstrate that the bribery attack can dominate strategies such as selfish mining or undercutting. Lastly, we present the mining distraction attack, where the adversarial pool incentivizes petty-compliant pools to abandon Bitcoin’s puzzle and mine for a simpler puzzle, thus wasting some part of their mining power. Similar to the previous attacks, this attack can lower the mining difficulty, but with the difference that it does not generate any evidence of mining power destruction, such as orphan blocks.

A Bitcoin miner who owns a sufficient amount of mining power can perform selfish mining to increase its relative revenue. Studies have demonstrated that the time-averaged profit of a selfish miner starts to rise once the mining difficulty level gets adjusted in favor of the attacker. Selfish mining profitability lies in the fact that orphan blocks are not incorporated into the current version of Bitcoin’s difficulty adjustment mechanism (DAM). Therefore, it is believed that considering the count of orphan blocks in the DAM can result in complete unprofitability for selfish mining. In this paper, we disprove this belief by providing a formal analysis of the selfish mining time-averaged profit. We present a precise definition of the orphan blocks that can be incorporated into calculating the next epoch’s target and then introduce two modified versions of DAM in which both main-chain blocks and orphan blocks are incorporated. We propose two versions of smart intermittent selfish mining, where the first one dominates the normal intermittent selfish mining, and the second one results in selfish mining profitability under the modified DAMs. Moreover, we present the orphan exclusion attack with the help of which the attacker can stop honest miners from reporting the orphan blocks. Using combinatorial tools, we analyze the profitability of selfish mining accompanied by the orphan exclusion attack under the modified DAMs. Our results show that even when considering orphan blocks in the DAM, selfish mining can still be profitable. However, the level of profitability under the modified DAMs is significantly lower than that observed under the current version of Bitcoin DAM, suggesting that orphan reporting can be an effective countermeasure against a payoff-maximizing selfish miner.

The algebraic degree of a vectorial Boolean function is one of the main parameters driving the cost of its hardware implementation. Thus, finding decompositions of functions into sequences of functions of lower algebraic degrees has been explored to reduce the cost of implementations. In this paper, we consider such decompositions of permutations over F 2 n . We prove the existence of decompositions using quadratic and linear power permutations for all permutations when 2 n − 1 is a prime, and we prove the non-existence of such decompositions for power permutations of differential uniformity strictly lower than 16 when 4 | n . We also prove that any permutation admits a decomposition into quadratic power permutations and affine permutations of the form ax + b if 4 ∤ n . Furthermore, we prove that any permutation admits a decomposition into cubic power permutations and affine permutations. Finally, we present a decomposition of the PRESENT S-Box using the power permutation x 7 and affine permutations.

The security of Bitcoin protocols is deeply dependent on the incentives provided to miners, which come from a combination of block rewards and transaction fees. As Bitcoin experiences more halving events, the protocol reward converges to zero, making transaction fees the primary source of miner rewards. This shift in Bitcoin's incentivization mechanism, which introduces volatility into block rewards, leads to the emergence of new security threats or intensifies existing ones. Previous security analyses of Bitcoin have either considered a fixed block reward model or a highly simplified volatile model, overlooking the complexities of Bitcoin's mempool behavior. This paper presents a reinforcement learning-based tool to develop mining strategies under a more realistic volatile model. We employ the Asynchronous Advantage Actor-Critic (A3C) algorithm, which efficiently handles dynamic environments, such as the Bitcoin mempool, to derive near-optimal mining strategies when interacting with an environment that models the complexity of the Bitcoin mempool. This tool enables the analysis of adversarial mining strategies, such as selfish mining and undercutting, both before and after difficulty adjustments, providing insights into the effects of mining attacks in both the short and long term. We revisit the Bitcoin security threshold presented in the WeRLman paper and demonstrate that the implicit predictability of valuable transaction arrivals in this model leads to an underestimation of the reported threshold. Additionally, we show that, while adversarial strategies like selfish mining under the fixed reward model incur an initial loss period of at least two weeks, the transition toward a transaction-fee era incentivizes mining pools to abandon honest mining for immediate profits. This incentive is expected to become more significant as the protocol reward approaches zero in the future.

It has been shown that the selfish mining attack enables a miner to achieve an unfair relative revenue, posing a threat to the progress of longest-chain blockchains. Although selfish mining is a well-studied attack in the context of Proof-of-Work blockchains, its impact on the longest-chain Proof-of-Stake (LC-PoS) protocols needs yet to be addressed. This paper involves both theoretical and implementationbased approaches to analyze the selfish proposing (As there is no mining process in PoS blockchains, we refer to this attack as "selfish proposing".) attack in the LC-PoS protocols. We discuss how factors such as the nothing-at-stake phenomenon and the proposer predictability in PoS protocols can make the selfish proposing attack in LC-PoS protocols more destructive compared to selfish mining in PoW. In the first part of the paper, we use combinatorial tools to theoretically assess the selfish proposer's block ratio in simplistic LC-PoS environments and under simplified network connection. However, these theoretical tools or classical MDP-based approaches cannot be applied to analyze the selfish proposing attack in real-world and more complicated LC-PoS environments. To overcome this issue, in the second part of the paper, we employ deep reinforcement learning techniques to find the near-optimal strategy of selfish proposing in more sophisticated protocols. The tool implemented in the paper can help us analyze the selfish proposing attack across diverse blockchain protocols with different reward mechanisms, predictability levels, and network conditions.

Since the first fault attack by Boneh et al. in 1997, various physical fault injection mechanisms have been explored to induce errors in electronic systems. Subsequent fault analysis methods of these errors have been studied, and successfully used to attack many cryptographic implementations. This poses a significant challenge to the secure implementation of cryptographic algorithms. To address this, numerous countermeasures have been proposed. Nevertheless, these countermeasures are primarily designed to protect against the particular assumptions made by the fault analysis methods. These assumptions, however, encompass only a limited range of the capabilities inherent to physical fault injection mechanisms. In this paper, we narrow our focus to fault attacks and countermeasures specific to ASICs, and introduce a novel parameterized fault adversary model capturing an adversary’s control over an ASIC. We systematically map (a) the physical fault injection mechanisms, (b) adversary models assumed in fault analysis, and (c) adversary models used to design countermeasures into our introduced model. This model forms the basis for our comprehensive exploration that covers a broad spectrum of fault attacks and countermeasures within symmetric key cryptography as a comprehensive survey. Furthermore, our investigation highlights a notable misalignment among the adversary models assumed in countermeasures, fault attacks, and the intrinsic capabilities of the physical fault injection mechanisms. Through this study, we emphasize the need to reevaluate existing fault adversary models, and advocate for the development of a unified model.

Masking is one of the most popular countermeasures to protect implementations against power and electromagnetic side-channel attacks because it offers provable security. Masking has been shown secure against d-threshold probing adversaries by Ishai et al. at CRYPTO'03, but this adversary's model doesn't consider any physical hardware defaults and thus such masking schemes were shown to be still vulnerable when implemented as hardware circuits. To address these limitations glitch-extended probing adversaries and correspondingly glitch-immune masking schemes have been introduced. This paper introduces glitch-stopping circuits, which coincide with circuits protected via glitch-immune masking when instantiated with registers. Then we show that one can instantiate glitch-stopping circuits without registers by using clocked logic gates or latches. This is illustrated for both ASIC and FPGA, offering a promising alternative to conventional register-based masked implementations. Compared to the traditional register-based approach, these register-free solutions can reduce the latency to a single cycle and achieve a lower area cost. We prove and experimentally confirm that the proposed solution is as secure as the register-based one. In summary, this paper proposes a novel method to address the latency of register-based hardware masking without jeopardizing their security. This method not only reduces the latency down to one clock cycle but also improves the area costs of the implementations.

The intermittent nature of renewable energy sources challenges the ability of grid operators to maintain balance between supply and demand of electricity. Demand response, or flexibility, is the ability of a load to modify its consumption in response to a control signal. The necessary two-way communications between end-users and grid operators introduce new risks on consumer privacy and data security. Consumer engagement in such programs tends to be low not only for privacy issues, but also because of the inappropriate incentive schemes. In this work, secure Multiparty Computation is used in a flexibility market where end-consumers provide demand response to grid operators in exchange for a monetary compensation. Multiparty computation is a cryptographic method that performs operations over encrypted data. Users submit their offers in encrypted form, and a novel way to characterize flexibility as a commodity and to determine device constraints with very little information from the consumers is developed. The market is cleared via a double auction-like process. The method is validated using flexibility offers from 200 devices of different types. We demonstrate the possibility to clear the market and allocate resources with encrypted orders for sole information.

Physical attacks pose a substantial threat to the secure implementation of cryptographic algorithms. While considerable research efforts are dedicated to protecting against passive physical attacks (e.g., side-channel analysis (SCA)), the landscape of protection against other types of physical attacks remains a challenge. Fault attacks (FA), though attracting growing attention in research, still lack the prevalence of provably secure designs when compared to SCA. The realm of combined attacks, which leverage the capabilities of both SCA and FA adversaries, introduces powerful adversarial models, rendering protection against them challenging. This challenge has consequently led to a relatively unexplored area of research, resulting in a notable gap in understanding and efficiently protecting against combined attacks. The CAPA countermeasure, published at CRYPTO 2018, addresses this challenge with a robust adversarial model that goes beyond conventional SCA and FA adversarial models. Drawing inspiration from the principles of Multiparty Computation (MPC), CAPA claims security against higher-order SCA, higher-order fault attacks, and their combination. In this work, we present a combined attack that breaks CAPA within the constraints of its assumed adversarial model. In response, we propose potential fixes to the design of CAPA that increase the complexity of the proposed attack, although not provably thwarting it. With this presented combined attack, we highlight the difficulty of effectively protecting against combined attacks.

In this work, we introduce the random fault model - a more advanced fault model inspired by the random probing model, where the adversary can fault all values in the algorithm but the probability for each fault to occur is limited. The new adversary model is used to evaluate the security of side-channel and fault countermeasures such as Boolean masking, error detection techniques, error correction techniques, multiplicative tags, and shuffling methods. The results of the security analysis reveal new insights both in the novel random fault model as well as in the established random probing model including: shuffling masked implementations does not significantly improve the random probing security over regular masking; error correction providing little security when faults target more bits (versus the significant improvement when using error detection); and the order in which masking and duplication are applied providing a trade-off between random probing and fault security. Moreover, the results also explain the experimental results from CHES 2022 and find weaknesses in the shuffling method from SAMOS 2021.

Over the last decades, fault injection attacks have been demonstrated to be an effective method for breaking the security of electronic devices. Some types of fault injection attacks, like clock and voltage glitching, require very few resources by the attacker and are practical and simple to execute. A cost-effective countermeasure against these attacks is the use of a detector circuit which detects timing violations - the underlying effect that glitch attacks rely on. In this paper, we take a closer look at three examples of such detectors that have been presented in the literature. We demonstrate four high-speed clock glitching attacks, which successfully inject faults in systems, where detectors have been implemented to protect. The attacks remain unnoticed by the glitch detectors. We verify our attacks with practical experiments on FPGA.

Deploying cryptography on embedded systems requires security against physical attacks. At CHES 2019, M&M was proposed as a combined countermeasure applying masking against SCAs and information-theoretic MAC tags against FAs. In this paper, we show that one of the protected AES implementations in the M&M paper is vulnerable to a zero-value SIFA2-like attack. A practical attack is demonstrated on an ASIC board. We propose two versions of the attack: the first follows the SIFA approach to inject faults in the last round, while the second one is an extension of SIFA and FTA but applied to the first round with chosen plaintext. The two versions work at the byte level, but the latter version considerably improves the efficiency of the attack. Moreover, we show that this zero-value SIFA2 attack is specific to the AES tower-field decomposed S-box design. Hence, such attacks are applicable to any implementation featuring this AES S-box architecture. Then, we propose a countermeasure that prevents these attacks. We extend M&M with a fine-grained detection-based feature capable of detecting the zero-value glitch attacks. In this effort, we also solve the problem of a combined attack on the ciphertext output check of M&M scheme by using Kronecker’s delta function. We deploy the countermeasure on FPGA and verify its security against both fault and side-channel analysis with practical experiments.

We provide three first-order hardware maskings of the AES, each allowing for a different trade-off between the number of shares and the number of register stages. All maskings use a generalization of the changing of the guards method enabling the re-use of randomness between masked S-boxes. As a result, the maskings do not require fresh randomness while still allowing for a minimal number of shares and providing provable security in the glitch-extended probing model. The low-area variant has five cycles of latency and a serialized area cost of 8.13 kGE. The low-latency variant reduces the latency to three cycles while increasing the serialized area by $$67.89\%$$ compared to the low-area variant. The maskings of the AES encryption are implemented on FPGA and evaluated with Test Vector Leakage Assessment (TVLA).

Threshold implementation is a method based on secret sharing to secure cryptographic ciphers (and in particular S-boxes) against differential power analysis side-channel attacks which was proposed by Nikova, Rechberger, and Rijmen in 2006. Until now, threshold implementations were only constructed for specific types of functions and some small S-boxes, but no generic construction was ever presented. In this paper, we present the first universal threshold implementation with $t+2$ shares that is applicable to any bijective S-box, where $t$ is its algebraic degree (or is larger than the algebraic degree). While being universal, our construction is also optimal with respect to the number of shares, since the theoretically smallest possible number, $t+1$ , is not attainable for some bijective S-boxes. Our results enable low latency secure hardware implementations without the need for additional randomness. In particular, we apply this result to find two uniform sharings of the AES S-box. The first sharing is obtained by using the threshold implementation of the inversion in $\mathbb {F}_{2^{8}}$ and the second by using two threshold implementations of two cubic power permutations that decompose the inversion. Area and performance figures for hardware implementations are provided.

Demand response has emerged as one of the most promising methods for the deployment of sustainable energy systems. Attempts to democratize demand response and establish programs for residential consumers have run into scalability issues and risks of leaking sensitive consumer data. In this work, we propose a privacy-friendly, incentive-based demand response market, where consumers offer their flexibility to utilities in exchange for a financial compensation. Consumers submit encrypted offer which are aggregated using Computation Over Encrypted Data to ensure consumer privacy and the scalability of the approach. The optimal allocation of flexibility is then determined via double-auctions, along with the optimal consumption schedule for the users with respect to the day-ahead electricity prices, thus also shielding participants from high electricity prices. A case study is presented to show the effectiveness of the proposed approach.

With the enormous increase in portable cryptographic devices, physical attacks are becoming similarly popular. One of the most common physical attacks is Side-Channel Analysis (SCA), extremely dangerous due to its non-invasive nature. Threshold Implementations (TI) was proposed as the first countermeasure to provide provable security in masked hardware implementations. While most works on hardware masking are focused on optimizing the area requirements, with the newer and smaller technologies area is taking a backseat, and low-latency is gaining importance. In this work, we revisit the scheme proposed by Arribas et al. in TCHES 2018 to secure unrolled implementations. We formalize and expand this methodology, to devise a masking scheme, derived from TI, designed to secure hardware implementations optimized for latency named Low-Latency Threshold Implementations (LLTI). By applying the distributive property and leveraging a divide-and-conquer strategy, we split a non-linear operation in layers which are masked separately. The result is a more efficient scheme than the former TI for any operation of algebraic degree greater than two, achieving great optimizations both in terms of speed and area. We compare the performance of first-order LLTI with first-order TI in securing a cubic gate and a degree-7 AND gate without using any registers in between. We achieve a 137% increase in maximum frequency and a 60% reduction in area for the cubic gate, and 3131 times reduction in area in the case of a degree-7 AND gate compared to TI. To further illustrate the power of our scheme we take a low-latency PRINCE implementation from the literature and, by simply changing the secure S-box with the LLTI version, we achieve a 46% max. frequency improvement and a 38% area reduction. Moreover, we apply LLTI to a secure a low-latency AES implementation and compare it with the TI version, achieving a 6.9 times max. freq. increase and a 47.2% area reduction.

The recent decade has seen a tremendous increase in volumes of data consumed and generated. Towards storing such data, companies typically make use of centralised cloud storage systems which allow for on-demand scalability and a pay-per-use model. These storage providers, while presenting many benefits, have several downsides in terms of (i) posing as a single point of failure (e.g. data breaches), (ii) featuring the potential for misuse of confidential or personal data, as well as (iii) being not nearly as competitive as they could be which has resulted in inflated prices. In recent years, along with blockchain-based technologies, novel distributed storage platforms such as Storj and Sia, have emerged that tackle these issues by enabling a dynamic storage market between hosts and renters. In comparison to traditional Peer-to-Peer (P2P) storage solutions (e.g. BitTorrrent), these platforms rely on incentivization-based P2P hosting which ensures file availability, robustness and price competitiveness, while also preserving confidentiality and ownership through end-to-end encryption. In this paper, we present a brief overview of such storage platforms, as well as provide two major contributions in the form of (i) an architectural overview, as well as (ii) a high-level security exploration on the dev./test environment of Storj. The latter has resulted in the discovery of a DoS vulnerability, which we experimentally evaluated to be highly feasible. We have contacted Storj and they assessed that their production system 1 is not vulnerable to such an attack.

NSUCRYPTO is the unique cryptographic Olympiad containing scientific mathematicalproblems for professionals, school and university students from any country. Its aim is to involveyoung researchers in solving curious and tough scientific problems of modern cryptography. Fromthe very beginning, the concept of the Olympiad was not to focus on solving olympic tasks but onincluding unsolved research problems at the intersection of mathematics and cryptography. TheOlympiad history starts in 2014. In 2019, it was held for the sixth time. We present the problemsand their solutions of the Sixth International Olympiad in cryptography NSUCRYPTO $$^{\prime}$$ 2019. Under consideration are the problems relatedto attacks on ciphers and hash functions, protocols, Boolean functions, Dickson polynomials, primenumbers, rotor machines, etc. We discuss several open problems on mathematical countermeasuresto side-channel attacks, APN involutions, S-boxes, etc. The problem of finding a collision for thehash function Curl27 was partiallysolved during the Olympiad.

We provide three first-order sharings of the AES each allowing for a different trade-off between the number of shares and the number of register stages. All sharings use a generalization of the changing of the guards method by allowing randomness to be used in the shared S-box. As a result, the sharings have minimal randomness requirements. The sharings are written out in detail to ease implementation efforts.