Fast Correlation Attacks on Grain-like Small State Stream Ciphers

In this paper, we study the security of Grain-like small state stream ciphers by fast correlation attacks, which are commonly regarded as classical cryptanalytic methods against LFSR-based stream ciphers. We extend the cascaded structure adopted in such primitives in general and show how to restore the full internal state part-by-part if the non-linear combining function meets some characteristic. As a case study, we present a key recovery attack against Fruit, a tweaked version of Sprout that employs key-dependent state updating in the keystream generation phase. Our attack requires 262.8 Fruit encryptions and 222.3 keystream bits to determine the 80-bit secret key. Practical simulations on a small-scale version confirmed our results

Fast Correlation Attacks on Grain-like Small State Stream Ciphers and Cryptanalysis of Plantlet, Fruit-v2 and Fruit-80

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 small state stream ciphers by the fast correlation attack. We first observe that the number of required parity-check equations can be reduced when there are multiple different parity-check equations. With exploiting the Skellam distribution, we introduce a sufficient condition to identify the correct LFSR initial state and derive a new relationship between the number and bias of the required parity-check equations. Then a modified algorithm is presented based on this new relationship, which can recover the LFSR initial state no matter what the round key bits are. Under the condition that the LFSR initial state is known, an algorithm is given against the degraded system and to recover the NFSR state at some time instant, along with the round key bits. As cases study, we apply our cryptanalytic techniques to Plantlet, Fruit-v2 and Fruit-80. As a result, for Plantlet our attack takes $2^{73.75}$ time complexity and $2^{73.06}$ keystream bits to recover the full 80-bit key. Regarding Fruit-v2, $2^{55.34}$ time complexity and $2^{55.62}$ keystream bits are token to determine the secret key. As for Fruit-80, $2^{64.47}$ time complexity and $2^{62.82}$ keystream bits are required to recover the secret key. More flexible attacks can be obtained with lower data complexity at cost of increasing attack time. Especially, for Fruit-v2 a key recovery attack can be launched with data complexity of $2^{42.38}$ and time complexity of $2^{72.63}$. Moreover, we have implemented our attack methods on a toy version of Fruit-v2. The attack matches the expected complexities predicted by our theoretical analysis quite well, which proves the validity of our cryptanalytic techniques

A new idea in response to fast correlation attacks on small-state stream ciphers

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

An Attack on the LILLE Stream Cipher

A few small-state stream ciphers (SSCs) were proposed for constrained environments. All of the SSCs before the LILLE stream cipher suffered from distinguishing attacks and fast correlation attacks. The designers of LILLE claimed that it is based on the well-studied two-key Even-Mansour scheme and so is resistant to various types of attacks. This paper proposes a distinguishing attack on LILLE, the first attack since 2018. The data and time complexities to attack LILLE-40 are 2^(50.7) and 2^(41.2), respectively. We verified practically our attack on a halved version of LILLE-40. A countermeasure is suggested to strengthen LILLE against the proposed attack. We hope our attack opens the door to more cryptanalyses of LILLE

Modern and Lightweight Component-based Symmetric Cipher Algorithms: A Review

Information security, being one of the corner stones of network and communication technology, has been evolving tremendously to cope with the parallel evolution of network security threats. Hence, cipher algorithms in the core of the information security process have more crucial role to play here, with continuous need for new and unorthodox designs to meet the increasing complexity of the applications environment that keep offering challenges to the current existing cipher algorithms. The aim of this review is to present symmetric cipher main components, the modern and lightweight symmetric cipher algorithms design based on the components that utilized in cipher design, highlighting the effect of each component and the essential component among them, how the modern cipher has modified to lightweight cipher by reducing the number and size of these components, clarify how these components give the strength for symmetric cipher versus asymmetric of cipher. Moreover, a new classification of cryptography algorithms to four categories based on four factors is presented. Finally, some modern and lightweight symmetric cipher algorithms are selected, presented with a comparison between them according to their components by taking into considerations the components impact on security, performance, and resource requirements

Tradeoff Attacks on Symmetric Ciphers

Tradeoff attacks on symmetric ciphers can be considered as the generalization of the exhaustive search. Their main objective is reducing the time complexity by exploiting the memory after preparing very large tables at a cost of exhaustively searching all the space during the precomputation phase. It is possible to utilize data (plaintext/ciphertext pairs) in some cases like the internal state recovery attacks for stream ciphers to speed up further both online and offline phases. However, how to take advantage of data in a tradeoff attack against block ciphers for single key recovery cases is still unknown. We briefly assess the state of art of tradeoff attacks on symmetric ciphers, introduce some open problems and discuss the security criterion on state sizes. We discuss the strict lower bound for the internal state size of keystream generators and propose more practical and fair bound along with our reasoning. The adoption of our new criterion can break a fresh ground in boosting the security analysis of small keystream generators and in designing ultra-lightweight stream ciphers with short internal states for their usage in specially low source devices such as IoT devices, wireless sensors or RFID tags

Multiple Sampling Fast Correlation Attack on Small State Stream Ciphers with Limited Round Key Period

The fast correlation attack (FCA) is a powerful cryptanalysis technique that targets stream ciphers based on linear feedback shift registers (LFSRs). Several FCAs were applied to small state stream ciphers (SSCs). In this paper, the idea of multiple sampling is proposed to use the available keystream bits more efficiently and decrease the data complexity of the attacks. This idea helps to overcome the limitation of SSCs on the number of output keystream bits. Moreover, we classify the parity check equations obtained from the different sampling rounds into different groups to ensure that the round keys used in these equations are the same. Our attack is applied to the Fruit-80 and reduces the data complexity from 2^56.82 to 2^49.82. This modified FCA can be applied to all SSCs with limited round key periods. Finally, we suggest a new design idea to strengthen SSCs against FCAs

Fast Correlation Attacks on Grain-like Small State Stream Ciphers

In this paper, we study the security of Grain-like small state stream ciphers by fast correlation attacks, which are commonly regarded as classical cryptanalytic methods against LFSR-based stream ciphers. We extend the cascaded structure adopted in such primitives in general and show how to restore the full internal state part-by-part if the non-linear combining function meets some characteristic. As a case study, we present a key recovery attack against Fruit, a tweaked version of Sprout that employs key-dependent state updating in the keystream generation phase. Our attack requires 262.8 Fruit encryptions and 222.3 keystream bits to determine the 80-bit secret key. Practical simulations on a small-scale version confirmed our results

Comparing Large-unit and Bitwise Linear Approximations of SNOW 2.0 and SNOW 3G and Related Attacks

In this paper, we study and compare the byte-wise and bitwise linear approximations of SNOW 2.0 and SNOW 3G, and present a fast correlation attack on SNOW 3G by using our newly found bitwise linear approximations. On one side, we reconsider the relation between the large-unit linear approximation and the smallerunit/ bitwise ones derived from the large-unit one, showing that approximations on large-unit alphabets have advantages over all the smaller-unit/bitwise ones in linear attacks. But then on the other side, by comparing the byte-wise and bitwise linear approximations of SNOW 2.0 and SNOW 3G respectively, we have found many concrete examples of 8-bit linear approximations whose certain 1-dimensional/bitwise linear approximations have almost the same SEI (Squared Euclidean Imbalance) as that of the original 8-bit ones. That is, each of these byte-wise linear approximations is dominated by a single bitwise approximation, and thus the whole SEI is not essentially larger than the SEI of the dominating single bitwise approximation. Since correlation attacks can be more efficiently implemented using bitwise approximations rather than large-unit approximations, improvements over the large-unit linear approximation attacks are possible for SNOW 2.0 and SNOW 3G. For SNOW 3G, we make a careful search of the bitwise masks for the linear approximations of the FSM and obtain many mask tuples which yield high correlations. By using these bitwise linear approximations, we mount a fast correlation attack to recover the initial state of the LFSR with the time/memory/data/pre-computation complexities all upper bounded by 2174.16, improving slightly the previous best one which used an 8-bit (vectorized) linear approximation in a correlation attack with all the complexities upper bounded by 2176.56. Though not a significant improvement, our research results illustrate that we have an opportunity to achieve improvement over the large-unit attacks by using bitwise linear approximations in a linear approximation attack, and provide a new insight on the relation between large-unit and bitwise linear approximations

Systematic Characterization of Power Side Channel Attacks for Residual and Added Vulnerabilities

Power Side Channel Attacks have continued to be a major threat to cryptographic devices. Hence, it will be useful for designers of cryptographic systems to systematically identify which type of power Side Channel Attacks their designs remain vulnerable to after implementation. It’s also useful to determine which additional vulnerabilities they have exposed their devices to, after the implementation of a countermeasure or a feature. The goal of this research is to develop a characterization of power side channel attacks on different encryption algorithms\u27 implementations to create metrics and methods to evaluate their residual vulnerabilities and added vulnerabilities. This research studies the characteristics that influence the power side leakage, classifies them, and identifies both the residual vulnerabilities and the added vulnerabilities. Residual vulnerabilities are defined as the traits that leave the implementation of the algorithm still vulnerable to power Side Channel Attacks (SCA), sometimes despite the attempt at implementing countermeasures by the designers. Added vulnerabilities to power SCA are defined as vulnerabilities created or enhanced by the algorithm implementations and/or modifications. The three buckets in which we categorize the encryption algorithm implementations are: i. Countermeasures against power side channel attacks, ii. IC power delivery network impact to power leakage (including voltage regulators), iii. Lightweight ciphers and applications for the Internet of Things (IoT ) From the characterization of masking countermeasures, an example outcome developed is that masking schemes, when uniformly distributed random masks are used, are still vulnerable to collision power attacks. Another example outcome derived is that masked AES, when glitches occur, is still vulnerable to Differential Power Analysis (DPA). We have developed a characterization of power side-channel attacks on the hardware implementations of different symmetric encryption algorithms to provide a detailed analysis of the effectiveness of state-of-the-art countermeasures against local and remote power side-channel attacks. The characterization is accomplished by studying the attributes that influence power side-channel leaks, classifying them, and identifying both residual vulnerabilities and added vulnerabilities. The evaluated countermeasures include masking, hiding, and power delivery network scrambling. But, vulnerability to DPA depends largely on the quality of the leaked power, which is impacted by the characteristics of the device power delivery network. Countermeasures and deterrents to power side-channel attacks targeting the alteration or scrambling of the power delivery network have been shown to be effective against local attacks where the malicious agent has physical access to the target system. However, remote attacks that capture the leaked information from within the IC power grid are shown herein to be nonetheless effective at uncovering the secret key in the presence of these countermeasures/deterrents. Theoretical studies and experimental analysis are carried out to define and quantify the impact of integrated voltage regulators, voltage noise injection, and integration of on-package decoupling capacitors for both remote and local attacks. An outcome yielded by the studies is that the use of an integrated voltage regulator as a countermeasure is effective for a local attack. However, remote attacks are still effective and hence break the integrated voltage regulator countermeasure. From experimental analysis, it is observed that within the range of designs\u27 practical values, the adoption of on-package decoupling capacitors provides only a 1.3x increase in the minimum number of traces required to discover the secret key. However, the injection of noise in the IC power delivery network yields a 37x increase in the minimum number of traces to discover. Thus, increasing the number of on-package decoupling capacitors or the impedance between the local probing site and the IC power grid should not be relied on as countermeasures to power side-channel attacks, for remote attack schemes. Noise injection should be considered as it is more effective at scrambling the leaked signal to eliminate sensitive identifying information. However, the analysis and experiments carried out herein are applied to regular symmetric ciphers which are not suitable for protecting Internet of Things (IoT) devices. The protection of communications between IoT devices is of great concern because the information exchanged contains vital sensitive data. Malicious agents seek to exploit those data to extract secret information about the owners or the system. Power side channel attacks are of great concern on these devices because their power consumption unintentionally leaks information correlatable to the device\u27s secret data. Several studies have demonstrated the effectiveness of authenticated encryption with advanced data (AEAD), in protecting communications with these devices. In this research, we have proposed a comprehensive evaluation of the ten algorithm finalists of the National Institute of Standards and Technology (NIST) IoT lightweight cipher competition. The study shows that, nonetheless, some still present some residual vulnerabilities to power side channel attacks (SCA). For five ciphers, we propose an attack methodology as well as the leakage function needed to perform correlation power analysis (CPA). We assert that Ascon, Sparkle, and PHOTON-Beetle security vulnerability can generally be assessed with the security assumptions Chosen ciphertext attack and leakage in encryption only, with nonce-misuse resilience adversary (CCAmL1) and Chosen ciphertext attack and leakage in encryption only with nonce-respecting adversary (CCAL1) , respectively. However, the security vulnerability of GIFT-COFB, Grain, Romulus, and TinyJambu can be evaluated more straightforwardly with publicly available leakage models and solvers. They can also be assessed simply by increasing the number of traces collected to launch the attack