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

Some cryptanalytic results on Lizard

Lizard is a lightweight stream cipher proposed by Hamann, Krause and Meier in IACR ToSC 2017. It has a Grain-like structure with two state registers of size 90 and 31 bits. The cipher uses a 120 bit Secret Key and a 64 bit IV. The authors claim that Lizard provides 80 bit security against key recovery attacks and a 60-bit security against distinguishing attacks. In this paper, we present an assortment of results and observations on Lizard. First, we show that by doing $2^{58}$ random trials it is possible to a set of $2^{64}$ triplets $(K,IV_0,IV_1)$ such that the Key-IV pairs $(K,IV_0)$ and $(K,IV_1)$ produce identical keystream bits. Second, we show that by performing only around $2^{28}$ random trials it is possible to obtain $2^{64}$ Key-IV pairs $(K_0,IV_0)$ and $(K_1,IV_1)$ that produce identical keystream bits. Thereafter, we show that one can construct a distinguisher for Lizard based on IVs that produce shifted keystream sequences. The process takes around $2^{51.5}$ random IV encryptions and around $2^{76.6}$ bits of memory. Finally, we propose a key recovery attack on a version of Lizard with the number of initialization rounds reduced to 223 (out of 256) based on IV collisions

A TMDTO Attack Against Lizard

Lizard is a very recently proposed lightweight stream cipher that claims 60 bit security against distinguishing (related to state recovery) and 80 bit security against key recovery attack. This cipher has 121 bit state size. In this paper, we first note that using $\psi$ key stream bits one can recover $\psi$ unknown bits of the state when $\tau$ state bits are fixed to a specific pattern. This is made possible by guessing the remaining state bits. This helps us in mounting a TMDTO attack with preprocessing complexity $2^{67}$, and the maximum of Data, Time and Memory complexity during the online phase as $2^{54}$. The parameters in the online phase are significantly less than $2^{60}$

Cryptanalysis of full round Fruit

In FSE 2015, Armknetcht et al. proposed a new technique to design stream cipher. This technique involves repeated use of keybits in each round of keystream bit generation. This idea showed the possibility to design stream ciphers where internal state size is significantly lower than twice the key size. They proposed a new cipher based on this idea, named Sprout. But soon Sprout was proved to be insecure. In Crypto 2015, Lallemand et al. proposed an attack on Sprout, which was $2^{10}$ times faster than the exhaustive search. But the new idea used in Sprout showed a new direction in the design of stream cipher, which led to the proposal of several new ciphers with small size of internal state. Fruit is another cipher in this direction proposed recently where both the key size and state size are 80. So far, there is no attack against this cipher. In this paper, we attack full round Fruit by a divide-and-conquer method. We use several types of sieving to reduce the possible candidates for an internal state. Our attack is equivalent to $2^{74.95}$ many Fruit encryption, which is around $16.95$ times faster than average exhaustive key search. This is the first proposed attack against Fruit

Necessary conditions for designing secure stream ciphers with the minimal internal states

After the introduction of some stream ciphers with the minimal internal state, the design idea of these ciphers (i.e. the design of stream ciphers by using a secret key, not only in the initialization but also permanently in the keystream generation) has been developed. The idea lets to design lighter stream ciphers that they are suitable for devices with limited resources such as RFID, WSN. We present necessary conditions for designing a secure stream cipher with the minimal internal state. Based on the conditions, we propose Fruit-128 stream cipher for 128-bit security against all types of attacks. Our implementations showed that the area size of Fruit-128 is about 25.2% smaller than that of Grain-128a. The discussions are presented that Fruit-128 is more resistant than Grain-128a to some attacks such as Related key chosen IV attack. Sprout, Fruit-v2 and Plantlet ciphers are vulnerable to time-memory-data trade-off (TMDTO) distinguishing attacks. For the first time, IV bits were permanently used to strengthen Fruit-128 against TMDTO attacks. We will show that if IV bits are not permanently available during the keystream production step, we can eliminate the IV mixing function from it. In this case, security level decreases to 69-bit against TMDTO distinguishing attacks (that based on the application might be tolerable). Dynamic initialization is another contribution of the paper (that it can strengthen initialization of all stream ciphers with low area cost)

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

On Analysis of Lightweight Stream Ciphers with Keyed Update

As the need for lightweight cryptography has grown even more due to the evolution of the Internet of Things, it has become a greater challenge for cryptographers to design ultra lightweight stream ciphers in compliance with the rule of thumb that the internal state size should be at least twice as the key size to defend against generic Time-Memory-Data Tradeoff (TMDT) attacks. However, recently in 2015, Armknecht and Mikhalev sparked a new light on designing keystream generators (KSGs), which in turn yields stream ciphers, with small internal states, called KSG with Keyed Update Function (KSG with KUF), and gave a concrete construction named Sprout. But, currently, security analysis of KSGs with KUF in a general setting is almost non-existent. Our contribution in this paper is two-fold. 1) We give a general mathematical setting for KSGs with KUF, and for the first time, analyze a class of such KSGs, called KSGs with Boolean Keyed Feedback Function (KSG with Boolean KFF), generically. In particular, we develop two generic attack algorithms applicable to any KSG with Boolean KFF having almost arbitrary output and feedback functions where the only requirement is that the secret key incorporation is biased. We introduce an upper bound for the time complexity of the first algorithm. Our extensive experiments validate our algorithms and assumptions made thereof. 2) We study Sprout to show the effectiveness of our algorithms in a practical instance. A straightforward application of our generic algorithm yields one of the most successful attacks on Sprout

On the Data Limitation of Small-State Stream Ciphers: Correlation Attacks on Fruit-80 and Plantlet

Many cryptographers have focused on lightweight cryptography, and a huge number of lightweight block ciphers have been proposed. On the other hand, designing lightweight stream ciphers is a challenging task due to the well-known security criteria, i.e., the state size of stream ciphers must be at least twice the key size. The designers of Sprout addressed this issue by involving the secret key not only in the initialization but also in the keystream generation, and the state size of such stream ciphers can be smaller than twice the key size. After the seminal work, some small-state stream ciphers have been proposed such as Fruit, Plantlet, and LIZARD. Unlike conventional stream ciphers, these small-state stream ciphers have the limitation of keystream bits that can be generated from the same key and IV pair. In this paper, our motivation is to show whether the data limitation claimed by the designers is proper or not. The correlation attack is one of the attack methods exploiting many keystream bits generated from the same key and IV pair, and we apply it to Fruit-80 and Plantlet. As a result, we can break the full Fruit-80, i.e., the designers\u27 data limitation is not sufficient. We can also recover the secret key of Plantlet if it allows about $2^{53}$ keystream bits from the same key and IV pair

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

On Ciphers that Continuously Access the Non-Volatile Key

Due to the increased use of devices with restricted resources such as limited area size, power or energy, the community has developed various techniques for designing lightweight ciphers. One approach that is increasingly discussed is to use the cipher key that is stored on the device in non-volatile memory not only for the initialization of the registers but during the encryption/decryption process as well. Recent examples are the ciphers Midori (Asiacrypt’15) and Sprout (FSE’15). This may on the one hand help to save resources, but also may allow for a stronger key involvement and hence higher security. However, only little is publicly known so far if and to what extent this approach is indeed practical. Thus, cryptographers without strong engineering background face the problem that they cannot evaluate whether certain designs are reasonable (from a practical point of view) which hinders the development of new designs. In this work, we investigate this design principle from a practical point of view. After a discussion on reasonable approaches for storing a key in non-volatile memory, motivated by several commercial products we focus on the case that the key is stored in EEPROM. Here, we highlight existing constraints and derive that some designs, based on the impact on their throughput, are better suited for the approach of continuously reading the key from all types of non-volatile memory. Based on these findings, we improve the design of Sprout for proposing a new lightweight stream cipher that (i) has a significantly smaller area size than almost all other stream ciphers and (ii) can be efficiently realized using common non-volatile memory techniques. Hence, we see our work as an important step towards putting such designs on a more solid ground and to initiate further discussions on realistic designs