Multidimensional Zero-correlation Research Articles

Zero-correlation attacks: statistical models independent of the number of approximations

Multiple and multidimensional zero-correlation linear cryptanalysis have been two of the most powerful cryptanalytic techniques for block ciphers, and it has been shown that the differentiating factor of these two statistical models is whether distinct plaintexts are assumed or not. Nevertheless, questions remain regarding how these analyses can be universalized without any limitations and can be used to accurately estimate the data complexity and the success probability. More concretely, the current models for multiple zero-correlation (MPZC) and multidimensional zero-correlation (MDZC) cryptanalysis are not valid in the setting with a limited number of approximations and the accuracy of the estimation for data complexity can not be guaranteed. Besides, in a lot of cases, using too many approximations may cause an exhaustive search when we want to launch key-recovery attacks. In order to generalize the original models using the normal approximation of the $$\chi ^2$$ -distribution, we provide a more accurate approach to estimate the data complexity and the success probability for MPZC and MDZC cryptanalysis without such approximation. Since these new models directly rely on the $$\chi ^{2}$$ -distribution, we call them the $$\chi ^{2}$$ MPZC and MDZC models. An interesting thing is that the chi-square-multiple zero-correlation ( $$\chi ^{2}$$ -MPZC) model still works even though we only have a single zero-correlation linear approximation. This fact puts an end to the situation that the basic zero-correlation linear cryptanalysis requires the full codebook under the known-plaintext attack setting. As an illustration, we apply the $$\chi ^{2}$$ -MPZC model to analyze TEA and XTEA. These new attacks cover more rounds than the previous MPZC attacks. Moreover, we reconsider the multidimensional zero-correlation (MDZC) attack on 14-round CLEFIA-192 by utilizing less zero-correlation linear approximations. In addition, some other ciphers which already have MDZC analytical results are reevaluated and the data complexities under the new model are all less than or equal to those under the original model. Some experiments are conducted in order to verify the validity of the new models, and the experimental results convince us that the new models provide more precise estimates of the data complexity and the success probability.

Improving algorithm 2 in multidimensional (zero-correlation) linear cryptanalysis using $$\chi ^2$$ χ 2 -method

The multidimensional linear cryptanalysis and the multidimensional zero-correlation linear cryptanalysis have been widely used in the attacks on block ciphers. In the multidimensional linear cryptanalysis with $$\chi ^2$$ź2-method and the multidimensional zero-correlation linear cryptanalysis, the statistics used to distinguish the right key and wrong keys are calculated from the probability distribution of multidimensional (zero-correlation) linear approximations. In this paper, we show that the statistics can be computed directly from the empirical correlations of multidimensional (zero-correlation) linear approximations for random plaintext set. In this way, the computation cost of the probability distribution can be removed. In the situation where FFT technique can be applied to calculate the correlations, our proposed computing method for the statistics can decrease the time complexity of multidimensional (zero-correlation) linear cryptanalysis. As an illustration, the Feistel network with bijective round functions consisting of the modular additions or XORs with subkeys and CAST-256 have been attacked with our revised multidimensional zero-correlation linear cryptanalysis. Our attacks on such kind of Feistel networks are the best according to the number of rounds and we improved the previous multidimensional zero-correlation attack on CAST-256 from 28 to 29 rounds. Compared with the best attack on 29-round CAST-256 with multiple zero-correlation linear cryptanalysis method, our attack leads to the same complexity but without any assumption of independence. Therefore our attack on CAST-256 is the best attack without any assumption.

Zero-Correlation Linear Cryptanalysis of Reduced-Round SIMON

In June 2013, the U.S. National Security Agency proposed two families of lightweight block ciphers, called SIMON and SPECK respectively. These ciphers are designed to perform excellently on both hardware and software platforms. In this paper, we mainly present zero-correlation linear cryptanalysis on various versions of SIMON. Firstly, by using missin-the-middle approach, we construct zero-correlation linear distinguishers of SIMON, and zero-correlation linear attacks are presented based on careful analysis of key recovery phase. Secondly, multidimensional zero-correlation linear attacks are used to reduce the data complexity. Our zero-correlation linear attacks perform better than impossible differential attacks proposed by Abed et al. in ePrint Report 2013/568. Finally, we also use the divide-and-conquer technique to improve the results of linear cryptanalysis proposed by Javad et al. in ePrint Report 2013/663.

Improved Linear Cryptanalysis of CAST-256

CAST-256, a first-round AES (Advanced Encryption Standard) candidate, is designed based on CAST-128. It is a 48-round Generalized-Feistel-Network cipher with 128-bit block accepting 128, 160, 192, 224 or 256 bits keys. Its S-boxes are non-surjective with 8-bit input and 32-bit output. Wang et al. identified a 21-round linear approximation and gave a key recovery attack on 24-round CAST-256. In ASIACRYPT 2012, Bogdanov et al. presented the multidimensional zero-correlation linear cryptanalysis of 28 rounds of CAST-256. By observing the property of the concatenation of forward quad-round and reverse quad-round and choosing the proper active round function, we construct a linear approximation of 26-round CAST-256 and recover partial key information on 32 rounds of CAST-256. Our result is the best attack according to the number of rounds for CAST-256 without weak-key assumption so far.

Zero-correlation linear cryptanalysis of reduced-round LBlock

Zero-correlation linear attack is a new method developed by Bogdanov et al. (ASIACRYPT 2012. LNCS, Springer, Berlin, 2012) for the cryptanalysis of block ciphers. In this paper we adapt the matrix method to find zero-correlation linear approximations. Then we present several zero-correlation linear approximations for 14 rounds of LBlock and describe a cryptanalysis for a reduced 22-round version of LBlock. After biclique attacks on LBlock revealed weaknesses in its key schedule, its designers presented a new version of the cipher with a revised key schedule. The attack presented in this paper does not exploit the structure of the key schedule or S-boxes used in the cipher. As a result, it is applicable to both variants of the LBlock as well as the block ciphers with analogous structures like TWINE. Moreover, we performed simulations on a small variant LBlock and present the first experimental results on the theoretical model of the multidimensional zero-correlation linear cryptanalysis method.

Multidimensional zero-correlation attacks on lightweight block cipher HIGHT: Improved cryptanalysis of an ISO standard

HIGHT is a block cipher designed in Korea with the involvement of Korea Information Security Agency. It was proposed at CHES 2006 for usage in lightweight applications such as sensor networks and RFID tags. Lately, it has been adopted as ISO standard. Though there is a great deal of cryptanalytic results on HIGHT, its security evaluation against the recent zero-correlation linear attacks is still lacking. At the same time, the Feistel-type structure of HIGHT suggests that it might be susceptible to this type of cryptanalysis. In this paper, we aim to bridge this gap.We identify zero-correlation linear approximations over 16 rounds of HIGHT. Based upon those, we attack 27-round HIGHT (round 4 to round 30) with improved time complexity and practical memory requirements. This attack of ours is the best result on HIGHT to date in the classical single-key setting. We also provide the first attack on 26-round HIGHT (round 4 to round 29) with the full whitening key.