In this paper, we present a framework for biclique cryptanalysis of block ciphers which extremely requires a low amount of data. To that end, we enjoy a new representation of biclique attack based on a new concept of cutset that describes our attack more clearly. Then, an algorithm for choosing two differential characteristics is presented to simultaneously minimize the data complexity and control the computational complexity. Then, we characterize those block ciphers that are vulnerable to this technique and among them, we apply this attack on lightweight block ciphers Piccolo-80, Piccolo-128, and HIGHT. The data complexity of these attacks is only 16-plaintext-ciphertext pairs, which is considerably less than the existing cryptanalytic results. In all the attacks, the computational complexity remains the same as the previous ones or even it is slightly improved.Index Terms-Biclique cryptanlysis, attack complexity, lightweight block ciphers.
SummaryHIGHT is a lightweight block cipher introduced in CHES 2006 by Hong et al as a block cipher suitable for low-resource applications. In this paper, we propose improved impossible differential and biclique attacks on HIGHT block cipher both exploiting the permutation-based property of the cipher's key schedule algorithm as well as its low diffusion. For impossible differential attack, we found a new 17-round impossible differential characteristic that enables us to propose a new 27-round impossible differential attack. The total time complexity of the attack is 2 120.4 where an amount of 2 59.3 chosen plaintext-ciphertext pairs and 2 107.4 memory are required.We also instantiate a new biclique cryptanalysis of HIGHT, which is based on the new idea of splitting each of the forward and backward keys into 2 parts where the computations associated to each one are performed independently. The time complexity and data complexity of this attack are 2 125.7 and 2 42 , respectively. To the best of our knowledge, this is the fastest biclique attack on full-round HIGHT.
Meet in the middle (MITM) attack is one of the most important and applicable methods for cryptanalysis of block ciphers. In this paper, a more generalized method for MITM attack is considered. For this purpose, a notion, namely cut-set, is utilized by which several numbers of MITM attacks can be performed. However, manual investigation on these cases is time-consuming and sometimes not errorfree. Therefore, a new search algorithm is also provided to obtain proper attacks in a timely manner. For examination, this new search algorithm, which could make an automated attack along with some certain ideas, is applied on HIGHT, Piccolo-128, CRAFT and AES-128 block ciphers. The least time complexities which are obtained by generalized MITM attack on full HIGHT, Piccolo-128, CRAFT and AES-128 are 2 125.08 , 2 126.78 , 2 123.25 and 2 125.53 , respectively. The results on full-round CRAFT are, to the best of our knowledge, the first cryptanalysis results in the single-key model except the designers' investigations. In addition, the results show some improvements for complexities of all the attacks, especially on HIGHT.
Hill is a classical cipher which is generally believed to be resistant against ciphertext-only attack. In this paper, by using a divide-and-conquer technique, it is first shown that Hill with d × d key matrix over Z 26 can be broken with computational complexity of O(d26 d), for the English language. This is much less than the only publicly known attack, i.e., the brute-force with complexity of O(d 3 26 d 2). Then by using the Chinese Remainder Theorem, it is shown that the computational complexity of the proposed attack can be reduced down to O(d13 d). Using an information-theoretic approach, it is shown that the minimum ciphertext length required for a successful attack increases by a factor of about 7 and 9.8, respectively for these two attacks in comparison with the brute-force attack. This is the only serious attack on Hill since its invention in 1929.
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