 Hi everyone, my name is Wang Zimpeng. My co-author is Hu Bin, Guan Jie, Zhang Kai, and Shi Taiyong. We all come from PLA SF, Information Engineering University. And I will present to our people whose title is exploring secret keys in searching integral distinguish based on division property. My presentation were including the following five parts. The first one, the introduction of division property. The second one, motivation. The third, bypass the influence of some security keys on BDBT proposition. The fourth, applications. The fifth, congratulations on the future works. The first part, the introduction of division property. Division property was proposed by Tudu at Eurocraft 2015. It's a general realization of integral property. It's a powerful in finding integral characteristics of blocker supers. Then the BDBT division property was proposed by Tudu and Mori at FIC 2016. There are two kinds of BDB division property. Conventional BDB division property denoted as CBDP and BDB division property using three subsets denoted as BDBT. We will introduce the definition of CBDP and BDBT. First, the definition of CBDP. Let X be a mod size whose element take the value of i full to n. And then, when the mod size X have the CBDP d key, where t denotes a set of n dimensional vector whose s element takes the value between 0 and 1. It fulfills the following equations. Here, we will introduce the two simple. XU means that the big product for XI and UI. And U greater or equal than key means that Ui greater or equal key equals for all i. Then we will research the sum of XU if there exists a key in key satisfying U greater than or equal key. It means that the sum is unknown, otherwise the sum is zero. Then we will introduce the definition of BDBT. The definition of BDBT is similar to the definition of CBDP. Let X be a mod size whose element take the value of f to n. When the mod size X have BDBT d key l, where key l denotes two sets of n dimensional vector whose s element takes the value between 0 and 1. It fulfills the following equations. The first one if there is key in key satisfying U greater than or equal key. It means that this sum is unknown. As if the first connection is not satisfied if there is air in air satisfying U equal air. Then we know that the sum of this is one, otherwise the sum is zero. The issue collapsed in 2016. Xiang Adao applied MRP method to the proposition of CBDP. They first introduced the concept of CBDP drill, which is defined as follows. Assume the initial CBDP of safer BD key 0, and the CBDP after s run function BD key r for key 0, key 1, and key r. If key i can proper j to key i plus 1 for all i, we call key 0, key 1, and key r around CBDP drill. Then they show the MRP model for the proposition of CBDP as follows. For CBDP drill, key 0, key 1, key r, and all the intranes are binary variables of m, v, a, r. Then model the CBDP propositions of basic operations, including copy, XOR, and xbox by layer in equalities, and the constraints are denoted as m, c, o, n. Some solvers like Groovy can efficiently evaluate the feasibility of CBDP drills if key link to ER is infeasible. The S bit is balanced, the sum is always zero. VRER is a unit vector whose only S bit is S1. At H-Craft 2019, Wang et al proposed protein techniques of CBDP for the first time. First of all, for April E, let's import bdpd, bd, k0, l0, and output bdpd, k1, and l1. Then for any vector k in k0, if there is no CBDP drill such that key to em, the bdpd proposition of this is equivalent to that of k0 and l0, on whether em in k1 and em in l1 are not, where k0 to key means remove key from k0. The second one, pouring air for April E, let's import bdpd, bd, k0, and l0, and output bdpd, bd, k1, and l1. Then for any vector l in l0, if there is no CBDP drill such that air to em, the bdpd proposition of this is equivalent to that of kd, k0, and l0, on whether em in k1 and em in l1 are not, where l0 to air means remove air from l0. Finally, the proposed MRP is a method of searching integral disengaged, based on bdpd accurately. The second part is motivation. SPIKE is a family of lightweight block slippers. For SPIKE 32, because the block size is only 32 meters, we can observe the behavior of all the planets under a fixed key. By testing 10 power of two random security keys, we experimentally found a better integral disengaged of 6 round SPIKE 32 with 30 active bitters. However, this experimental integral disengaged cannot be proved by bdpd. Namely, either the above experimental 6 round disengaged doesn't work for all the keys, or the existing methods cannot find accurate integral disengaged. So, there still exists a gap between the proved disengaged and the experimental one. As part of FAC 2016, the proposition of bdpd simply regards this as a no. If either this or this is a no, that is, the beta-based division property cannot explore the following facts that the parity may be always 0 or 1, although this and this are unknown, how to improve the accuracy of bdpd is an important issue worth studying. The second part is bypassing the influence of some secret keys on the proposition of bdpd. Here we propose theorem 3, let EX be a simple if Fi is an X with the secret key function denotes as this. Where R key is the secret key for the initial math set satisfying D key 0 L0, let D key i L i be the input bdpd of E i. Then if the algorithm bdpd returns 0, we have this equation, where L i is this and E R key equal 0 is M's output beta's observer whose secret key is fixed as 0, because the secret key R key is a constant beta whose value is unknown. When the condition this is satisfied, we have this. Namely, if we want to research the integrity thing is of EX, we only need to research the integral property of E R key equal 0. When R key equal 0, the X with the secret key function Fi will become the identity map and we do not need to consider the influence of the secret key R key and more, that is the influence of the secret key R key can be bypassed. The first part is application. According to the bypass technique, we propose an improved searching algorithm. The main framework of the algorithm is as follows, like a function BFI and its input bdpd bd key i L i. The first we will identify whether it is X OR with the secret key function or not. If the answer is yes, we will use theorem 3 to identify can it bypass the secret key? If yes, then we bypass the secret key. If no, we will use the proposition rules of bdpd to get its output bdpd. If it is not the X with the secret key function, we will use the proposition rules of bdpd to get its output bdpd. Then, we apply our algorithm to spike, cantile, semen, semic, semen102, present, and rectangle blocksipers, and some better integrity distinguish are found. For spike32, we propose that the experimental integrity distinguish works for all the keys, that is a give between the experimental integrity distinguish and the proved one is filled. For spike blockipers, we found more balanced bitters, and for cantile 164 blockipers, we improve the length of the integrity distinguish. For spike32, semen32, semic32, semen102, and cantile32, because the block size is only 32 bitters, we can observe the behavior of all the planets and fix the keys. Then we experimentally propose that the integrity distinguish found by our automatic algorithm are the best integrity distinguish that works for all secret keys. That means our algorithm is very accurate in searching integrity distinguish. Concludes, a new bdpd proposition rules of XOR with the secret keys is proposed. It shows that some secret keys bitters can be bypassed. Then we propose an improved automatic algorithm of searching integrity distinguish, and apply it to some blockipers. With this algorithm, some better integrity distinguish have been found. Future works, for sepers with large block size due to the limit of computing resources, we cannot give the experimental proof as far as we know. There is still no result on the probable security against integral attack. This will be our future work. Thank you for listening.