This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n > 2 of variables with at least sub-optimal algebraic immunity is provided.

The F5 algorithm [8] is generally believed as one of the fastest algorithms for computing Gröbner bases. However, its termination problem is still unclear. The crux lies in the non-determinacy of the F5 in selecting which from the critical pairs of the same degree. In this paper, we construct a generalized algorithm F5GEN which contain the F5 as its concrete implementation. Then we prove the correct termination of the F5GEN algorithm. That is to say, for any finite set of homogeneous polynomials, the F5 terminates correctly.

The development of agricultural farming has evolved from traditional agricultural machinery due to its efficiency and autonomy. Intelligent agricultural machinery is capable of autonomous driving and remote control, but due to its limited perception of farmland and field obstacles, the assistance of unmanned aerial vehicles (UAVs) is required. Although existing intelligent systems have greater advantages than traditional agricultural machinery in improving the quality of operations and reducing labor costs, they also produce complex operational planning problems. Especially as agricultural products and fields become more diversified, it is necessary to develop an adaptive operation planning method that takes into account the efficiency and quality of work. However, the existing operation planning methods lack practicality and do not guarantee global optimization because traditional planners only consider the path commands and generate the path in the rectangular field without considering other factors. To overcome these drawbacks, this paper proposes a novel and practical collaborative path planning method for intelligent agricultural machinery based on unmanned aerial vehicles. First, we utilize UAVs for obstacle detection. With the field information and operation data preprocessed, automatic agricultural machinery could be assisted in avoiding obstacles in the field. Second, by considering both the historical state of the current operation and the statistics from previous operations, the real-time control of agricultural machinery is determined. Therefore, the K-means algorithm is used to extract key control parameters and discretize the state space of agricultural machinery. Finally, the dynamic operation plan is established based on the Markov chain. This plan can estimate the probability of agricultural machinery transitioning from one state to another by analyzing data, thereby dynamically determining real-time control strategies. The field test with an automatic tractor shows that the operation planner can achieve higher performance than the other two popular methods.

In 2018, an attack named fast-near-collision attack (FNCA) was proposed, which is an improved version of near-collision attack (NCA) on Grain-v1, one of the three hardware-oriented finalists of the eSTREAM project. FNCA is designed as a key recovery attack and takes a divide-and-conquer strategy that needs a merging phase. We propose an improved FNCA where the merging phase is optimized by a linear programming based strategy. It decreases the candidates of the internal state vectors (ISVs) in each step of merging and has a reduction in the overall time complexity. Since the merging phase is vital for a divideand-conquer strategy, where the most of bits of the full internal state are recovered, other analyses on Grain family with FNCA can get optimized by our method in varying degrees. This paper offers an experiment on a reduced Grain and a theoretical analysis on Grain-v1 to confirm the results. In the case of the reduced Grain of an 80-bit internal state, the time complexity is 2 37.1096 , which has a 27.8% reduction. For Grain-v1, its theoretical time complexity is around 2 73.4 , which is reduced by 79.4% compared with the original one. INDEX TERMS Cryptanalysis, grain, near collision, stream ciphers, time-memory-data tradeoff attacks.