A desirable property of iterated cryptographic algorithms, such as stream ciphers or pseudo-random generators, is the lack of short cycles. Many of the previously mentioned algorithms are based on the use of linear feedback shift registers (LFSR) and nonlinear feedback shift registers (NLFSR) and their combination. It is currently known how to construct LFSR to generate a bit sequence with a maximum period, but there is no such knowledge in the case of NLFSR. The latter would be useful in cryptography application (to have a few taps and relatively low algebraic degree). In this article, we propose a simple method based on the generation of algebraic equations to describe iterated cryptographic algorithms and find their solutions using an SAT solver to exclude short cycles in algorithms such as stream ciphers or nonlinear feedback shift register (NLFSR). Thanks to the use of AIG graphs, it is also possible to fully automate our algorithm, and the results of its operation are comparable to the results obtained by manual generation of equations. We present also the results of experiments in which we successfully found short cycles in the NLFSRs used in Grain-80, Grain-128 and Grain-128a stream ciphers and also in stream ciphers Bivium and Trivium (without constants used in the initialization step).

Urban green spaces (UGS) play an important role in the structure of urbanized areas. Providing adequate access to them may contribute to shaping more pro-health behaviours among city residents. There are many proven benefits of access to UGS. They can have a significant impact on improving mental and physical health. The proximity of green areas in a city has a positive impact on basic environmental indicators: they improve air quality, contribute to reducing the urban heat island effect and are places conducive for socializing. In a world dominated by cars and a sedentary lifestyle, it is difficult to find time to be physically active. Therefore, the presence of park spaces can significantly affect the provision of the required minimum levels of physical activity. The subject of interest of this article is a review of selected academic publications, whose authors attempted to create objective tools for measuring the accessibility of green spaces in an urban environment. The study contains a tabular list of selected research methods and defines the basic purpose of each study and data source. Green area accessibility indices can be an important tool in shaping the spatial policy of cities. Summarizing the academic achievements in this field may constitute an incentive to conduct research of a similar nature and significance in Poland. Effective mapping of accessibility indices may become a clear tool for communication between local governments responsible for making key decisions in cities and the Polish academic community.