2D physically unclonable functions of the arbiter type

Objectives. The problem of constructing a new class of physically unclonable functions of the arbiter type (APUF) is being solved, based on the difference in delay times for the inputs of numerous modifications of the base element, due to both an increase in the number of inputs and the topology of their connection. Such an  approach allows building two-dimensional physically unclonable functions (2D-APUF), in which, unlike  classical APUF, the challenge generated for each basic element selects a pair of paths not from two possible, but from a larger number of them. The relevance of such a study is associated with the active development of  physical cryptography. The following goals are pursued in the work: the construction of the basic elements of the APUF and their modifications, the development of a methodology for constructing 2D-APUF.Methods. The methods of synthesis and analysis of digital devices are used, including those based on  programmable logic integrated circuits, the basics of Boolean algebra and circuitry. Results. It is shown that the classical APUF uses a standard basic element that performs two functions,  namely, the function of choosing a pair of paths Select and the function of switching paths Switch, which, due to their joint use, allow achieving high performance. First of all, this concerns the stability of the APUF functioning, which is characterized by a small number of challenge, for which the response randomly takes one of two  possible values 0 or 1. Modifications of the base element in terms of the implementations of its Select and Switch functions are proposed. New structures of the base element are presented in which the modifications of their  implementations are made, including in terms of increasing the number of pairs of paths of the base element from which one of them is selected by the challenge, and the configurations of their switching. The use of  various basic elements makes it possible to improve the main characteristics of APUF, as well as to break the regularity of their structure, which was the main reason for hacking APUF through machine learning. Conclusion. The proposed approach to the construction of physically unclonable 2D-APUF functions, based on the difference in signal delays through the base element, has shown its efficiency and promise. The effect of improving the characteristics of such PUFs has been experimentally confirmed with noticeable improvement in the stability of their functioning. It seems promising to further develop the ideas of constructing two-dimensional physically unclonable functions of the arbiter type, as well as experimental study of their characteristics, as well as resistance to various types of attacks, including using machine learning.