We present a method to iteratively construct new bent functions of variables from a bent function of variables and its cyclic shift permutations using minterms of variables and minterms of 2 variables. In addition, we provide the number of bent functions of variables that we can obtain by applying the method here presented, and finally we compare this method with a previous one introduced by us in 2008 and with the Rothaus and Maiorana-McFarland constructions. 1. Introduction Boolean functions are widely used in different types of cryptographic applications, such as block ciphers, stream ciphers, and hash functions [1–3], and in coding theory [4, 5], among others. For example, the implementation of an S-box needs nonlinear Boolean functions to resist attacks such as the linear and differential cryptanalysis [6–9]. For an even number of variables, Boolean functions bearing maximum nonlinearity are called bent functions [10, 11]. The construction of one-to-one S-boxes so that any linear combination of the output functions is balanced has already been explained [12, 13] and also the issue of making such linear combination a bent function . However, no conclusive approaches have been presented yet for the construction of all S-boxes so that they satisfy the property that any linear combination of the outputs is also bent. It is precisely for this reason that a thorough study of the properties of bent functions as well as of the methods to construct them has occupied the minds of many authors in the last decades (see, e.g., [9, 11, 15–35] and the references therein). Bent functions constitute a fascinating issue in cryptography but, unfortunately, there is a mist hovering over their properties, their classification, and their actual number. The origin of the concept of bent function takes us back to a theoretical article by McFarland  where he discussed difference sets in finite noncyclic groups. Dillon , a year later, systematized and further elaborated McFarland’s insights and provided proofs for a great number of properties; Dillon’s Ph.D. dissertation has been an excellent source in the field of bent functions up to the mid s. But it was Rothaus  who came up with the name for the concept. These functions are called perfect nonlinear Boolean functions by Meier and Staffelbach . There are different ways to obtain bent functions; most of them are based on the algebraic normal form of a Boolean function and the Walsh transform. However, there are very few constructions of bent functions based on the truth table of Boolean functions, for
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