On Boolean functions of many variables

More on the influence of variables on boolean functions

In this lecture we will look at the following natural question– do there exist balanced boolean functions f on n variables such that for every variable x the influence of x on f is “small” and how small can this bound be made? (“Balanced” means that Pr(f = 0) = Pr(f = 1) = 12 but Ef = α for some α bounded away from 0 and 1 is just as interesting.) In the last lecture we showed that for the “tri...

The Influence of Variables on Boolean Functions (Extended Abstract)

Plateaued Rotation Symmetric Boolean Functions on Odd Number of Variables

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

Classification of Cubic Boolean Functions in 7 Variables

A well-known and widely used approach in the study of algebraic objects is the investigation of their sub-objects and quotient objects. Consider the set of Boolean functions on F2 of degree less than or equal to r for 0 ≤ r ≤ n, which can also be seen as the Reed-Muller code RM(r, n) of order r. The automorphism group of RM(r, n) is equal to the general affine group AGL(n, 2) for all 1 ≤ r ≤ n ...