Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences

Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences

We study [2m−1, 2m]-binary linear codes whose weights lie between w0 and 2m−w0, where w0 takes the highest possible value. Primitive cyclic codes with two zeros whose dual satisfies this property actually correspond to almost bent power functions and to pairs of maximum-length sequences with preferred crosscorrelation. We prove that, for odd m, these codes are completely characterized by their ...

Sequences and Linear Codes from Highly Nonlinear Functions

On Feedback Functions of Maximum Length Nonlinear Feedback Shift Registers

Feedback shift registers are basic building blocks for many cryptographic primitives. Due to the insecurities of Linear Feedback Shift Register (LFSR) based systems, the use of Nonlinear Feedback Shift Registers (NFSRs) became more popular. In this work, we study the feedback functions of NFSRs with period 2n. First, we provide two new necessary conditions for feedback functions to be maximum l...

The weight distributions of irreducible cyclic codes of length 2m

Let m be a positive integer and q be an odd prime power. In this short communication , the weight distributions of all the irreducible cyclic codes of length 2 m over F q are determined explicitly, directly from their generating polynomials.

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...