An irreducible polynomial of degree 8 over GF(2) is given as f(x) =x+x+x'+x +1. This canbe used to define GF(2)=GF(256) which is frequently used to design a code over the ASCIIsymbols consisting of 8 bits.We will use the following notation, for a, e GF(2),e ar + a,r+ ar ++ aa +a,(A) Write a computer program of addition and multiplication for all the binary 8-tuples as aboveand answer to the following questions:(B) Find any member a in GF(256) with the property that a, a², a²̟., a5 are all distinct,Calculate as al28, and a4.ANSWER:) :a binary 8-tuple):a binary 8-tuple):a binary 8-tuple):a binary 8-tuplea = (a4 = (a12 =(ass = ((C) Calculate the multiplications a a, att . atza, and a al0 using your program in (A).Verify, for example, that a at = al+64 = ats, a*. a1zi - att12- al92 etc.(D) Define a linear function g from GF(256) to itself such that g(x) = x for any x in GF(256).Here, the linearity implies that g preserves two operations of the field.That is, for any x,y in GF(256), we haveg(x + y) = g(x) + g(y) and g(x-y) = g(x) - gV).Either prove that g is 1-1 or find a counterexample that g is NOT 1-1.Either prove that g is onto or find a counterexample that g is NOT onto.Report must contain your program source code and the answers to the above three problems.

Answered: Image /qna-images/answer/c20c31bf-1b39-4ee5-8cdb-a22a9ead8718.jpg

Answered: (A) Write a computer program of…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

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