The MixColumn transformation of AES consists of a matrix–vector multiplication in the field GF(2^8) with P(x)=x^8 +x^4 +x^3 +x +1. Let b =(b7 x^7 +...+b0) be one of the (four) input bytes to the vector–matrix multiplication. Each input byte is multiplied with the constants 01, 02 and 03. Your task is to provide exact equations for calculating the results of those three constant multiplications. We denote the result by d =(d7 x^7 +...+d0). 1. Write expressions for computing the 8 bits of d=01 · b as functions of the bi`s: d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . 2. Write expressions for computing the 8 bits of d=02 · b as functions of the bi's. If a XOR operation of two bits is required write it as, for example, b0+b1. d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . 3. Repeat for d =03 · b: d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . Note: The AES specification uses “01” to represent the polynomial 1, “02” to represent the polynomial x, and “03” to represent x +1 You mayript this quProblem 4.11 in the textbook: The MixColumn transformation of AES consists of a matrix-vector multiplication in the field GF(2^8) withP(x)=x^8 +x^4 +x^3 +x+1.Let b =(b7 x^7 +...+b0) be one of the (four) input bytes to the vector-matrix multiplication. Each input byte is multiplied with the constants01, 02 and 03. Your task is to provide exact equations for calculating the results of those three constant multiplications. We denote theresult by d =(d7 x^7 +...+do).1. Write expressions for computing the 8 bits of d=01 - b as functions of the bi's:d0-].d1=[d2=d3=d4=[d5=d6=and d7=2. Write expressions for computing the 8 bits of d=02 b as functions of the bi's. If a XOR operation of two bits is required write it as, forexample, b0+b1.d0=d7=3. Repeat for d=03. b:d0=d1=101d2=d2=d3=d3=d4=d5=d1=d6=and d7=Note: The AES specification uses "01" to represent the polynomial 1. "02" to represent the polynomial x. and "03" to represent x +1.d4=d6=d5=and

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Answered: Problem 4.11 in the textbook: The…

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

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The MixColumn transformation of AES consists of a matrix–vector multiplication in the field GF(2^8) with P(x)=x^8 +x^4 +x^3 +x +1. Let b =(b7 x^7 +...+b0) be one of the (four) input bytes to the vector–matrix multiplication. Each input byte is multiplied with the constants 01, 02 and 03. Your task is to provide exact equations for calculating the results of those three constant multiplications. We denote the result by d =(d7 x^7 +...+d0). 1. Write expressions for computing the 8 bits of d=01 · b as functions of the bi`s: d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . 2. Write expressions for computing the 8 bits of d=02 · b as functions of the bi's. If a XOR operation of two bits is required write it as, for example, b0+b1. d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . 3. Repeat for d =03 · b: d0= , d1= , d2= , d3= , d4= , d5= , d6= and d7= . Note: The AES specification uses “01” to represent the polynomial 1, “02” to represent the polynomial x, and “03” to represent x +1

You may
ript this qu
Problem 4.11 in the textbook: The MixColumn transformation of AES consists of a matrix-vector multiplication in the field GF(2^8) with
P(x)=x^8 +x^4 +x^3 +x+1.
Let b =(b7 x^7 +...+b0) be one of the (four) input bytes to the vector-matrix multiplication. Each input byte is multiplied with the constants
01, 02 and 03. Your task is to provide exact equations for calculating the results of those three constant multiplications. We denote the
result by d =(d7 x^7 +...+do).
1. Write expressions for computing the 8 bits of d=01 - b as functions of the bi's:
d0-
].d1=[
d2=
d3=
d4=[
d5=
d6=
and d7=
2. Write expressions for computing the 8 bits of d=02 b as functions of the bi's. If a XOR operation of two bits is required write it as, for
example, b0+b1.
d0=
d7=
3. Repeat for d=03. b:
d0=
d1=
101
d2=
d2=
d3=
d3=
d4=
d5=
d1=
d6=
and d7=
Note: The AES specification uses "01" to represent the polynomial 1. "02" to represent the polynomial x. and "03" to represent x +1.
d4=
d6=
d5=
and

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