Galois Field multiplication in AES, I got E3 using my method, but the answer is D3 in book.

[shivajikobardan]

This is taken from this book:

CRYPTOGRAPHY AND INFORMATION SECURITY, THIRD EDITION

The main objective of this book is to cater to the need of a quality textbook for education in the field of information security. The present third edition of the book covers the principles, design, and implementation of various algorithms in cryptography and information security domain. The...

books.google.com.np

Page 102

I've used this method given in this pdf below to calculate "mix column" step output.

https://www.networkdls.com//Articles/AESbyExample.pdf

It's in page number 9.

I'm trying to find+ means XOR here)

1*36+2*b9+3*a5+3*38

=36+69+f4+48

=e3

 

[blamocur]

How did you get [imath]2\star b9 = 69[/imath] ?

 

[blamocur]

How did you get [imath]2\star b9 = 69[/imath] ?

I take it back: after looking closer I get 69 too. Moreover, using the table from the PDF you referenced I get E3 for the final result as well.

It seems that the book is using a multiplication method which is different from the one used in the PDF. This could mean that they are using different representations of [imath]GF(2^8)[/imath], but as far as I could see, AES defines only one representation of the field (https://en.wikipedia.org/wiki/Advanced_Encryption_Standard)

 

[blamocur]

This is taken from this book:
View attachment 33852

CRYPTOGRAPHY AND INFORMATION SECURITY, THIRD EDITION

The main objective of this book is to cater to the need of a quality textbook for education in the field of information security. The present third edition of the book covers the principles, design, and implementation of various algorithms in cryptography and information security domain. The...

books.google.com.np

Page 102

I've used this method given in this pdf below to calculate "mix column" step output.

https://www.networkdls.com//Articles/AESbyExample.pdf

It's in page number 9.

I'm trying to find+ means XOR here)

1*36+2*b9+3*a5+3*38

=36+69+f4+48

=e3

I believe you've found a bug in the book: the 1110 0011 binary string corresponds to hexadecimal E3, nod D3: the binary for D3 would be 1101 0011!

Please disregard my post about different representations of GF: both the book and the PDF use the same representation as used in AES, but the book has a typo.

 

[shivajikobardan]

I believe you've found a bug in the book: the 1110 0011 binary string corresponds to hexadecimal E3, nod D3: the binary for D3 would be 1101 0011!

Please disregard my post about different representations of GF: both the book and the PDF use the same representation as used in AES, but the book has a typo.

thanks for the information