Converting binary to entries of GF(2^5)

JBee

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Nov 17, 2020
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Hi! So, I'm currently reading this modified proposed algorithm for the hill cipher. It uses finite fields and the logic operator XNOR. So far it has been an understandable process of encrypting a message, I have chosen a 4x4 nonsingular matrix as the key, converted the plaintext into ciphertext by multiplying the key and plaintext matrix of mod 31. From there I converted each entry into 5-bit binary and created another 4x4 matrix that will be used in finding another matrix using the XNOR operation. If you want to read the report, I'll link it at the bottom. I'm up to the point where I need to convert the entries from [M][/XNOR] into elements of GF(2^5) with the polynomial form of x^5 +x^2+1=0. How exactly would I go about doing this? I'm unsure whether or not I should post the entire [M][/XNOR] since it is a 4x45 matrix to encompasses all the entries of the message, so I'll just give a few of my binary codes.

01000 10111 00010 01110 01101 00011 01001 0100101000 10111 00010 01110 01101 00011 01001 01001

I appreciate any help that I can receive :)

Link to the report: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.402.5641&rep=rep1&type=pdf
 
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