How to do galois multiplication?

Suppose I have 2 cell array inputs as shown below:

A={'fe' 'ff' 'e9' '92' '86' '65' '73' '1c' '6d' '6a' '8f' '94' '67' '30' '83' '08'};
H={'b8' '3b' '53' '37' '08' 'bf' '53' '5d' '0a' 'a6' 'e5' '29' '80' 'd5' '3b' '78';

How to muliply these inputs using galois field multiplication?? Can somebody helpme?

Answer 1

[Akira Agata]

If you have the Communications System Toolbox, please try the following script.

% Convert to GF(2^8)
gfA = gf(hex2dec(A),8);
gfH = gf(hex2dec(H),8);

% Multiplication in GF(2^8) field
gfAH = gfA .* gfH;

[Darsana P M]

I got this error, when i did this:

Error: File: hash1.m Line: 19 Column: 5
The expression to the left of the equals sign is not
a valid target for an assignment.
Line 19 is, gfA = gf(hex2dec(A),8);
What to do ??

[Akira Agata]

Seems strange... Let me check two points.

1) Has the Communications System Toolbox been already installed ?

2) What is your MATLAB version?

[Darsana P M]

The error was solved. It was a minor mistake of missing a semi-colon. The code is correct. Can i convert the final answer, ie, gfA into a hexa decimal value?? I tried dec2hex(gfA), but i got an error. what should i do?

[Akira Agata]

Since gfA is a Galois field array, you can not apply dex2hex directly.

But gfA.x returns corresponding numeric array, so please try dec2hex(gfA.x) to obtain hexa values.

[Darsana P M]

 I got an error stating :
>> hash1

Undefined function or variable 'gf2dec'.

Error in hash1 (line 23)
gfAH= gf2dec(gff.x);

gff = gfA .* gfH;

What must be done??

[Darsana P M]

can somebody help me to solve this error??

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/12542-galois-field-array-to-decimal-array-conversion for gf2dec

However, you can use

cellstr(dec2hex(gfA.x)).'

[Darsana P M]

function DecOutput = gf2dec(GFInput)
GFInput=[172 106 200 187 68 251 103 2 149 131 25 55 237 110 129 231];
%GFInput = GFInput(:)';% force a row vector
GFRefArray = gf([0:(2^1)-1]);
for i=1:length(GFInput)
    for k=0:(2^1)-1
        temp = isequal(GFInput(i),GFRefArray(k+1));
        if (temp==1)
            DecOutput(i) = k;
        end
    end
end

This is the function, I got from the above example. Still i am getting an error.

Error in gf2dec (line 2)
GFInput=[172 106 200 187 68 251 103 2 149 131 25 55 237 110 129 231];

Output argument "DecOutput" (and maybe
others) not assigned during call to
"gf2dec".

Error in hash1 (line 24)
gfAH= gf2dec(gff.x);

Error in encrygc (line 84)
HA=hash1(g);

[Darsana P M]

What might be the issue?

[Walter Roberson]

GFRefArray = gf([0:(2^1)-1]);

contains only 0 and 1 because that is what you asked for. It would need to be

function DECout = gf2dec(HA)
N = 8;
c = 0 : (2^N)-1;
GFRefarray = gf(c, N);
for i = 1:length(HA)
    for k = c
        if isequal(HA(i),GFRefarray(k+1));
            DECout(i)=k;
        end
    end
end