MATLAB: Modular arithmetic for encryption

encryptionmodular arithmetic

I'm trying to implement an encryption technique using Matlab for a college project.

However I'm facing some difficulties in modular calculation.

For example I have matrix A = [ 1 , 0 ; 1/2 , 1 ] , and I need to calculate A mod 29.

what I'm getting in matlab is [ 1 , 0 ; 1/2 ,1 ],

while what I'm supposed to get is [ 1 , 0 ; 15 , 1 ] as in https://planetcalc.com/8326/

Actually I don't understand the math behined the fact that (1/2 mod 29) = 15 .

So, if any one can help me in getting this result in Matlab, I would be grateful.

Best Answer

"1/2" is integer (let us call it "a") so that

a*2 = 1 mod 29

This can be obtained by GCD function

>>  [~,a]=gcd(2,29)
a =
   -14
>> a = mod(a,29)
a =
    15

Related Solutions

MATLAB: Finding matrix modular for encryption

You will have problems with this due to the limited precision available to real numbers. For example, 1/3 and 1/10 cannot be exactly represented in binary floating point arithmetic.

A first step would be converting the floating point number into a rational, but doing that is risky. How, for example, do you know for sure that 0.52941176470588235947190014485386200249195098876953125 is intended as 9/17 and not as 4768517252509937/9007199254740992 ?

My recommendation would be not to do what you are trying to do. You would be better off using a pair of rationals, such as [-3, 2] or [9, 17] instead of -1.5 and 0.52941176470588235947190014485386200249195098876953125

MATLAB: Using mod function for checking integers

Why not play with mod? See what it does? Lets see what we can do.

K = 1:10;

Now, pick some number that we want to use to test for divisibility.

p = 3;

So, which elements of K will P divide exactly? We would expect 3, 6, and 9 for this vector of integers K and divisor P. So if you understand how mod works, what does this tell you?

mod(K,p)
ans =
     1     2     0     1     2     0     1     2     0     1
find(mod(K,p) == 0)
ans =
     3     6     9

So when mod(K,p) is zero, that tells us that p divides K, or the corresponding element thereof for vector K.

Similarly, does 17 divide 34?

mod(34,17)
ans =
     0

Yes, it does. But not 35.

mod(35,17)
ans =
     1

As far as your assignment goes, you need to spend some time working it out. But this should get you started.

Best Answer

Related Solutions

MATLAB: Finding matrix modular for encryption

MATLAB: Using mod function for checking integers

Related Question