So now let us understand, encrypting with them a fine.
Now, one downside to using the multiplicative cipher is that the letter capitally always maps to letter
capitally.
The reason is that capital is the index number and zero multiplied by anything will be zero.
Now, we can fix this particular issue by adding a second key to perform a single cipher encryption
after the multiplicative ciphers, multiplication and modding is done.
Not this extra step changes the multiplicative cipher into a fine.
Not a fine cipher has to say, for example, key and B not 60.
E is the integer you use to multiply the letters number and multiply the plaintext by eight.
You are key to the product and then you're more the sum by 66 as you did in the original.
So this means that the Afie inside four has six to six times as many possibilities as a multiplicative
cipher.
It also ensures that the letter A. does always encrypt itself.
OK, now if we come to the decrypting with the fine sign now in the Sisa Saiful, you used addition
to encrypt and subtraction to decrypt in the afine side, for you have used multiplication to encrypt.
Naturally, you might think you can divide to decrypt the defined safe, but if you try this, you will
see that it doesn't work to decrypt with your fine cipher, you need to multiply the keys modular involves.
Now this reveals the more operations from the encryption process.
A modular inverse of two numbers is represented by an expression say for example, A multiplied by modulo
M if it's equal to one.
OK, now where the AI is the modular inverse and anima two numbers.
For example, the modular inverse of five more seven would be some number I would fire into.
I am modulo seven is equal to one.
Now you can brute force this calculation for example like one is is in the modular inverse of five more
seven because firing the one modulo seven is five and second is in the modular inverse of five more
seven because firing the two modulo seven constantly.
So three is the modular inverse of five and seven because if you see five in two three modules when
it comes to one.
So although the encryption and the decryption keys for the Caesar cipher part of the offensive four
are the same, the encryption key and the decryption keys for multiplicative side four are two different
encryption keys can be anything you choose as long as it's relatively blind to the size of this Envisat
which in this case is it?
And if you choose the key fifty three for encrypting with the fine for decryption key in the modular
inverse of fifty three more sixty six.
So that in that case you will have to check for in numerical one because say for example if you see
fifty three.
Multiplied by one more and this whole we would put it in a bracket to Morillo 66.
Now this comes to 53.
So one is not possible.
Similarly, if we just cooperate on this multiple times and just replace this value 53 into two.
Now, this comes to say 40.
If we say 53 into three, and that comes to say twenty seven.
If we say fifty three into four and this comes to say 14.
And here if we say 53 to five, this comes to one.
OK, so now in this case, because now your five is a modular inverse of fifty three and sixty six,
you know that they are fine for decryption keys.
Also five, decrypt a ciphertext letter, multiply that number by five and then model 266.
And the result is the number of original plaintext letters that you have.
So since six to six characters in this set, let's end the war of particular words, the cat using the
key 53.
OK, so if we say over here, OK, now save you capital C will be at the indexical.
OK, so if we say two multiplied by fifty three that will come to say one zero six, which is larger
than this implicit size because the size is sixty six.
So we need two more, one zero six by sixty six.
So if we say one zero six modulo six to six, if this comes to the results for the character of the
index 14, the symbol set that is equal to say zero.
OK, so the symbol C encrypts now.
So if we give you a B, this falls to zero.
I will use the same step for the next letter that is available.
Now this we have done it for C, so if we take a look now the string is at the index number twenty six,
which is equal to twenty six.
And if we say twenty six multiplied by fifty three then modulo sixty six.
Now that comes to say fifty eight and the index at fifty eight is equal to seven.
OK, so we have that eight to seven.
OK now this ring that is being that is Malti.
OK, so over here, this comes at an index of forty five.
So if we see forty five multiplied by fifty three modulo six to see this comes to nine and the index
nine you have the capital G.
So therefore diversity has been encrypted to zero seven right now.
Similarly, if you have to decrypt this zero seven back to the original then we'll have to multiply
the modular inverse that is say fifty three modulo sixty six.
OK, now this comes to five.
So the symbol zero is that the index 40.
Right.
So we say 40 multiplied by five.
Then again modulo sixty six.
And this comes to two which is the index of capital C, symbol seven.
Is that the index.
Fifty eight.
So if we just take it over here, the first one that is we have ok.
OK, so all the index is 40.
OK now the next index is seven seven letters of the index of that is the fifty eight.
So now if we try to do fifty eight multiplied by five modulo sixty six that comes to twenty six.
OK, which is equal to eight.
And then the symbol capital G the index is nine.
OK, and here we say nine multiplied by five modulo sixty six which is equal to forty five, which is
equal to be for the ciphertext zero seven G has encrypted or decrypted back to see eighty with these
capital, which is original plaintext just as expected.
Right.