1 compute 12248 mod 172 show steps 2 let p67 q89 i using ne...

(1) Compute 12^248 (mod 172). Show steps. (2) Let p=67, q=89. (i) Using (n,E) = (5963,53) as the public key, write down the encryption function fe (remember to include "mod n"). (ii) Compute the decryption function fd. (Recall fd(x) = x^D (mod n)) (iii) Compute fe(4). Show steps. (iv) Let y = fe(4). Compute fd(y). Show steps.

Transcript

00:01 So, let us start with the concept which we are going to use here for this question.

00:07 So basically affine cheaper function technique is used to encrypt a message.

00:13 So, let's suppose if you haven't given the function, cheaper function as f of x is equal to of the type ax plus b and you will be told that the mod 26 likewise the general form of affine cheaper function.

00:29 So here basically x is the number assigned for a letter and remainder of mod of 26 are assigned for all the 26 letters.

00:44 For example, if i will say a is equal to 0 then b would be equal to 1, c is equal to 2 and it will be so on up to z that is 25.

00:55 Right? so, here we have to decipher the text.

01:00 So we will use function in a reverse that is a multiplier has to be found before mod 26 and hence we will say the multiplier is whole number which is calculated using the formula 26 multiplied by n plus 1 that whole divided by the k where k is the coefficient of x which is 9 in the question and is the natural number.

01:29 So basically here n is going to be 1.

01:32 So let us say the 26 multiplied by why we are taking 26 because we have to state for mod of 26.

01:39 Okay, then n is 1 plus 1 or the value of k according to question is 9.

01:45 So this will comes out equals to 3.

01:47 Now 3 is coming here that means we have to multiply it by 3.

01:52 Basically, 3 is multiplier.

01:56 3 is what? the multiplier.

01:58 Now we can decipher text ucr by a u of 20 that is number assigned to you then c of 2 number assigned to c and let's say r be 17 that is number assigned to r.

02:20 So generally if i will try to find out for u which we have assigned to 20.

02:28 So basically it should be minus of 2 that will be comes out equals to 18.

02:35 So that means to say this 9x plus 2 will be subtracted from number assigned to the alphabets and hence we get the multiplier times of 18 this should be equals to 3 into 18.

02:50 So this will comes out 54.

02:53 So basically 54 mod of 26 this will gives us 2...

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