(6 points + 4 points) Given p = 71, q = 97, find φ(n). If e = 197, find d. Accordingly, given message m = 8720, find the encrypted message and decrypted message. Show your work. Show how the factorization of n breaks RSA.

The value of φ(n) is 6720, while the value of d is 6413 and the Encrypted message is C=3984 while the decrypted one is M=8720.

Step-by-step explanation:

p is given as 71

q is given as 97

so n is

Now the φ(n) is given as

So the value of φ(n) is 6720.

Now

As e is 197 so

The value of d is 6413.

m=8720 so the Encryption is given as

Now the decryption is

So the Encrypted message is C=3984 while the decrypted one is M=8720.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,