Answer:
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
[tex]n=pq=71\times 97=6887[/tex]
Now the φ(n) is given as
[tex]\phi(n)=(p-1)(q-1)=(71-1)(97-1)=(70)(96)=6720[/tex]
So the value of φ(n) is 6720.
Now
[tex]ed=1 mod \phi(n)[/tex]
As e is 197 so
[tex]ed=1 mod \phi(n)\\d=(1 mod 6720)/197\\d=6413[/tex]
The value of d is 6413.
m=8720 so the Encryption is given as
[tex]C=m^e mod n\\C=8720^{197} mod 6887\\C=3984[/tex]
Now the decryption is
[tex]M=c^d mod\, n\\M=3984^{6413} mod \, 6887\\M=8720[/tex]
So the Encrypted message is C=3984 while the decrypted one is M=8720.
