show that the encryption procedure C=P^e(mod n) and decryption procedure P=C^d(mod n) in RSA cryptosystem are identical when encryption is done using modular eponentiation with modulus n=35 and enciphering key e=5
show that the encryption procedure C=P^e(mod n) and decryption procedure P=C^d(mod n) in RSA cryptosystem are identical when encryption is done using modular eponentiation with modulus n=35 and enciphering key e=5
They will be identical as your encryption and decryption key are identical for the following reasons;
If e=5 and mod m= 35, then in order to get your decryption key you need to find
$\displaystyle \frac{1}{5} mod\
\phi(35)$
Since this key will be the same as the encryption key, encrypting and decrypting will use the same exponent, not very secure.
Just remember that d and e should satisfy $\displaystyle de = 1\text{ mod }\phi(35)$
And $\displaystyle \phi(35) = (7-1)(5-1) = 24$. Now you will have to solve for
$\displaystyle 5d = 1\text{ mod }24$. Clearly $\displaystyle d=5$
Thus $\displaystyle d=e=5$ and hence encryption and decryption keys are identical