Question

(a) What is the difference between a public key and a private key cryptosystem?

(b) Explain why using shift chippers is a private key system.

(c) Explain why the RSA cryptosystem is a public key system.

Short answer

(a) With a private key cryptosystem, you can quickly ascertain the decryption key if you know the encryption key.

With a public key cryptosystem, you cannot ascertain the decryption key if you know the encryption key.

(b) Shift chipper is a private key system because we can easily determine the decryption key from the encryption key.

(c) A RSA cryptosystem is a public key system, because you cannot determine the decryption key from the encryption key.

Step-by-step solution

Finding the difference between a public key and a private key cryptosystem

(a)

With a private key cryptosystem, you can quickly ascertain the decryption key if you know the encryption key.

With a public key cryptosystem, you cannot ascertain the decryption key if you know the encryption key.

Explaining why using shift chippers is a private key system

(b)

A shift chipper is a private key because when you know the encryption key k, then the encryption function is .

Then, we also know the decryption key which is and the decryption function is$f\left(p\right)=(p+k)mod26$

$f^{-1}\left(p\right)=(p-k)mod26$.

Hence, shift chipper is a private key system because we can easily determine the decryption key from the encryption key.

Explain why the RSA cryptosystem is a public key system

(c)

RSA cryptosystem is a public key system because you cannot determine the decryption key from the encryption key.