Question

rsa algorithms are widely used to generate public and private key pairs. let e and d denote the public and private key respectively. answer the following questions: a. a public key is used to encrypt a plaintext m (m < n). what is the ciphertext?

Answer 1

In RSA, the ciphertext is calculated by raising the plaintext to the power of the public key exponent and taking the modulus with respect to the RSA modulus. The corresponding private key exponent reverses this process to decrypt the ciphertext.

Step-by-step explanation:

The RSA algorithm is one of the most popular and secure public-key cryptographic methods. When you have a plaintext message m, which is less than n (where n is the modulus used in the RSA algorithm), and you want to encrypt it using a public key, the resulting ciphertext c can be calculated using the equation:

c = me mod n.

Here, e represents the exponent component of the public key, whereas d represents the exponent of the private key. To encrypt a plaintext m, you raise m to the power of e and then take the modulus with respect to n. The result of this operation is the ciphertext c, which can be securely transmitted. The recipient of the message, who possesses the corresponding private key, can decrypt the ciphertext by following a similar procedure, raising the ciphertext to the power of d and again taking the modulus with respect to n.

It's important to note that for the security of RSA, the values of e and d are chosen such that e * d mod φ(n) = 1, where φ is Euler's totient function. This relationship ensures that the encryption and decryption processes are inverses of each other.