Final answer:
To solve the RSA problem, the multiplicative inverse of e is calculated with respect to the totient of n. The value of d is determined to be 187. The encryption of m=100 under RSA algorithm results in a ciphertext of 62.
Step-by-step explanation:
The subject question pertains to the RSA encryption algorithm, which is based on number theory and modular arithmetic. The specific question involves finding the multiplicative inverse of the public key exponent e with respect to the totient of n (denoted as φ(n)) and then using it to encrypt a message m.
First, we compute φ(n) where n = p * q and p = 11, q = 29:
- φ(319) = (p-1)*(q-1) = (11-1)*(29-1) = 10*28 = 280
Then, we find the multiplicative inverse d of e mod φ(n) using the Extended Euclidean Algorithm:
- e = 3
- φ(n) = 280
- d = e⁻¹ mod 280
- The value of d that satisfies 3d ≡ 1 (mod 280) is 187
To encrypt the message m=100, the ciphertext c is calculated as:
- c = m^e mod n
- c = 100^3 mod 319
- c = 1000000 mod 319
- c = 62