Using 'RSA' algorithm, if 𝑝 = 13,𝑞 = 5 and 𝑒 = 7. the value of 𝑑 and…

Step 1: Compute n and phi(n).

n = p * q = 13 * 5 = 65. phi(n) = (p-1)*(q-1) = 12 * 4 = 48.

Step 2: Find d such that d * e ≡ 1 (mod 48).

We need the modular inverse of e = 7 modulo 48. Since 7 * 7 = 49 ≡ 1 (mod 48), we have d = 7.

Step 3: Encrypt m = 6 using the public key (e, n) = (7, 65).

Compute powers of 6 modulo 65 to get 6^7 mod 65:

• 6^2 = 36

• 6^3 = 6^2 * 6 ≡ 36 * 6 = 216 ≡ 21 (mod 65)

• 6^4 ≡ 21 * 6 = 126 ≡ 61 (mod 65)

• 6^5 ≡ 61 * 6 = 366 ≡ 41 (mod 65)

• 6^6 ≡ 41 * 6 = 246 ≡ 51 (mod 65)

• 6^7 ≡ 51 * 6 = 306 ≡ 46 (mod 65)

Therefore d = 7 and the ciphertext for message 6 is 46. Final answer: d = 7, ciphertext = 46.