The plain text message BAHI is encrypted with the RSA algorithm using e = 3, d…

RSA encrypts a numeric block m (with 0 ≤ m < n) using the public exponent e as c = me mod n, and decrypts it using the private exponent d as m = cd mod n, where e and d satisfy e·d ≡ 1 (mod φ(n)). When a message is encrypted character-by-character, each letter is first converted to its assigned number, and only that number is raised to the power e modulo n — independently of the other characters.

Here e = 3, n = 33, and letters are coded A = 1, B = 2, …, Z = 26 (matching the range stated in the question). For the plaintext B A H I:

1. B = 2 → 23 = 8, and 8 mod 33 = 8, which corresponds to the letter H.

2. A = 1 → 13 = 1, and 1 mod 33 = 1, which corresponds to the letter A.

3. H = 8 → 83 = 512, and 512 mod 33 = 17 (33 × 15 = 495; 512 − 495 = 17), which corresponds to the letter Q.

4. I = 9 → 93 = 729, and 729 mod 33 = 3 (33 × 22 = 726; 729 − 726 = 3), which corresponds to the letter C.

Ciphertext: HAQC

Cross-check: since φ(33) = (3 − 1)(11 − 1) = 20 and e·d = 3 × 7 = 21 ≡ 1 (mod 20), decrypting each ciphertext value with d = 7 must return the original plaintext number:

1. 87 mod 33 = 2, which is B.

2. 17 mod 33 = 1, which is A.

3. 177 mod 33 = 8, which is H.

4. 37 mod 33 = 9, which is I.

Decryption recovers B A H I exactly, confirming that the A = 1 … Z = 26 coding is applied consistently in both directions and that the ciphertext is HAQC.