Question

Use the RSA cipher with public key n = 713 = 23 · 31 and e = 43. Encode the word "KING" into its numeric equivalent and encrypt it. (Encode one letter at a time. Assume the letters of the alphabet are encoded as follows: A = 001, B = 002, C = 003, ..., Z = 026. Enter your answer using a fixed number of digits: 001 for 1, 002 for 2, ..., 099 for 99.)

Answer 1

Encrypted message = 1.006×10⁵ 1.800×10¹ 3.209×10⁹ 3.648×10⁻⁴

Step-by-step explanation:

KING

K → 011

I → 009

N → 014

G → 007

Encryption (e , n) = (43 , 713)

C =
`m^(e)mod(n)`

∴

K = (011)⁴³mod 713 = 100630.6 => 1.006×10⁵

I = (009)⁴³mod 713 = 18 => 1.800×10¹

N = (014)⁴³mod 713 = 3.2088×10⁹ => 3.209×10⁹

G = (007)⁴³mod 713 = 0.0003648 => 3.648×10⁻⁴