Question

Encrypt the plain text message NUM THY IS QUE OF MATH using RSA algorithm with key (n, k)= (1643, 223). What is the recovery exponent for the crypto system? Assume that digit equivalence of the alphabets that A = 01, B = 02, ..., Y=25, Z = 26, space = 00

Answer 1

Please like the solution

Answer 2

To encrypt the plain text message "NUM THY IS QUE OF MATH" using the RSA algorithm with the key (n, k) = (1643, 223), we first need to convert the message into numerical values based on the given digit equivalence.

Here's the numerical representation of the message: N = 14 U = 21 M = 13 (space) = 00 T = 20 H = 08 Y = 25 (space) = 00 I = 09 S = 19 (space) = 00 Q = 17 U = 21 E = 05 (space) = 00 O = 15 F = 06 (space) = 00 M = 13 A = 01 T = 20 H = 08

Now, we can encrypt each numerical value using the RSA algorithm with the key (n, k) = (1643, 223). The encryption formula for RSA is:

Ciphertext = Plaintext^k mod n

Let's calculate the ciphertext for each numerical value:

Encrypted values: C1 = 14^223 mod 1643 C2 = 21^223 mod 1643 C3 = 13^223 mod 1643 C4 = 00^223 mod 1643 C5 = 20^223 mod 1643 C6 = 08^223 mod 1643 C7 = 25^223 mod 1643 C8 = 00^223 mod 1643 C9 = 09^223 mod 1643 C10 = 19^223 mod 1643 C11 = 00^223 mod 1643 C12 = 17^223 mod 1643 C13 = 21^223 mod 1643 C14 = 05^223 mod 1643 C15 = 00^223 mod 1643 C16 = 15^223 mod 1643