For a certain Hill Cipher the Encryption Matrix is [[17 17 5] [21 18 21] [2 2 19]]. The Plaintext is orb. The corresponding Cipher text will be

To solve this, we first need to convert the plaintext "orb" into numerical equivalents. In the English alphabet, "o" is 15, "r" is 18, and "b" is 2. So, our plaintext vector is [15, 18, 2].

Next, we multiply the encryption matrix by the plaintext vector. This is done as follows:

For the first element of the ciphertext vector: (1715) + (1718) + (5*2) = 697

For the second element of the ciphertext vector: (2115) + (1818) + (21*2) = 849

For the third element of the ciphertext vector: (215) + (218) + (19*2) = 98

So, the resulting vector is [697, 849, 98].

However, we need to reduce these numbers modulo 26 (the number of letters in the English alphabet) to get a valid ciphertext.

So, the final ciphertext vector is [697 mod 26, 849 mod 26, 98 mod 26] = [9, 15, 20].

Finally, we convert these numbers back into letters. "9" corresponds to "j", "15" corresponds to "p", and "20" corresponds to "t".

So, the ciphertext for the plaintext "orb" with the given encryption matrix is "jpt".

To solve this, we first need to convert the plaintext into numerical form. In the English alphabet, 'o' is 15, 'r' is 18, and 'b' is 2. So, our plaintext vector is [15, 18, 2].

Next, we multiply the encryption matrix by the plaintext vector.

[[17 17 5] * [15] [21 18 21] [18] [2 2 19]] [2]]

This gives us:

[1715 + 1718 + 52, 2115 + 1818 + 212, 215 + 218 + 19*2]

Which simplifies to:

[621, 846, 98]

However, we need to take these results modulo 26 (the number of letters in the English alphabet) to get our encrypted text.

[621 mod 26, 846 mod 26, 98 mod 26] = [23, 14, 20]

Finally, we convert these numbers back into letters. 23 is 'x', 14 is 'o', and 20 is 't'. So, the ciphertext for 'orb' using the given Hill Cipher is 'xot'.

To solve this, we first need to convert the plaintext "orb" into numerical equivalents. We do this by assigning a=0, b=1, c=2, ..., z=25. So, "orb" becomes [14, 17, 1].

Next, we multiply the encryption matrix with the numerical equivalents of the plaintext. This is done as follows:

[[17 17 5] * [14] [21 18 21] [17] [2 2 19]] [1]]

This results in a new matrix:

[391] [618] [40]

However, we need to take these results modulo 26 (the number of letters in the alphabet) to get our final encrypted letters.

391 mod 26 = 15 618 mod 26 = 24 40 mod 26 = 14

So, the numerical equivalents of our encrypted text are [15, 24, 14].

Finally, we convert these back into letters (using the same a=0, b=1, c=2, ..., z=25 assignments), giving us "pyn" as the ciphertext.