Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2)
To decrypt the given ciphertext "CBBGYAEBBFZCFEPXYAEBB" using the Affine Cipher with key \((7,2)\), we follow these steps: ### Step 1: Understand the Affine Cipher The Affine Cipher encryption function is: \[ E(x) = (ax + b) \mod 26 \] ________ _____ ________ ___ __________.
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In this exercise, we introduce you to Hill cipher. In this cipher, we convert our message to numbers, just as in affine cipher. However, instead of encrypting character by character, we encrypt pairs of characters by multiplying them with an invertible matrix with co-efficients in .
Here is an example: Suppose we want to ENCRYPT "ALLISWELL". Since we require the plaintext to have even number of characters, we pad the message with the character ‘X’. We break up the message into pairs of characters AL, LI, SW, EL and LX. We convert each pair of characters into a pair elements in as follows:
Next, we choose an inveritble 2×2 matrix with coefficients in , for example,
This matrix has determinant and 5 is a unit in
with inverse
We write each pair of elements in
as a column vector and multiply it by A:
We then convert each pair of numbers to a pair of characters and write them down. In this example, we get the cipher text "LSPFYGXUEN" corresponding to the plain text "ALLWELL". To decrypt, we convert pairs of characters to pairs of numbers and multiply by
and we have
Decrypt the text "TWDXHUJLUENN" which was encrypted using the Hill’s cipher with the matrix as the encryption matrix
i) Bob uses ElGamal cyrptosystem with parameters p = 47, g = 5 and the secret value
x = 3. What values will he make public?
ii) Alice wants to send Bob the message M = 15. She chooses k = 5. How will she compute
the cipher text? What information does she send to Bob?
iii) Explain how Bob will decrypt the message.
Decrypt the message c = 23 that was encrypted using RSA algorithm with e = 43 and n = 77.
Solve the discrete logarithm problem (mod 47) using Baby-Step, Giant-Step algorithm.
Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2)
Find the inverse of 13 (mod 51) using extended euclidean algorithm
Another version of the columnar transposition cipher is the cipher using a key word. In this cipher, we encrypt as follows: Given a key word, we remove all the duplicate characters in the key word. For example, if the key word is ‘SECRET’, we remove the second ‘E’ and use ‘SECRT’ as the key word. To encrypt, we form a table as follows: In the first row, we write down the key word. In the following rows, we write the plaintext. Suppose we want to encrypt the text ‘ATTACKATDAWN’. We make a table as follows:
| S | E | C | R | T |
| A | T | T | A | C |
| K | A | T | D | A |
| W | N | X | X | X |