6. (a) Encipher the message HAPPY DAYS ARE HERE using the autokey cipher with seed Q. (b) Decipher the message BBOT XWBZ AWUVGK, which was produced by the autokey cipher with seed RX.

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Question 6

208
ELEMENTARY NUMBER THEORY
4. In a lengthy ciphertext message, sent using a linear cipher C = a P + b (mod 26), the
most frequently occurring letter is Q and the second most frequent is J.
(a) Break the cipher by determining the values of a and b.
[Hint: The most often used letter in English text is E, followed by T.]
(b) Write out the plaintext for the intercepted message WCPQ JZQO MX.
5. (a) Encipher the message HAVE A NICE TRIP using a Vigenère cipher with the keyword
MATH.
(b) The ciphertext BS FMX KFSGR JAPWL is known to have resulted from a Vigenère
cipher whose keyword is YES. Obtain the deciphering congruences and read the
message.
6. (a) Encipher the message HAPPY DAYS ARE HERE using the autokey cipher with
seed Q.
(b) Decipher the message BBOT XWBZ AWUVGK, which was produced by the autokey
cipher with seed RX.
7. (a) Use the Hill cipher
C1 = 5P1 + 2P2 (mod 26)
biopje
C2 = 3P¡ +4 P2 (mod 26)
to encipher the message GIVE THÊM TIME.
(b) The ciphertext ALXWU VADCOJO has been enciphered with the cipher
C1 = 4P1+11P2 (mod 26)
bo
Geft
-130
C2 = 3P1 + 8 P2 (mod 26)
Derive the plaintext.
8. A long string of ciphertext resulting from a Hill cipher
C1 = lc
a P1 + b P2 (mod 26)
our beuog
C2 = cP1+d P2 (mod 26)
coveeled that the most frequently occurring two-letter bl0cks were HO and PP, in that
order.
(a) Find the values of a, b, c, and d.
THint: The most common two0-letter biocks in the English language are TH, followed
(b) What is the plaintext for the intercepted meson
Transcribed Image Text:208 ELEMENTARY NUMBER THEORY 4. In a lengthy ciphertext message, sent using a linear cipher C = a P + b (mod 26), the most frequently occurring letter is Q and the second most frequent is J. (a) Break the cipher by determining the values of a and b. [Hint: The most often used letter in English text is E, followed by T.] (b) Write out the plaintext for the intercepted message WCPQ JZQO MX. 5. (a) Encipher the message HAVE A NICE TRIP using a Vigenère cipher with the keyword MATH. (b) The ciphertext BS FMX KFSGR JAPWL is known to have resulted from a Vigenère cipher whose keyword is YES. Obtain the deciphering congruences and read the message. 6. (a) Encipher the message HAPPY DAYS ARE HERE using the autokey cipher with seed Q. (b) Decipher the message BBOT XWBZ AWUVGK, which was produced by the autokey cipher with seed RX. 7. (a) Use the Hill cipher C1 = 5P1 + 2P2 (mod 26) biopje C2 = 3P¡ +4 P2 (mod 26) to encipher the message GIVE THÊM TIME. (b) The ciphertext ALXWU VADCOJO has been enciphered with the cipher C1 = 4P1+11P2 (mod 26) bo Geft -130 C2 = 3P1 + 8 P2 (mod 26) Derive the plaintext. 8. A long string of ciphertext resulting from a Hill cipher C1 = lc a P1 + b P2 (mod 26) our beuog C2 = cP1+d P2 (mod 26) coveeled that the most frequently occurring two-letter bl0cks were HO and PP, in that order. (a) Find the values of a, b, c, and d. THint: The most common two0-letter biocks in the English language are TH, followed (b) What is the plaintext for the intercepted meson
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