1) Decrypt the ciphertext message LFDPH LVDZL FRQTX HUHG, which has been encryptedusing the Caesar cipher.
2) Encrypt the message THE RIGHT CHOICE using the affine transformation C ≡ 15P + 14 (mod 26).
3) Decrypt the message RTOLK TOIK, which was encrypted using the affine transformation C ≡ 3P + 24 (mod 26).
4) The message KYVMR CLVFW KYVBV PZJJV MVEKV VE was encrypted using a shift transformation C ≡ P + k (mod 26). Use frequencies of letters to determine the value of k. What is the plaintext message?
5) If the two most common letters in a long ciphertext, encrypted by an affine transformation C ≡ aP+ b (mod 26), are X and Q, respectively, then what are the most likely values for a and b?
6) Find the product cipher obtained by using the transformation C ≡ aP+ b (mod 26) followed by the transformation C ≡ cP+ d (mod 26), where (a, 26) = (c, 26) = 1.
7) Decrypt the following message, which was enciphered using the Vigen'ere cipher with encrypting key SECRET: WBRCS LAZGJ MGKMF V.
8) Cryptanalyze the given ciphertext, which was encrypted using a Vigen'ere cipher.
S I I WZ F D I B N H U D E U WQ J H P J K R N K
R L A C T WX B I M MHM P J O F U F P WV E O G
P Q P E L V P Z Y D A X I A G P I TMA X F S SS
GWP BW I WO F OT FWV F J S X P L B J O T P
S U D I J J X F N R F P A F G R P S X I WX J O R
P P X S Q I
11) Explain how you would go about decrypting a message that was encrypted in blocks of length two using an affine transformation C ≡ AP + B (mod 26), where A is a 2 × 2 matrix with integer entries and (detA, 26) = 1, and B is a 2 × 1 matrix with integer entries.
12) Using the prime p = 2621and encryption key e = 7, encrypt the message SWEET DREAMS using modular exponentiation.
13) What is the plaintext message that corresponds to the ciphertext 1213 0902 0539 1208 1234 1103 1374 that is produced using modular exponentiation with modulus p = 2591 and encryption key e = 13?
14) Find the primes p and q if n = pq= 4,386,607 and φ(n) = 4,382,136.
15) Explain why we should not choose primes p and q that are too close together to form the encrypting exponent n in the RSA cryptosystem. In particular, show that using a pair of twin primes for p and q would be disastrous. (Hint: Recall Fermat's factorization method.)
16) Encrypt the message BUY NOW using the knapsack cipher based on the sequence obtained from the super-increasing sequence (17, 19, 37, 81, 160), by performing modular multiplication with multiplier w = 29 and modulus m = 331.
17) Find the sequence obtained by applying successively the modular multiplications with multipliers and moduli (7,92), (11,95), and (6,101), respectively, on the super-increasing sequence (3, 4, 8, 17, 33, 67).
18) Using the Diffie-Hellman key agreement protocol, find the common key that can be used by two parties with keys k1= 7 and k2= 8 when the modulus is p = 53 and the base isr = 2.
19) Romeo and Juliet have as their RSA keys (5, 19 ·67) and (3, 11 ·71), respectively.
a) Using the method in the text, what is the signed ciphertext message sent by Romeo to
Juliet when the plaintext message is GOODBYE SWEET LOVE?
b) Using the method in the text, what is the signed ciphertext message sent by Juliet to Romeo when the plaintext message is ADIEU FOREVER?
20) Decrypt the ciphertext message UW DM NK QB EK, which was encrypted using the digraphic cipher that sends the plaintext block P1P2into the ciphertext block C1C2, with
C1≡ 23P1+ 3P2 (mod 26)
C2≡ 10P1+ 25P2 (mod 26).