1. The message forwarded to a user with public key (47, 5, 10) and private key k = 19 ptosystem and SI (b) Indicate how the ciphertext can be decrypted using the recipient's private ke
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A: Solution :
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- Let M be the message to be sent by using RSA cryptosystem. If (n, e) is the public key and (n, d) is the private key, which of the following is the encryption function that will yield the cipher text that corresponds to M? О Е(M) — Ме mod (p - 1) (q — 1) О Е[M) — ма mod (p - 1)(q — 1) O E(M) = Me mod n О ЕМ) — Ма mod nUse symmetric ciphers to encrypt message "“promise" and decrypt message "FOG". The representation of characters in modulo 26 is described as follows: Plaintext - a bcdefg|hijk1 mnopar stuvwx y z Ciphertext A BCD|EFG|HIJKL|M|NO|P|Q|R s T|U|VwxY|Z Value 00 01 02|03 04 05 06|07|08|09|10|11 12|13|14|15 16|17 18|19 20 21 22 23 24 25 The mathematical equations for encryption and decryption can be described as follows: Encryption Ea:i→i+kmod 26 Decryption Da : i→i-k mod 26 i represents the messages (plaintext or cipher), k represents a symmetric key. In this case k=20Alice sets up an RSA public/private key, but instead of using two primes, she chooses three primes p, q, and r and she uses n=pqr as her RSA-style modulus. She chooses an encryption exponent e and calculates a decryption exponent d. Encryption and Decryption are defined: C ≡ me mod n and m ≡ Cd mod n where C is the ciphertext corresponding to the message m. Decryption: de ≡ 1 mod φ(n) | Let p = 5, q = 7, r = 3, e = 11, and the decryption exponent d = -13. n = 105 & φ(n) = 48 Q: Alice upgrades to three primes that are each 200 digits long. How many digits does n have?
- IH A cryptography student has accidentally used the same keystream to encrypt two different messages, M1 and M2. We know that the ciphertexts are C¡ = 0x2e38ac20ƒe51b68c and C2 = 0x638cd0bla9114b4d. We also happen to know that M1 = 0x2b1d510e6a67ae98. a) What is M2 in hexadecimal? Please give your answer a leading Ox and use lowercase letters only. b) What is the keystream? Please give your answer a leading Ox and use lowercase letters only.] You receive a message that was encrypted using the RSA system with public key (43, 143), where 43 is the public exponent. A message encrypted using this cryptosystem was captured by an enemy and consisted of the following numbers: 6 82 132 115. Can you decipher what was the original message? (Hint: As a first step, you need to find p and q.)In an RSA system, the public key (n,e) of a given user is (323, 11). 1. What is the value of the exponent in the private key (n, d), of this user? 2. Suppose you want to send this user the message m = 45, write down the expression to generate the ciphertext for this message. 3. Suppose that your ciphertext, c, is 5, write down the expression to generate the plaintext matching this ciphertext. 4. Can you encrypt the message m=322 with this public key? O a. Yes O b. No
- Suppose the two prime numbers p = 23 and q = 37 are used for an RSA encryption scheme. What are the values of the connection key n, the encryption e and the decryption key d, given that d < e? e = d =suppose, RHT and NAT are using the RSA algorithm for PUBLIC-KEY CRYPTOGRAPHY Having chosen 3 and 11 to be the initial prime numbers p and q along with 3 and 7 to be the integers e and d, RHT encrypts and sends the message "H" to NAT. * What are the private and the public keys for RHT? * Determine what NAT receives. *Determine the message after NAT decrypts it. In this problem, all the symbols have their usual meaning.Two aspirants talking to each other use the RSA algorithm to encrypt their messages. They encrypt the message character by character. The value of p, q and d are 5, 17 and 13 respectively, where p, q and d are their integers having usual meaning in the RSA algorithm. Identify the sum of integers in cipher text for corresponding characters in plain text: "IIT". Assume that corresponding cipher characters are placed in their corresponding plain text character places. Also each character is converted to ASCII value before applying RSA (ASCII value of A, B, C.... and so on are 1, 2, 3,..., respectively).
- A symmetric block encryption algorithm is shown below. 16-bit blocks of plaintext P are encrypted using a 32-bit key. Encryption is defined as: C = (P EX_OR Ko) + K1 C is the ciphertext, K is the secret key, Ko is the leftmost 16 bits of K, K1 is the rightmost 16 bits of K, EX_OR is bitwise exclusive OR, and + is binary addition. a. The ciphertext C must be the same size as the plaintext P, that is, it must not be larger than 16 bits. How can this be achieved? b. Show the decryption equation. How will the encrypted message be decrypted?Answer ALL questions. The ciphertext message below was encrypted using affine transformation C = P + k(mod 26),0 ≤ C ≤ 25. YFXMP CESPZC JTDBF PPYZQX LESPX LETND a) By completing the following table, find the most frequently occurring letter in the ciphertext. Letter Number of Occurrence Question (b) is based on the information in tables below and answer in Question (a). A B C 1 2 3 Numerical 0 equivalent Frequency 7 (in %) Letter Numenical equivalent Frequency 8 (in %) N 13 ABCD E FGHIJKLMNOPQRSTUVWXYZ 1 0 14 7 P 15 3 D 4 Q 16 <1 E 13 13 R 17 8 F 5 3 S 18 6 G 2 T 19 9 H L 3 U 20 3 8 V 21 1 JK 9 <1 W 22 10 <1 LM <1 11 4 X Y 23 24 2 12 3 Z 25 <1 The tables show that the most frequently occurring letters in English text are E, T, N, R, I, O and A, with E occurring substantially more than the other letters. b) Determine what is the letter that represents C and P in affine transformation C = P + k(mod 26),0 ≤ C≤ 25. Then, show that the value of k = 11(mod 26). c) What is the plaintext…On Groundhog Day, the groundhog randomly chooses and sends one of two possible messages: m0 = SIXMOREWEEKSOFWINTER m1 = SPRINGARRIVESINMARCH. To add to the mystery, the groundhog encrypts the message using one of the following methods: shift cipher, Vigenère cipher with key length 4 (using four distinct shifts), one-time pad. For each of the following ciphertexts, determine which encryption methods could have produced that ciphertext, and for each of these possible encryption methods, decrypt the message or explain why it is impossible to decrypt. a. ABCDEFGHIJKLMNOPQRST b. UKZOQTGYGGMUQHYKPVGT c. UQUMPHDVTJYIUJQQCSFL.