Alice and Bob use the ElGamal scheme with a common prime q= 131 and a primitive root a = 6. Let Bob's public key be YB = 3. W
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- Alice and Bob use the ElGamal scheme with a common prime q=131 and a primitive root a=6. Let Bob's public key be Yn= 3. A. What is the ciphertext of M=9 if Alice chooses the random integer k=4? B. If Alice uses the same k to encrypt two messages M₁ and M₂ as (12, 65) and (12, 64), what is the relation between M₁ and M₂?Alice and Bob use the ElGamal scheme with a common prime q=131 and a primitive root a=6. Let Bob's public key be Yn=3. A. What is the ciphertext of M-9 if Alice chooses the random integer k=4? B. If Alice uses the same k to encrypt two messages M₁ and M₂ as (12, 65) and (12, 64), what is the relation between M₁ and M₂?Let's assume that Bob and Alice share a secret key in a symmetric key system. Bob wishes tobegin a conversation with Alice, and sends her a message that essentially says "let's talk". Aliceis suspicious that the person contacting her might not be Bob, so Alice generates a single-userandom number (a nonce) and sends it to Bob. Bob encrypts the nonce with the secret key heshares with Alice and sends it back. Alice decrypts this message and retrieves the same nonceshe sent to Bob. Which of the following is true, provided the secret key K has not been compromised?
- Alice 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?The Lingala Language of Republic of Congo has 35 letters. Consider an Affine cipher, which encrypts each letter according to the rule: C=(p×k1+k2) mod 35. Here C, p, k1, and k2 are each members in the range 0 to 34, where C represents the ciphertext letter, p the plaintext letter, and k1 and k2 are constant keys. How many possible keys does this affine system have? Explain in details.Suppose that Alice and Bob communicate using ElGamal cipher and f (p. 9. Z) is common public values. Bob generates his private key d ER Z and then computes the corresponding and public public key y=g" (mod p). To save time, Bob uses the same number r each time he encrypts a plaintext message m (ie., r is a fixed nonce of Bob, and it is not randomly generated each time encryption is performed). Assume that Alice compute the ciphertext for the message m as (cc) = (g mod p, mxy mod p). and for the message m as (1,2)=(g" mod p, xy' mod p). Show how an adversary who possesses a plaintext-ciphertext pair (m. (c.ca)) can decrypt (1, 2) without knowing the private key d of Bob.
- 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 nData Encryptions and Cryptography Suppose Conny and Shelby apply ElGamal scheme with a common prime q = 71 and a primitive root a = 7. If Conny has public key Yp = 3 and Shelby choose the random integer k = 2, what is the ciphertext of M = 30? If Shelby now chooses a different value of k so that the encoding of M = 30 is C = (59, C2), what is the integer C2 ?Bob's public key is (55,3). Alice wants to send Bob the "message" 6. What is the cyphertext (encrypted version) of her message in the RSA cryptosystem? (Show the arithmetic, and you can use a calculator.)
- Alice uses RSA to send a key to Bob for use in encryption of future messages. The key is the word "CINEMA" and the encoding from letters to numbers is done using the ASCII: A = 65... Z = 90, space = 99. The public parameters (n, e) = (9379, 11) are shared. Encrypt Alice's key word, using 2-letter blocks. Please show work.Let Π = (Gen,Enc,Dec) be a private-key encryption scheme that has indistinguishable en- cryptions in the presence of an eavesdropper. Which of the following encryption schemes are also necessarily secure against an eavesdropper? If you think a scheme is secure, sketch a proof, if not, provide a counterexample. Here, for a bit string s, parity(s) is 1 if the number of 1’s in s is odd, and 0 otherwise. The || symbol stands for concatenation. So, for strings if x = 00 and y = 11, x||y = 0011. (a) Enc1k(m) = 0||Enck(m)(b) Enc2k(m) = Enck(m)||parity(m) (c) Enc3k(m) = Enck(m)||Enck(m)(d) Enc4k(m) = Enck(m)||Enck(m + 1). Here think of m as an integer. Please type answer note write by hend.Let Π = (Gen,Enc,Dec) be a private-key encryption scheme that has indistinguishable en- cryptions in the presence of an eavesdropper. Which of the following encryption schemes are also necessarily secure against an eavesdropper? If you think a scheme is secure, sketch a proof, if not, provide a counterexample. Here, for a bit string s, parity(s) is 1 if the number of 1’s in s is odd, and 0 otherwise. The || symbol stands for concatenation. So, for strings if x = 00 and y = 11, x||y = 0011. (a) Enc1k(m) = 0||Enck(m) (b) Enc2k(m) = Enck(m)||parity(m) (c) Enc3k(m) = Enck(m)||Enck(m) (d) Enc4k(m) = Enck(m)||Enck(m + 1). Here think of m as an integer. (a) Enc1k(m) = 0||Enck(m)(b) Enc2k(m) = Enck(m)||parity(m) (c) Enc3k(m) = Enck(m)||Enck(m)(d) Enc4k(m) = Enck(m)||Enck(m + 1). Here think of m as an integer.