Suppose that users Alice and Bob carry out the 3- pass Diffie-Hellman protocol with p = 101. Suppose that Alice chooses a1 = 19 and Bob chooses b1 = 13. If Alice wants to send the secret message m=5 to Bob, show all the messages exchanged between Alice and Bob
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- Alice sends to Bob two messages m1 and m2 encrypted with a one time pad. The cipher text for both messages mt and m2 are the same, namely c. Bob receives the cipher text c two times. Eve also intercepts c two times. Which of the following is true? O Eve concludes that k1=k2. O Eve concludes that m1-m2. OEve concludes that Bob will not be able to tell the difference. O Eve cannot conclude anything.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.Alice wants Bob (the Bank) to sign a cheque, c. She has Bob's public key e and modulus N, and chooses a random number r such that gcd(r,N) = 1. She computes re (mod N) and then multiplies the cheque, c, by this number (mod N) and sends the resulting message off to Bob to be signed. When she receives his reply, m, what should she do with it to produce the signed cheque? Select one: a. Divide the reply, m, by rd. b. Divide the reply, m, by r. c. Divide the reply, m, by re. d. Nothing - the reply is the signed cheque
- Alice wants Bob (the Bank) to sign a cheque, c. She has Bob's public key e and modulus N, and chooses a random number r such that gcd(r,N) = 1. She computes re (mod N) and then multiplies the cheque, c, by this number (mod N) and sends the resulting message off to Bob to be signed. When she receives his reply, m, what should she do with it to produce the signed cheque? Select one: a. Divide the reply, m, by rd. b. Divide the reply, m, by r. c. Divide the reply, m, by re. No - that won't do it. d. Nothing - the reply is the signed chequeMsg3. B→A : B, N1, Ks, Message2, h(B, N1, Message2) Whereas: h(m) represents the digest of the message (m). {m}{K} represents the encryption of message (m) using the key (K) PK is public key N1 is a random number. 1. What are the main problems in Msg3?In the Diffie-Hellman Protocol, each participant selects a secret number x and sends the other participant αx mod q for some public number α. What would happen if the participants sent each other αx for some public number αinstead? Give at least one method Alice and Bob could use for agreeing on a key. Can Eve break your system without finding the secret numbers? Can Eve find the secret numbers? In TLS, why is there a separate Change Cipher Spec Protocol, rather than including a change_cipher_spec message in the Handshake Protocol?
- Alice and Bob has designed an RSA algorithm based on n = 152416431947009. Bob chooses the public key eB = 11. (a) Find the private key dB of Bob so that 0 < dB. Justify each step. (b) What should Alice do to send the message 123456789 to Bob? What message Bob receives? (c) What should Bob do to decrypt the message he receives from Alice? Please solve all partMany forms of cryptography are based on the following discrete log problem. Choose a cyclic group G (produced by one generator g) with finitely many elements. Alice and Bob want to set up a secret communication and need a secret key for that, which becomes a group element from G. They set up the following exchange (the so-called Diffie-Hellman protocol): 1. Alice chooses a secret group element a and sends unsecured g^a to Bob 2.Bob chooses a secret group element b and sends unsecured g^b to Alice 3. Alice calculates (g^b )^a and keeps this group element secret 4.Bob calculates (g^a )^b and keeps this group element secret Since a cyclic group is abelian, Alice and Bob now share the secret key (g^b )^a=(g^a )^b. The blue group elements are publicly known, the red elements are secret. The discrete log problem presented to an eavesdropper is computing say a from the publicly known data G,g,g^a. The naming of the problem comes from the solution a= glog(ga ) which is generally difficult to…Bob sent Alice an encrypted message. The message consists of 3 words. In each word, Bob encoded the letters as follows: A = 01, B = 02, C = 03, ., Z = 26. The he wrote the codes next to each other to form a number that represent the word. For example, the word "WE" is encoded as: 2305 since it consists of 2 letters W=23 and E=05. After encoding, Bob encrypted each encoded word with RSA using Alice public key(pq, e) where p=100000007, q=10000019, e=13. Alice received the following 3 encrypted words from Bob: 451095483713115 570203572152011 958266071840609 She used here RSA private key (d) to decrypt the message. The first word of the message that Bob sent was: WE. Q1. What is the private key d? (enter you answer as an éxact number) ord) Q2. What is the second word of the message that Bob sent to Alice? (enter you answer as one Q3. What is the third word of the message that Bob sent to Alice? (enter you answer as one word)
- Can anyone please explain to me why we have such equations below in part b) and c)? They are the solutions to the questions, but I can't really understand why and how to get that. Many thanks. ==== QUESTION ==== In the Shamir secret sharing scheme, we distribute a secret among q different users as follows. If our secret is a message (m1, . . . , mk) from V (k, q) then, we encode it as a codeword of the Reed-Solomon RSk(q) and give one coordinate to each user. In this problem, we will use q = 7, k = 4 and the parity check matrix H4 below for RS4(7). H4 = [1 1 1 1 1 1 1, 0 1 2 3 4 5 6, 0 1 4 2 2 4 1] a) Write a generator matrix for RS4(7) b) A new secret is selected and user #1 receives share value 0, user #2 receives share value 6 and user #3 receives share value 1 and are collaborating to discover the new secret. Explain why they can’t recover the secret with only this information. c) Now, suppose users #1, #2 and #3 (as in the previous item) discover, in addition to the values of…A cryptography student has accidentally used the same keystream to encrypt two different messages, M1 and 0x7894c0d145 fd8536 and C2 = 0x faf61234a0e65dc2. We also M2. We know that the ciphertexts are C1 happen to know that M1 = Ox ƒ70bca4869ded9a5. a) What is M, 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. Hint: These are all 8 byte numbers and will fit in an unsigned long type on most systems.Bob sent Alice an encrypted message. The message consists of 3 words. In each word, Bob encoded the letters as follows: A = 01, B = 02, C = 03, ..., Z = 26. The he wrote the codes next to each other to form a number that represent the word. For example, the word "WE" is encoded as: 2305 since it consists of 2 letters W=23 and E=05. After encoding, Bob encrypted each encoded word with RSA using Alice public key(pq, e) where p=100000007, q=10000019, e=13. Alice received the following 3 encrypted words from Bob: 451095483713115 570203572152011 762324289903198 She used here RSA private key (d) to decrypt the message. The first word of the message that Bob sent was: WE.