4. Suppose the prime p = DepRob want to use the Diffie-Hellman key agreement protocol to 251 and base s = 53 are published. Alice olects a number at random: a = 63. Bob also selects a number at random: 6 = 55. What is the key that they agree on?
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- Elgamal Signature Scheme: Given the following table describing the procedure for Alice to send a signed message with Elgamal signature to Bob, calculate the unknown entities and verify that Bob has received the correct message sent by Alice. Alice Bob Chooses p=23 Chooses a primitive element α=5 Choose a random integer d=4 Compute β = αd mod p = Public key is kpub = (p, α, β) = Private key is kpr = d = Send Public key kpub = (p, α, β) to Bob: Receives Alice’s public key kpub = (p, α, β)= Choose an ephemeral key KE = 7 Message to send is m=8 Computes signatures (s,r) for m r= αKE mod p = Compute KE-1 mod (p-1) s= (m-d*r)* KE-1 mod (p-1) = Send (m, (r,s)) to Bob: Receives (m, (r,s)) = Compute t = βr * rs mod p = Verifies if t = αm mod p =Suppose you and your friend would like to use Diffie-Hellman key exchange system to exchange a keyword. Both of you have decided to use the following p = 4138327577, q = 3742197127.If you decide b = 1767005, and your friend has picked a number a that you don’t know. But you havereceived q a mod p from your friend, and the number is 980246808. Find out the common shared key.Suppose Alice and Bob performs the Diffie-Hellman key exchange, using the public parameters with prime p=11 and primitive element α=2 . Alice chooses her secret x A =2 and Bob chooses his secret x B =8 . What does Alice send to Bob? (Enter only a number in the box.) What is the key that Bob and Alice agree on? (Enter only a number in the box.)
- You witness Alice and Bob agree on a secret key using the Diffie-Hellman key exchange. Alice andBob chose p = 97 and g = 5. Alice send Bob the number 3 and Bob sent Alice the number 7. Bruteforce crack their code: What is the secret key that Alice and Bob agreed upon? What were theirsecret keys?Question 15 For Questions 15.1 - 15.2 consider the following integers: In a RSA cryptosystem with public- key (3233, 59), compute: 15.1 the private-key and give you final answer as an ordered pair (n, d).Given the following Diffie-Hellman scheme, which of the sentences below is/are correct? Select all that apply. Alice to Bob - "I'm Alice", [gª mod plalice Bob to Alice - g mod p {.) is encryption with specified PUBLIC key. [. is encryption with specified PRIVATE key. Trudy can exchange a key between herself and Alice Trudy can share gabmod p with both parties O Trudy can exchange a key between herself and Bob Trudy cannot share any key with the two parties
- 6. In a Rivest, Shamir and Adleman (RSA) cryptosystem, a particular user uses two prime numbers P and Q to generate the public key and the private key. If P is 23 and Q is 29, using RSA algorithm, find the following: a) n b) Ø(n) c) e d) dAlice 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 chequeIn an RSA system, the public key of a given user is e = 65, n = 2881. What is the private key of this user? Hint: First use trial-and-error to determine p and q; then use the extended Euclidean algorithm to find the multiplicative inverse of 31 modulo n. Write it understandable.
- 1. Let (01, 02, 03,..., 026!} be the set of permutations of the alphabet A = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z}, and consider the simple substitution cryptosystem with ok = A B C D E F G H I J K L M X MTAK ZQB NO LES N O P Q R S T U V W X Y Z IF G R V JH CY UDP W and key k. (a) Compute C = e(AUBUR NUNIV ERSIT YATMO NTGOM ERY, k). (b) Compute M = d(NIZFV SXHNF IHBKF VPXIA KIHVF GP, k).Elliptic Curves: Let E5(0,1) be an elliptic curve defined over Z5. E5(0,1): y2 mod 5=x3+1 mod 5 Assume two people A and B want to exchange a secret key using Elliptic Curve Diffie-Hellman Key Exchange (ECDH) method. Given the two private key nA=3 and nB=2, please calculate the public keys PA and PB and the secret key K. NO SPAM!!! PLEASE SHOW PROCEDURES WITH CORRECT ANSWER!!!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 part