Part I: Basic (Shorter) Problems (a) Compute the Entropy for the set {SPAM, SPAM, HAM, SPAM, SPAM, HAM} (b) What is the Gini index for the set of part (a)?
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- The set of letters S consists of 30 As, 6 Bs, 24 Cs, 15 Ds, and 15 Es. The set of letters T consists of 25 As, 20 Bs, 15 Cs, 5 Ds and 35 Es. What is the mutual index of coincidence between sets S and T? Leave your answer as a fraction in lowest termsMany 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…Why does PGP generate a signature before applying compression? How does PGP use the concept of trust? Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root α = 2. Show that 2 is a primitive root of 11. If user A has public key YA = 9, what is A’s private key XA? If user B has public key YB = 3, what is the secret key K shared with A?
- Consider a Diffie-Hellman scheme with a common prime q = 17 and a primitive root α = 3. a) If user A has a private key XA=4, what is A’s public key, YA? b) A sends YA to B. If B has a private key XB=6, what is the shared secret key, K that B can calculate and share with A? c) If B computes YB and sends it to A, what is the shared secret Key, K computed by A?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.Consider a Diffie-Hellman scheme with a common prime q = 23 and a generator g = 5. Bob has public key PUB(B) = 8, what is the shared secret key K?
- Discuss the trade-off between fairness and throughput of operations in the readers-writers problem. Propose a method for solving the readers-writers problem without causing starvation.Suppose (X[mX]+Y [mY ]) > 0. What can you infer about each of the four subproblems (namely, (X1, Y1), (X1, Y2), (X2, Y1), and (X2, Y2))? Clearly identify the ones that do not have to solved anymore, and those that still have to be solved. Briefly justify.Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root α = 2. Show that 2 is a primitive root of 11. If user A has public key YA = 9, what is A’s private key XA? If user B has public key YB = 3, what is the secret key K shared with A?
- 29. Banker's algorithm deals with a. deadlock prevention b. deadlock avoidance c. deadlock recovery d. mutual exclusion7. For each of the following relations on the set of all real numbers, determine whether it isreflexive, symmetric, antisymmetric, transitive. Here xRy if and only if:(a) x + 2y = 0 (b) x = 2y(c) x − y is a rational number (d) xy = 0(e) xy ≥ 0 (f) x = 1 or y = 1 (f) x = 1 or y = 1(g)x is a multiple of y (h) xy = 1 PS:Please help me by doing all the subparts as it is connected correctly on a word processing document.Is (p ∨ ¨q) ⊕ ¨ (q ∧ p) a tautology, contradiction or contingency?