The parent Rubidium87 has a halflife of 50 billion years .pdf

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The parent Rubidium-87 has a half-life of 50 billion years. The daughter Strontium-87 increases as expected. Draw a graph to show the decrease in the parent isotope and the increase in the daughter product. Draw the graph on a blank piece of paper, take a picture of it and submit the picture here. Remember all graphs have both axis labeled and the points along the axis are reasonably proportional..

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The program below is written in C++ language using an Object Oriented Programming (OOP) style. The following tasks are to be performed by you with respect to this code: Your Tasks (Creativity is very important): (i) Working on the code line-by-line, if possible, study the entire code and describe the purpose of each instruction on each line. (ii) Using Visual Studio C++, copy this code into the editor and run/compile the code by complete the required inputs..

The program below is written in C++ language using an Object.pdf

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The protocol will use the following building blocks. The Inner Product Prediction Challenge for RSA. Recall that the RSA based cryptographic constructions involve a composite integer NN where N=pq for large primes p,qN. Additionally, a public exponent e is chosen along with N, whereas the secret exponent d satisfies de =1mod(p1)(q1) and is known by only one of the two players. Recall that de=1mod(p1)(q1) ensures xed=xmodN, whereas given (N,e), recovering d is as hard as factoring N. In the protocol below we will write (N,e,d)RSA.Gen() to indicate that (N,e,d) are generated as above. Finally, recall that the RSA assumption assumes that when (N,e,d)RSA .Gen () and xZN is drawn, one cannot output x if given (N,e,y) where y=xe (of course if one is given (N,e,d,y) then one can simply compute x=yd ). In homework 6 1, problem 3 we saw the following "inner product prediction" version of the RSA game: given (N,e,y,r) where (N,e,d)RSA. Gen(),xZN,y=xe and r{0,1}n where n=log(N), output x,r. We showed that any adversary who can win the inner product prediction game for RSA with probability 1/2+ for non-negligible >0 can be used to build (via the techniques of Goldreich-Levin) another adversary who can break the RSA assumption with non-negligible probability. Blum's Commitment Scheme. The protocol below will use Blum's non-interactive commitment scheme as a building block. While Blum's scheme allows Alice to commit to a single bit, Alice can commit to an n-bit string by committing independently to each bit. For an n-bit string u{0,1}n, we write (z,k)Com(u) to indicate that z and k are respectively the collections of commitment and decommitment strings when Blum's scheme is used to commit to each bit of x. Recall binding says that for any z, there is at most one k such that the decommitment procedure succeeds when run with input (z,k). Recall the hiding game for this commitment scheme is played between a challenger C and adversary A as follows. - A sends (u0, u1) to C where u0,u1{0,1}n; - C draws b{0,1} and (z,k)Com(ub) and sends z to A; - A sends b{0,1} to C signaling the end of the game; A wins if b=b. Hiding security demands that no efficient adversary can win this hiding game except with probability 1/2+ for negligible >0.Zero-Knowledge Proofs. Our OT protocol will use a ZK proof system as a key building block for one of the parties to prove to the other that a particular quantity in the protocol has been computed correctly. As a simple example to help understand the role that the ZK proof plays, imagine that early on in the protocol, A sends z to B where (z,k)Com(0). Then while z is supposed to be a commitment to 0 , hiding says that B cannot actually tell what value is hidden inside, so it is possible that an adversarial A might have actually drawn (z,k)Com(1). In this case, it might be useful to have A prove to B using a ZK proof that in fact z is a commitment to 0 . For this to work, the statement is " zL " where membership in L holds whenever ther.

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