What are the probabilities of outcomes 0 and 1 if the first qubit of |i is measured?
Question:
What are the probabilities of outcomes 0 and 1 if the first qubit of |i is measured? (ii) What are the probabilities of outcomes 0 and 1 if the second qubit of |i is measured? (iii) What is the state of the system after the first qubit of |i is measured to be a 0? (iv) What is the state of the system if the second qubit of |i is measured to be a 1? (v) What are the probabilities of outcomes 0 and 1 if the second qubit of the system is measured, after the first qubit of |i has been measured to be 0? (vi) What are the probabilities of outcomes 0 and 1 if the first qubit of the system is measured, after the second qubit of |i has been measured to be 1? [2 marks each]
Sketch a circuit for implementing the operator F2 using any combination of 1-qubit Hadamard gates; 1-qubit Pauli gates; 2-qubit C-NOT gates; controlled phase shifts and swap gates (the swap gate S is defined by S|xyi = |yxi). Briefly explain your circuit. [8 marks] 8 CST.2015.8.9 9 Security II You are working on an encryption device with your new colleague, Mallory Baish, who proposes that you use a pseudo-random generator ri = h1(si), si+1 = h2(si) where s0 G is the random initial state and the other si G are subsequent internal states, all invisible to adversaries. The h1, h2 : G G are two secure one-way functions. Adversaries may see any of the past outputs r0, . . . , rn1. If they can predict from those, with non-negligible probability, the next value rn, then the security of your device will be compromised. (a) Give a rough estimate for the probability that an adversary can predict rn, as a function of n and |G|. Explain your answer. [6 marks] (b) Mallory also suggests a specific implementation: h1(x) = f(u x mod p) p = a 2056-bit prime number h2(x) = f(v x mod p) u, v = two numbers from Z p f(x) = x mod 22048 G = Z2 2048 (i) The constants p, u and v will be known to the adversary. What conditions should they fulfill so that h1 and h2 can reasonably be described as one-way functions, and how would you normally generate suitable numbers u and v? [Hint: quadratic residues] [4 marks] (ii) If f were replaced with the identity function, how could an adversary distinguish the ri emerging from this pseudo-random generator from a sequence of elements of Z p picked uniformly at random? [4 marks] (iii) After you choose a value for p, Mallory urges you to use two particular values for u and v generated in your absence. You briefly see "v = u e mod p" scribbled on a whiteboard. You become suspicious that Mallory is trying to plant a secret backdoor into your pseudo-random generator. Explain how Mallory could exploit such a backdoor.
Write java program to read a last name. Print the number of characters in the name and also the number of vowels in the name. a java program to read in a 32-bit pattern and translate to a IEEE-754 floating point number. Be sure to look for infinity, -infinity, zero and NaN patterns
(a) Explain what factors limit the complexity and performance of an SoC at the heart of a portable electronic device. [4 marks] (b) Compare and contrast the use of hardware and software to implement a compute-intensive algorithm on an SoC, such as data encryption. Include customised processors and co-processors in your analysis. [5 marks] (c) (i) Define the term fully-pipelined with respect to a hardware component. [2 marks] (ii) Describe and compare three designs for a fixed or floating-point multiplier that vary in performance: one at least should be fully pipelined. [6 marks] (iii) Define the term structural hazard and explain why these can affect system performance. Which of your designs from part(c)(ii) might present such a hazard and why? [3 marks] 11 Topical Issues (a) Compare and contrast the radio channels used by Bluetooth Low Energy (BLE) and WiFi in the 2.4 GHz ISM radio band. Explain why BLE uses only three channels for advertisements and how the three were selected. [6 marks] (b) Consider a wireless mouse computer peripheral. Analyse the use of WiFi, BLE and a proprietary radio system for communication with the computer, giving advantages and disadvantages for each. [10 marks] (c) Bluetooth 4.0 specifies a per-packet Cyclic Redundancy Check (CRC) to protect each 31-octet BLE packet as a whole. In contrast the longer WiFi packets contain a separate CRC for each of the packet header and the packet payload. When Bluetooth 4.1 introduced longer BLE packets, it retained a single CRC for the entire packet. What are the consequences of this decision? [4 marks] 10 CST.2015.8.11 12 Topics in Concurrency This question is on an authentication protocol using a key server and symmetric keys. Key(X, Y ) represents the symmetric key used to encrypt messages sent by X to Y , and symbols K and K0 are used as variables over keys. SPL terms representing a key server S, an initiator A and responder B are: S = !(in {X, Y }Key(X,S) . out {Key(X, Y ), Key(Y, X), Y }Key(S,X)) A = out {A, B}Key(A,S) . in {K, K0 , B}Key(S,A) . out {m}K. in {m, m}K0 B = out {B, A}Key(B,S) . in {K0 , K, A}Key(S,B) . in {}K. out {, }K0 (a) (i) The capabilities assumed of an attacker when public-key cryptography is used for authentication, as when studying the Needham-Schroder-Lowe protocol, are that it can pair messages, split paired messages, encrypt messages under a public key and decrypt messages under a public key if it has access to the private key. Give four SPL processes Spy1 , . . . , Spy4 representing these capabilities. [4 marks] (ii) Give a further two processes Spy5 , Spy6 representing the capability of an attacker to encrypt and decrypt messages when symmetric-key cryptography is used. [2 marks] (b) Let PSpy =!(f i{1,...,6} Spyi ). Draw the events of the Petri net for PSpy k S k A k B. For PSpy, only show those from Spy5 and Spy6
Business Analytics Communicating With Numbers
ISBN: 9781260785005
1st Edition
Authors: Sanjiv Jaggia, Alison Kelly, Kevin Lertwachara, Leida Chen