Describe the purpose of hash functions, message authentication codes and digital signatures, sketching a possible construction for each of them. [12 marks] A funds transfer system authenticates messages between its member banks by having the sending and receiving banks compute a MAC on each message using a key which each pair of correspondent banks in the system establishes monthly using public key techniques. The sending bank then computes a digital signature on the MAC using a long-term signing key. If the MAC is 32 bits long, is this arrangement more, or less, secure than signing a 128-bit hash of the message, and why? [5 marks] To what extent would matters be changed if all messages handled by the system were logged by a trusted third party?

The following shows simple context free grammar (CFG) for a fragment of English. S -> NP VP Adj -> angry Vbe -> is VP -> Vbe Adj Adj -> big N -> dog NP -> Det N Adj -> former N -> cat N -> Adj N P -> at Adj -> Adj PP P -> on PP -> P NP Det -> the (a) Show the parse tree that this grammar would assign to (1). (1) the dog is angry at the cat [3 marks] (b) One respect in which this grammar overgenerates is that some adjectives, including former, occur only before a noun (see (2)) and that PPs do not combine with adjectives occurring before a noun (see (3)). (2) * the dog is former (3) * the angry at the cat dog is big Show how the grammar given above could be modified to prevent this type of overgeneration. [4 marks] (c) The grammar also behaves incorrectly with examples (4), (5) and (6): (4) * the dog is big at the cat (big does not take a PP) (5) * the dog is angry on the cat (angry only takes PPs where the P is at) (6) * the dog is angry at the cat at the cat (adjectives may not combine with multiple PPs) Show modifications to the grammar which would prevent these types of overgeneration. [5 marks] (d) Describe how the overgeneration in part (c) could be dealt with in a feature structure (FS) grammar, giving full lexical entries for angry and big and details of rules and other lexical entries as necessary to explain your account.

(a) Prove that 4n + 6n ? 1 ? 0 (mod 9) for all natural numbers n. [5 marks] (b) (i) State one of the standard characterizations of the reflexive-transitive closure R? ? A A of a binary relation R on a set A. [1 mark] (ii) For the given characterization for a binary relation R on a set A, prove that R? = S n?N Rn where R0 = ? and, for n ? N, Rn+1 = idA ? (R ? Rn). You may use standard results provided that you state them clearly. [8 marks] (c) Let F ? P(N) be a family of pairwise-disjoint subsets of natural numbers; that is, such that ? S, T ? F. S 6= T =? S ? T = ?. State whether or not the set F may be uncountable and prove your claim.

Write program to print out a triangle using nested loops in C

Write to program to calculate the salary of an employee Write program to calculate the area of a rectangle

The following tables are part of a library's database system. Book(book id, title, number owned, number borrowed) Person(person id, name, address) Borrowed(person id, book id, number) The primary keys of each table are in bold. In the table Book the column number owned is the number of copies of the book owned by the library, while the column number borrowed is the number of copies currently out on loan. In table Borrowed the column person id is a foreign key into the Person table, the column book id is a foreign key into the Book table. The column number is the number of copies of the book borrowed by the associated person. (This library is used by primary school teachers who frequently check out many copies of a book for the use in their classes.) If the database is internally consistent, then the column number borrowed is redundant information that can be computed from the actual number borrowed, and this can be derived from the Borrowed table. (a) Write an SQL query that checks the internal consistency of this database. It should return records of the form (book id, number borrowed, actual number borrowed) only for those books where number borrowed and actual number borrowed are not equal. That is, if the database is consistent the query will return no records.

(b) Your job is to redesign this schema so that there is no need for such consistency checks. The first step is to design an Entity-Relationship model. You will do this by introducing a new entity called Copy Of. Each copy of a book owned by the library will be associated with a unique member of the Copy Of entity. Design an Entity-Relationship diagram based on this idea and argue that cardinality constraints will ensure that the database is internally consistent.

(c) Discuss at least two options for implementing your ER model in an SQL database. (d) Using one of your relational implementations from the previous part, write an SQL query that reproduces the contents of the Book table from the original design. That is, write an SQL query that returns records of the form (book id, title, number owned, number borrowed).

In each part you are given the result of an SQL query together with a possibly incorrect conclusion drawn from this result. In each case your task is to argue for or against the conclusion. You must clearly justify your reasoning. If the SQL query can be corrected, then do so. (a) The following query returns 1422. Conclusion: Our database contains information on 1422 directors. select count(*) from has_position where position = 'director'; [6 marks] (b) The following query returns these records: PERSON_ID NAME POSITION TOTAL --------- ------------ -------- ----- nm0498278 Stan Lee writer 15 Conclusion: Stan Lee did not produce any of the movies in our database. select person_id, name, position, count(*) as total from has_position as hp join people as p on p.person_id = hp.person_id where position 'actor' and name = 'Stan Lee' group by person_id, name, position

) Alice and Bob participate in a public-key infrastructure that enables them to exchange legally binding digital signatures. (i) Name two reasons why, for some purposes, Alice might prefer to use a message authentication code, instead of a digital signature, to protect the integrity and authenticity of her messages to Bob. [4 marks] (ii) Outline a protocol for protecting the integrity and authenticity of Alice's messages to Bob that combines the benefits of a public-key infrastructure with those of using a message authentication code. [4 marks] (b) Your colleague proposes a new way for constructing a message authentication code using a block cipher E : {0, 1} 64 {0, 1} 128 ? {0, 1} 128. He takes the n-bit input message M, appends p = 64 dn/64e ? n zero-bits, and splits the result into k = (n + p)/64 64-bit blocks M1||M2|| . . . ||Mk = M||0 p . He then calculates the message authentication code as CK(M) = EM1 (EM2 (EM3 (. . . EMk (K). . .))) where K is the 128-bit secret key shared between sender and recipient. Show two different ways in which an attacker who observes a pair (M, CK(M)) can, without knowing K, create a new pair (M0 , CK(M0 )) with M0 6= M. [6 marks] (c) Show how a 128-bit message authentication code CK(M) with 64-bit key K can be constructed for an n-bit long message M using (i) a secure hash function H : {0, 1} ? ? {0, 1} 256, such as SHA-256; [2 marks] (ii) a block cipher E : {0, 1} 128 {0, 1} 256 ? {0, 1} 256.

Nowadays, timepieces (such as clocks, wristwatches, etc.) have a variety of functions. They not only tell the time and date but they can speak to you, remind you when it's time to do something, and provide a light in the dark, among other things. Mostly, the interface for these devices, however, shows the time in one of two basic ways: as a digital number such as 23:40 or through an analog display with two or three hands - one to represent the hour, one for the minutes, and one for the seconds. In this question, we ask you to design a new timepiece for your own use. This could be in the form of a wristwatch, a mantelpiece clock, an electronic clock, or any other kind of timepiece you fancy. (a) Think about the interactive product you are designing: describe what you want it to do for you. Write a list of functional and non-functional requirements. [4 marks] (b) Sketch out an initial low-fidelity prototype for the timepiece and develop at least two distinct alternatives that both meet your set of requirements listed above. [8 marks] (c) Nielsen's heuristics used for Heuristic Evaluation are: (1) visibility of system status, (2) match between system and real world, (3) user control and freedom, (4) consistency and standards, (5) error prevention, (6) recognition rather than recall, (7) flexibility and efficiency of use, (8) aesthetic and minimalist design, (9) help users recognize and recover from errors, and (10) help and documentation. Evaluate the two low-fidelity prototypes using Heuristic Evaluation.

INNOVATION TD SUIWWE AND THRIVE FOR FUIIFILM Change is the one constant In our lives. One may view It as a threat, or an opportunity. When it comes to business, response to change immensely impacts the fortunes of many. Startups go from rusty Honda Civics to Ferrari riches. Industry giants continue to grow or shrink into irrelevance. The radically divergent fates of Kodak and Fuiilm offer one such example. Two legacy companies doing similar things, with radically different responses to disruptive technologies. One company failed, the other thrived. "lo on often-unpredictable business world, a peak ohvoys conceals a treacherous volley." Shlgetolro Tomorl (CEO, Fujlfflm} 1. The Attempt to Rise and Fall Of Kodak In 199?, just as digital innovation was starting to upbraid the traditional camera market, Kodak's stock price hit an alltime high of $94.?5. George Fisher, who headed the photo Industry iuggernaut as CEO from 1993 to 1999, had pushed through an initiative to pump $2 billion into research and development for digital tech. While he and other top executives were strong advocates for Kodak's traditional analog business, they couldn't ignore the enormity of the digital threat. They chose to confront it head-on. i. Springing into action, Kodak quickly installed 10,000 self-serve kiosks for printing digital camera photos in partner stores. They figured such a bold move would get them one step ahead of the nascent digital printing market. ii. In 1996, the company rolled out the Advanced Photo System {APE} with their line of Advantix cameras and lm, featuring drop-in cartridges and a magnetic stripe on the filmwhich stored date, time, and format Informationfor ordering extra copies. Iii. LaterAdvontlx Preview cameras had digital displays for previewing images on the back of the camera A la digital models, straddling the divide between mediums past and future. iv. That same year also saw the release of the M, Kodak's first digital camera priced to sell at $299 a pop. It was a very simple hobbyist camerano ash and no LCD display, but it did take digital images and it was super compact. The 0025, DC120 and other subseguent models in the series steadily improved storage size and image resolution while adding increasingly better LCD screens for image preview. However, each product line ultimately failed, as did the kloslr initiative. The 0:20 produced low-quality images and cost too much for what it was, annoying traditional Kodak customers [and many other people besides}. Later models in the series failed to bring anything new to the table as Sony, Canon, and Nikon quickly closed the price gap and produced more consumersentric products