This problem concerns the Galois field GF (2) with the irreducible polynomial P(x) = x+x+x+x+1. Let...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
This problem concerns the Galois field GF (2³) with the irreducible polynomial P(x) = x³+x+x³+x+1. Let A(x) = x+x³ and B(x) = x³+x³+1. (a) How many elements are in the field GF (2³)? (b) What is the maximum degree of any polynomials in GF(2³) (c) List all elements (i.e. polynomials) in GF (2³) with degree 3. (d) Compute A(x) + B(x) mod P(x). (e) Compute A(x) * B(x) mod P(x). (f) Find A¹(x) and B-¹(x) by using Table 4.2. (g) Verify your answer in (f) by performing GF (2³) multiplication. Your task is to compute the S-Box, i.e., the ByteSub, values for the input bytes 29, F3, and 01, where each byte is given in hexadecimal notation. (a) First, look up the inverse using Table 4.2 to obtain values B. (b) Now, perform the affine mapping by computing the matrix-vextor multiplication and addition. (c) Verify your result using the S-Box Table 4.3. (d) What is the value of S(0)? Table 4.2 Multiplicative inverse table in GF (28) for bytes xy used within the AES S-Box Y 0 1 2 3 4 5 6 7 89 A B C DE F 0 00 01 8D F6 CB 52 7B D1 E8 4F 29 C0 B0 E1 E5 C7 174 B4 AA 4B 99 2B 60 5F 58 3F FD CC FF 40 EE B2 23A 6E 5A F1 55 4D A8 C9 C1 0A 98 15 30 44 A2 C2 3 2c 45 92 6C F3 39 66 42 F2 35 20 6F 77 BB 59 19 4 1D FE 37 67 2D 31 F5 69 A7 64 AB 13 54 25 E9 09 5 ED 5C 05 CA 4C 24 87 BF 18 3E 22 F0 51 EC 61 17. 6 16 5E AF D3 49 A6 36 43 F4 47 91 DF 33 93 21 3B 7 79 B7 97 85 10 B5 BA 3C B6 70 DO 06 A1 FA 81 82 X 8 83 7E 7F 80 96 73 BE 56 9B 9E 95 D9 F7 02 B9 A4 9 DE 6A 32 6D D8 8A 84 72 2A 14 9F 88 F9 DC 89 9A A FB 7C 2E C3 8F B8 65 48 26 C8 12 4A CE E7 D2 62 BOC EO 1F EF 11 75 78 71 A5 8E 76 3D BD BC 86 57 COB 28 2F A3 DA D4 E4 OF A9 27 53 04 1B FC AC E6 D7A 07 AE 63 C5 DB E2 EA 94 8B C4 D5 9D F8 90 6B EB1 OD D6 EB C6 0E CF AD 08 4E D7 E3 5D 50 1E B3 F5B 23 38 34 68 46 03 8C DD 9C 7D A0 CD 1A 41 1c Table 4.3 AES S-Box: Substitution values in hexadecimal notation for input byte (xy) y 3 5 6 7 4 9 A B C D E F F2 6B 6F C5 30 01 67 2B FE D7 AB 76 7B 7D FA 59 47 F0 AD D4 A2 AF 9C A4 72 CO 3 04 C7 23 26 36 3F F7 CC 34 A5 E5 F1 71 D8 31 15 C3 18 96 05 9A 07 12 80 E2 EB 27 B2 75 09 83 2C 1A 1B 6E 5A A0 52 3B D6 B3 29 E3 2F 84 6A CB BE 39 4A 4C 58 CF 4 5 53 D1 00 ED 20 FC B1 5B 6 DO EF AA FB 43 4D 33 85 45 F9 02 7F 50 3C 9F A8 7 51 A3 40 8F 92 9D 38 F5 BC B6 DA 21 10 FF F3 D2 X 8 CD 0C 13 EC 5F 97 44 17 C4 A7 7E 3D 64 5D 19 73 9 60 81 4F DC 22 2A 90 88 46 EE B8 14 DE SE OB DB A EO 32 3A 0A 49 06 24 5C C2 D3 AC 62 91 95 E4 79 BE7 C8 37 6D 8D D5 4E A9 6C 56 F4 EA 65 7A AE 08 CBA 78 25 2E 1C A6 B4 C6 E8 DD 74 1F 4B BD 8B 8A D 70 3E B5 66 48 03 F6 OE 61 35 57 B9 86 C1 ID 9E E E1 F8 98 11 69 D9 8E 94 9B 1E 87 E9 CE 55 28 DF F 8C AI 89 OD BF E6 42 68 41 99 2D OF B0 54 BB 16 0 1 2 63 7C 77 1 CA 82 C9 2 B7 FD 93 0 8 This problem concerns the Galois field GF (2³) with the irreducible polynomial P(x) = x³+x+x³+x+1. Let A(x) = x+x³ and B(x) = x³+x³+1. (a) How many elements are in the field GF (2³)? (b) What is the maximum degree of any polynomials in GF(2³) (c) List all elements (i.e. polynomials) in GF (2³) with degree 3. (d) Compute A(x) + B(x) mod P(x). (e) Compute A(x) * B(x) mod P(x). (f) Find A¹(x) and B-¹(x) by using Table 4.2. (g) Verify your answer in (f) by performing GF (2³) multiplication. Your task is to compute the S-Box, i.e., the ByteSub, values for the input bytes 29, F3, and 01, where each byte is given in hexadecimal notation. (a) First, look up the inverse using Table 4.2 to obtain values B. (b) Now, perform the affine mapping by computing the matrix-vextor multiplication and addition. (c) Verify your result using the S-Box Table 4.3. (d) What is the value of S(0)? Table 4.2 Multiplicative inverse table in GF (28) for bytes xy used within the AES S-Box Y 0 1 2 3 4 5 6 7 89 A B C DE F 0 00 01 8D F6 CB 52 7B D1 E8 4F 29 C0 B0 E1 E5 C7 174 B4 AA 4B 99 2B 60 5F 58 3F FD CC FF 40 EE B2 23A 6E 5A F1 55 4D A8 C9 C1 0A 98 15 30 44 A2 C2 3 2c 45 92 6C F3 39 66 42 F2 35 20 6F 77 BB 59 19 4 1D FE 37 67 2D 31 F5 69 A7 64 AB 13 54 25 E9 09 5 ED 5C 05 CA 4C 24 87 BF 18 3E 22 F0 51 EC 61 17. 6 16 5E AF D3 49 A6 36 43 F4 47 91 DF 33 93 21 3B 7 79 B7 97 85 10 B5 BA 3C B6 70 DO 06 A1 FA 81 82 X 8 83 7E 7F 80 96 73 BE 56 9B 9E 95 D9 F7 02 B9 A4 9 DE 6A 32 6D D8 8A 84 72 2A 14 9F 88 F9 DC 89 9A A FB 7C 2E C3 8F B8 65 48 26 C8 12 4A CE E7 D2 62 BOC EO 1F EF 11 75 78 71 A5 8E 76 3D BD BC 86 57 COB 28 2F A3 DA D4 E4 OF A9 27 53 04 1B FC AC E6 D7A 07 AE 63 C5 DB E2 EA 94 8B C4 D5 9D F8 90 6B EB1 OD D6 EB C6 0E CF AD 08 4E D7 E3 5D 50 1E B3 F5B 23 38 34 68 46 03 8C DD 9C 7D A0 CD 1A 41 1c Table 4.3 AES S-Box: Substitution values in hexadecimal notation for input byte (xy) y 3 5 6 7 4 9 A B C D E F F2 6B 6F C5 30 01 67 2B FE D7 AB 76 7B 7D FA 59 47 F0 AD D4 A2 AF 9C A4 72 CO 3 04 C7 23 26 36 3F F7 CC 34 A5 E5 F1 71 D8 31 15 C3 18 96 05 9A 07 12 80 E2 EB 27 B2 75 09 83 2C 1A 1B 6E 5A A0 52 3B D6 B3 29 E3 2F 84 6A CB BE 39 4A 4C 58 CF 4 5 53 D1 00 ED 20 FC B1 5B 6 DO EF AA FB 43 4D 33 85 45 F9 02 7F 50 3C 9F A8 7 51 A3 40 8F 92 9D 38 F5 BC B6 DA 21 10 FF F3 D2 X 8 CD 0C 13 EC 5F 97 44 17 C4 A7 7E 3D 64 5D 19 73 9 60 81 4F DC 22 2A 90 88 46 EE B8 14 DE SE OB DB A EO 32 3A 0A 49 06 24 5C C2 D3 AC 62 91 95 E4 79 BE7 C8 37 6D 8D D5 4E A9 6C 56 F4 EA 65 7A AE 08 CBA 78 25 2E 1C A6 B4 C6 E8 DD 74 1F 4B BD 8B 8A D 70 3E B5 66 48 03 F6 OE 61 35 57 B9 86 C1 ID 9E E E1 F8 98 11 69 D9 8E 94 9B 1E 87 E9 CE 55 28 DF F 8C AI 89 OD BF E6 42 68 41 99 2D OF B0 54 BB 16 0 1 2 63 7C 77 1 CA 82 C9 2 B7 FD 93 0 8
Expert Answer:
Related Book For
Statistics For Business And Economics
ISBN: 9780538481649
11th Edition
Authors: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams
Posted Date:
Students also viewed these organizational behavior questions
-
Table 4 lists U.S. crude oil production as a percentage of total U.S. energy production for selected years. Let x represent years since 1960 and y represent the corresponding percentage of oil...
-
Table 4 gives the percentage of the U.S. population living in the northeast region during the indicated years. The following transition matrix P is proposed as a model for the data, where N...
-
Table 6.5 shows a 2 Ã 2 Ã 2 contingency table for the binary variables A and B at different values of the control variable C. (a) Compute the Ï coefficient for A and B when C = 0,...
-
Jeffrey Glockzin was an employee of Nordyne, Inc. (Nordyne), which manufactured air conditioning units. Sometimes Glockzin worked as an assembly line tester. The job consisted of using bare metal...
-
What are the key functions and responsibilities of the U.S. Government Accountability Office?
-
At December 31, 2009, Braddock Company had a balance of $15,000 in the Allowance for Doubtful Accounts. During 2010, Braddock wrote off accounts totaling $13,000. One of those accounts ($1,800) was...
-
Use the financial data for Randa Merchandising, Inc., in Exercise 13-13 to prepare its income statement for calendar-year 2017. (Ignore the earnings per share section.) Data From Exercise 13.13 In...
-
For Lodes Company, the relevant range of production is 4080% of capacity. At 40% of capacity, a variable cost is $4,000 and a fixed cost is $6,000. Diagram the behavior of each cost within the...
-
Mary, Shannon, and Anika each invested $9,000, $25,000, and $18,000, respectively, into a business. a. Calculate their investment ratio reduced to the lowest terms. 0 : 0 : 0
-
(a) For the circuit in Fig. 4.138, obtain the Thevenin equivalent at terminals a-b. (b) Calculate the current in RL = 8(. (c) Find RL for maximum power deliverable to RL. (d) Determine that maximum...
-
KBC Inc. just paid a dividend of $12.00 per share but plans to pay $5.00 per share from the next year till year 22 , after which, the dividend will grow at 5% for good. The required rate of return on...
-
In triangle ( ABC ), if ( a = 10 ), ( b = 14 ), and ( \angle A = 30^\circ ), find ( \angle B ) using the Law of Sines.
-
Many accounting departments are usinginformation systems as a means to "collect and process transaction data and communicatethe financial information to interested parties. There are many types of...
-
What does this theory conclude about individuals that have a strong sense of self-efficacy? What type of goals are these individuals usually selecting for themselves? How about their focus? Do they...
-
Discuss financial leverage and why it differs between industries. Discuss the three primary factors that are considered in determining the optimal proportion of debt versus equity for an industry,...
-
Is the U.S. stock market efficient? If so, to what degree? What are the implications of your answer in terms of investor returns and investor investment strategy?
-
what is the expected rate of return form this investment? Camel & Co is given a proposal to purchase a piece of land. The land can be developed into a commercial cum residential project. The...
-
Privitera and Freeman (2012) constructed a scale to measure or estimate the daily fat intake of participants; the scale was called the estimated daily intake scale for fat (EDIS-F). To validate the...
-
Chicago O'Hare and Atlanta Hartsfield-Jackson are the two busiest airports in the United States. The congestion often leads to delayed flight arrivals as well as delayed flight departures. The Bureau...
-
Where do women most often buy casual clothing? Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets (The Wall Street Journal,...
-
Cond Nast Traveler publishes a Gold List of the top hotels all over the world. The Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List (Cond Nast Traveler, January...
-
A steam turbine operates on a Carnot cycle, with a maximum pressure of 20 bar and a condenser pressure of 0.5 bar. Calculate the salient points of the cycle, the energy addition and work output per...
-
Van der Waals equation for water is given by \[p=\frac{0.004619 T}{v-0.0016891}-\frac{0.017034}{v^{2}}\] where \(p=\) pressure (bar), \(v=\) specific volume \(\left(\mathrm{m}^{3} / \mathrm{kmol}...
-
A steam power plant operating on a basic Rankine cycle has the following parameters: maximum (boiler) pressure 20 bar; minimum (condenser) pressure 0.5 bar. Calculate the thermal efficiency of the...
Study smarter with the SolutionInn App