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Week two! 8 groups of 2 5 rounds Math 1 Modern history Math 2 Computer Programming Analyzing and comparing Cryptosystems 10 questions per round Each question is worth 1 point 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Find a field with 7 elements. Find a field with 9 elements. Multiply + 1 + 3 in 25 = ℤ5 mod 2 − 2. Find 10 + 3 in 256 = ℤ2 mod 8 − 4 − 3 − − 1 Find all quadratics in 256 . Find 77 Convert 00011101 2 to 256 . Convert 00011101 2 to hex. Convert 0x5 to decimal. How many bits would it take to represent a 100digit number? 1. 2. 3. 4. 5. Name a fundamental paradigm shift in cryptography that occurred in the 70’s. This cryptosystem was developed in the 70’s by IBM, with help from the NSA, and lasted through the 90’s. This cryptosystem handles the majority of worldwide cryptography today. In the above cryptosystem, how many bits are required in the key for “top secret” documents. What is the “newest” cryptosystem we have talked about? 6. 7. 8. 9. 10. What country discovered RSA before it was known publically? What does DES stand for? What does AES stand for? What does RSA stand for? What does ECC stand for? 1. 2. 3. 4. 5. Encrypt 2 in the RSA system with = 21 and = 8. S 0 1 2 3 Decrypt 5 in the same RSA system. 0 a b c d Run 13 through the S-box. 1 e f g h Find 4 points on E2,1 ℤ5 2 i j k l Find the slope of the line connecting 2,3 and 6,8 6. 7. 8. 9. 10. Find the equation for the line containing 0,4 and 1,7 . How many squares are there in ℤ11 ? Find an upper bound on the number of points on E5,8 ℤ37 . Perform the “shift rows” operation from AES on the accompanying AES message. Perform the “mix columns” operation on the accompanying column. 0x01 0 1 2 3 0x00 4 5 6 7 0x00 8 9 A B 0x00 C D E F 1. 2. 3. What is the value of A? What is the value of B? What is the value of C? A = 5; B = 3; C = A + B * B; 4. 5. What is the value of A? What is the value of B? A = 5; B = A; A = 4; 6. 7. How many multiplications are used in the following program? What is the value of A? A = 2; Count = 1; While(Count < 4) A = A * A; End 8. 9. How many multiplications are used in the following program? What is the value of A? A = 1; While(A < 2^3) A = A * 2; End 10. True or false: A = B A = 5; B = A; A = 4; 1. 2. 3. 4. 5. Which of these encrypt the slowest? DES, AES, RSA, ECC. Why is AES preferred to DES? Why is ECC preferred to RSA? AES consists of 4 operations: xor’ing a key, mixing columns, S-box substitution, and _____________. How is the DES S-box and AES S-box fundamentally different? 6. 7. 8. 9. 10. RSA and ECC have _________ security. AES has __________ security. DES has __________ security. Which would be more secure? RSA built from two 64-bit primes, or RSA built from four 32-bit primes? Which of these would require the most operations to encrypt one message? 128-bit AES, 128-bit RSA, or 128-bit ECC? The End Created in the summer of 2013 by Dr. Jeffrey Beyerl for use in a cryptography class. This is just a vanilla PowerPoint, but of course like anything you download from the internet: use at your own risk.