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Specifications - Written Assignment must be readable. - Any assignment will be due on the date of next week - Late Submission criteria is set to deduct 10% per day for late submissions - Cases of plagiarism will be penalized Question 1 (1.5 mark) a) Use the Euclidean algorithm to find the greatest common divisor of 851 and 2479 . b) Cakculate (2479). We know from (a) that 37 is a prime factor of 2479 ; e) Does the inverse of 851 modulo 2479 , exist? If so, find it. If not, explain why it does not exist. Question 2(1 mark) Use Fermat's Little or Euler's Theorems as appropriate to calculate (8),(12),(21) Question 3(1 mark) a) Find the Greatest Common Divisor (GCD) of 15 and 56 and find the incegers s and t solving the equation 15t+56d. What is the inverse of 15mod56(151mod56) ? b) Find the Greatest Common Divisor (GCD) of 252 and 198 and find the integers x and t solving the equation 198t+252s=d. What is the inverse of 198mod252(1981mod252) ? Question 4(1.5 mark) a) If we can check 100,000,000 keys a secoud, how long (in years, to the nearest year) would it take try all possible keys in DES? (1) b) This problem provides a aumerical example of eneryption using one round version of DES. (I) 1. If Kl=000110110000001011101111111111000111000001110010, compute Kl+E(R) ? 2. If B2=010001, compute S2(B2)