Points: 20
Q1. Using Euclidean algorithm find GCD(378, 336). Show you work.
Q2. Using Extended Euclidean algorithm find the multiplicative inverse of 9 in mod 37 domain. Show
your work including the table. (All rows may not be needed)
i ri qi–1 si ti
0 37 1 0
1 9 0 1
2
3
4
5
6
Q3. Determine φ(3200). (Note that 1,2,3,5, 7, … etc. are the primes). Show your work.
Q4. Find the multiplicative inverse of 9 in GF(37) domain using Fermat’s little theorem. Show your work.
Q5. Using Euler’s theorem, find the following exponential: 7300 mod 31. Show how you have employed Euler’s theorem here. Bonus question [10 extra points ]: Write a program (in any programming language) to implement Extended Euclidean algorithm with two input parameters a and b, and return the output as b–1 mod a. Run the program with a=47 and b= 7 as input and print the results. Submit the source code and the output. What to submit? Submit a pdf file with your answers via the Blackboard. Show your work
Q1. Using Euclidean algorithm find GCD(378, 336). Show you work.
Q2. Using Extended Euclidean algorithm find the multiplicative inverse of 9 in mod 37 domain. Show
your work including the table. (All rows may not be needed)
i ri qi–1 si ti
0 37 1 0
1 9 0 1
2
3
4
5
6
Q3. Determine φ(3200). (Note that 1,2,3,5, 7, … etc. are the primes). Show your work.
Q4. Find the multiplicative inverse of 9 in GF(37) domain using Fermat’s little theorem. Show your work.
Q5. Using Euler’s theorem, find the following exponential: 7300 mod 31. Show how you have employed Euler’s theorem here. Bonus question [10 extra points ]: Write a program (in any programming language) to implement Extended Euclidean algorithm with two input parameters a and b, and return the output as b–1 mod a. Run the program with a=47 and b= 7 as input and print the results. Submit the source code and the output. What to submit? Submit a pdf file with your answers via the Blackboard. Show your work
