MATH/CSCI 4116
Algorithm | 代写math – 该题目是一个常规的math 的练习题目代写, 包括了math 等方面, 这个项目是assignment代写的代写题目
Cryptography
assignment 8
- (a) Use the Euclidean Algorithm to compute gcd(239,124).
(b) Use your calculations above (that is, use the extended Euclidean algorithm) to represent the gcd as a linear combination of 239 and 124.
- (a) Find integersxandy such that 17x+ 101y= 1.
(b) Use the result in (a) to find 17^1 (mod 101).
- Question 2 indicates how the extended Euclidean algorithm can be used to determine modular inverses (if they exist). Use this to find (a) 357^1 (mod 1234); (b) 3123^1 (mod 9987).
- (a) Compute the subgroup generated by 2 + 17Zin (Z/ 17 Z).
(b) Compute the order of 2 (mod 1237).
(Hint: Use the results from Sect. 5.2 to decide which orders arepossible.)
- Determine the orders of all elements in (Z/ 15 Z).
Note: Only after Fridays class you will be able to do the following ques- tion.
- (a) Use Fermats little theorem to compute 2^122 (mod 13).
(b) Use Eulers theorem to find the last digit in the decimal representa- tion of 3^400.
Due: Thursday, March 23, 2023