(1) This problem computes discrete logarithms, (a) Describe a Baby Step, Giant Step attack to nd a: in 3'" E 57 (mod 137). (b) (D grade question) In this exercise you will independently study the Pohlig- Hellman algorithm (Section of 10.2.1 of the textbook). Apply the Pohlig- Hellman algorithm to nd y in 33' E 45 (mod 137). (c) (HD grade question) Without using a Baby Step, Giant Step attack or the PohligHellman algorithm or brute force, compute manually 3z 2 95 (mod 137). Note: In this Whole question, you may use sagemath to compute the intermediate modular exponentiations that you Will encounter. 10+18+6=34 marks Part (a) The student receives 10 marks for a correct application of the Baby step, Giant step attack. This includes 8 marks for the creation of the two relevant lists, and 2 marks for giving the correct answer. For dierent levels of correctness, the student receives between 9 and 0 marks. Part (b) The student receives 18 marks for a correct application of the Polih-Hellman algorithm. This includes 14 marks for the correct application of the algo rithm to certain factors, 4 marks for the correct application of the Chinese remainder theorem and for the nal answer. For different levels of correct ness, the student receives between 17 and 0 marks. Part (c) The student receives 6 marks for a correct answer, with all the steps well justied. For different levels of correctness, the student receives between 5 and 0 marks