Use Sage to solve the following problems. 

USE SAGE TO SOLVE THE FOLLOWING PROBLEMS.

Use Sage to solve the following problems.

For this questions assume that we are using dsa with domain parameters:

p = 7,877,914,592,603,328,881

q = 44449

g = 2,860,021,798,868,462,661

Use these domain parameters to determine if the signatures are valid in parts (a)-(c)

  1. public key y = 3798043471854149631, hash value H = 59367, and signature (r,s) = (31019, 4047)
  2. public key y = 1829820126190370021, hash value H = 77241, and signature (r,s) = (24646, 43556)
  3. public key y = 4519088706115097514, hash value H = 48302, and signature (r,s) = (36283, 32514)

Perform a signing operation for the below parts (a)-(b)

  1. private key x = 8146, hash value H = 22655
  2. private key x = 1548, hash value H = 32782