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

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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
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