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Please provide any code that was used to solve: The National Bank of Crimea requires all members to conduct business on - line, and to

Please provide any code that was used to solve: The National Bank of Crimea requires all members to conduct business on-line, and to
use El-Gamal signatures to close transactions. It published the following prime number p
and primitive root g to be used in the signature algorithm:
p=634404508895808192310313936486634711780110256438029402544697478374579200001
g=369453800891893802517289247828810138682703208596756001785976436264055339058
Alice, one of the clients of National Bank of Crimea, published as her public signature
key the following
b=206713254758099776851768543289940039539605032684783111021316389446087521630.
Last Friday Alice received a letter from the bank that unless she pays the $100 she
promised to the bank, the bank will repossess her stereo system. Alice, surprised by the
request, asked the bank to provide proof that she owes the bank $100. The bank
presented the following evidence:
Plaintext="I will pay $100
y=5823678520857072221167
s=
283153022158607625107842056887562165281621743987479476610628619918477927399
(a) Determine whether (y,s) is a valid signature for Alice's key. The answer must be
supported with a computational evidence.
A. The signature is valid.
B. The signature is not valid.
(b) Alice does not recall this promissory note, and decided to investigate further. She
asked her family member who works for the Digital Crimes Federal Bureau of
Investigation for help. This family member reported a few weeks later to Alice the following information: "The bank manager revealed that the discrete
logarithm of y is r=825693824659243777." Show how this information can be used
to generate a valid signature for Alice on the message "I will not pay $100",
without knowledge of Alice's private key.
Hint: Note that M1=1 will pay $100 and M2=I will not pay $100 are two diflerent messages. Use the
difference of S1(signature on M1) and S2(signature on M2) to show that one can generate a valid signature on
the message "I will not pay $100" without knowing the private key.
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