Alice has a message M=51 to send to Bob securely using ElGamal encryption algorithm. Bob chooses...
Alice has a message M=51 to send to Bob securely using ElGamal encryption algorithm. Bob chooses p= 8167, g=4063, x=71. Alice chooses r=29. Show the encryption and decryption steps.
Homework Answers
ElGamal Algorithm:
Encryption:
Bob chooses 1) a prime number, p= 8167,
2) a number g between 1 and (8167-1) 8166 as 4063
and 3) a random number (private key), x=71
He calculates Y using the formula Y=Gx mod P =5081.
Bob Public Key now is [P,G,Y]=[8167,4063,5081]
Alice creates a message to send. i.e., M=51 and chooses random value, r=29.
Two new values are calculated using the formulae:
a=GrmodP=7820
b=Yr M modP=6181
Cipher Text C=(7820,6181)
Decryption:
Next Bob Decrypts the message using the formula b/(ax) mod P
Message Decrypted = 51 which is equal to Plain Text (M)
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