Download Assignment #7

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Problem 4: The ElGamal message transmission
(a) The ElGamal protocol:
This encrypts a given message m in F_p using the public key (g, y, p)
- requires random numbers in the range [2,..p-2].
Output: M = [M1, M2] = [g^k, m*y^k], where k is a random number.
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(b) A decryption program, using Maple's discrete log program:
The following program computes the discrete log DL_g(y) in F_p.
It can (and will) be used to find the secret key x = DL_g(y).
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This program will be used in the following decoding program which recovers
the original message m from M:= [M1, M2].
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(c) Test the above programs:
Encode the message m = 20080919 twice, using the public key (g,y,p) = (2222, 35029140,
112233449)
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Note that each call of the encryption program yields a different ciphertext.
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20080919
20080919
Thus, both encrypted messages decrypt to the same original message.
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