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NEW QUESTION: 1
Which of the following is NOT a characteristic of the ElGamal public
A. It can be used to generate digital signatures.
B. It can perform encryption.
C. It can perform encryption, but not digital signatures.
D. It is based on the discrete logarithm problem.
The ElGamal public key cryptosystem can perform both encryption
and digital signatures based on the discrete logarithm problem.
These three characteristics are shown in the examples that follow.
To generate a key pair in the ElGamal system:
A. Choose a prime number, p.
B. Choose two random numbers, g and x (g and x must both be less
C. Calculate y = g x mod p.
D. The private key is x and the public key is y, g, and p.
To encrypt a message, M, in the ElGamal system:
A. Select a random number, j, such that j is relatively prime to p-1.
Recall that two numbers are relatively prime if they have no
common factors other than 1.
B. Generate w = g j mod p and z = y j M mod p.
C. w and z comprise the ciphertext.
To decrypt the message, M, in the ElGamal system, calculate M =
z/w xmod p. This can be shown by substituting the values of z and w
in the equation as follows:
M = y j M mod p/ g jx mod p
Since y j = g xj mod p
M = (g xj M / g jx ) mod p
To sign a message, M, in the ElGamal system:
A. Select a random number, j, such that j is relatively prime to p-1. The value of j must not be disclosed. Generate w = g j mod p.
B. Solve for z in the equation M = (xw + jz) mod (p-1). The solution to this equation is beyond the scope of this coverage. Suffice to say that an algorithm exists to solve for the variable z.
C. w and z comprise the signature.
D. Verification of the signature is accomplished if g M mod p = y w w z mod p.