Consider the elliptic curve
E: y 2 = x 3 + Ilx; + 19 (mod 167)
a. Verify that the point P = (2,7) is on E.
b. Suppose this E and P = (2,7) are used in an ECC Diffie-Hellman key exchange, where Alice chooses the secret value A = 12 and Bob chooses the secret value B = 31.
What value does Alice send to Bob?
What does Bob send to Alice?
What is the shared secret?
You can prevent a forward search attack on a public key cryptosystem by padding with random bits.
a. Why would we like to minimize the amount of random padding?
b. How many bits of random padding are needed? Justify your answer.
c. Other than padding, is there another simple and practical method for preventing a forward search attack?
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