Exercises TSIT03 Cryptology: Elliptic Curve Cryptography [PDF]

Exercises TSIT03 Cryptology: Elliptic Curve Cryptography 1) Determine all points on the elliptic curve E = {(x, y) : y 2 = x3 + x + 6 mod 11} 2) Use the elliptic curve E to calculate kα for 1 < k < 14, where α = (2, 7) 3) Use the elliptic curve E and the generator point α in ECC ElGamal encryption, and calculate a) the public key when the secret key is 6 b) the public key when the secret key is 2 c) the public key when the secret key is 7 4) Use the elliptic curve E and the generator point α in ECC ElGamal encryption, with the recipient’s secret key 7. One use of your random number generator gives you the number 3. a) Encrypt the message 10 b) Decrypt the cryptogram, and verify that you can retrieve the message 5) Use the elliptic curve E and the generator point α in ECC Diffie-Hellman key exchange. What is the shared key when the secrets keys are 2 and 6 respectively? 6) Use the elliptic curve E and the generator point α in ECC ElGamal digital signatures, with your secret key 6. One use of your random number generator gives you the number 3. a) Sign the message 10 b) Verify the signature using the public key 7) Show that if P = (x, 0) is a point on an elliptic curve, then 2P = ∞