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Consider the ElGamal encryption scheme over an elliptic curve E: y2 =x3+x+6 over GF(11) and let...

Consider the ElGamal encryption scheme over an elliptic curve E: y2 =x3+x+6 over GF(11) and let P=(2,7) be a group generator, given a private key x=9,

1. Compute the public key;

2. Compute the ciphertext of M=(8,3), given k=7 and the public key;

3. Decrypt the ciphertext with the private key.

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