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Q1. Consider the curve y2 ≡ x3 + 3x + 5 mod 17.

(i) Confirm that it is an elliptic curve.

(ii)

Determine three points on the curve over real numbers

(iii) Determine three points on the curve over integer numbers

(iv) For one of the points P in (iii), find 2P (or double)

(v) For two of the points P and Q in (iii), find P+Q

(vi) Find the bound for the number of points on this curve using Hesse's theorem.

Q2. Using an example, show how ECDH can be implemented using this curve.

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