Question

4. Let E be the elliptic curve y^2 = x^3 + 2x + 3 (mod 19). (a) Show that the point (1,5) lies on the curve. (3 pts) (b) Find an integer k such that k(1,5) = (9,3). (3 pts) (c) For this subtask, you are going to factorize n = 2773 using an elliptic curve. Tasks to do: (4p) i. Choose an Elliptic Curve E modulo n and a point A on the curve. ii. Find the points 2A, 3A, 4A, ... on the curve until you can no longer find more points. Explain why you cannot proceed, and determine the prime factors of n as well.

          4. Let E be the elliptic curve y^2 = x^3 + 2x + 3 (mod 19).
(a) Show that the point (1,5) lies on the curve. (3 pts)
(b) Find an integer k such that k(1,5) = (9,3). (3 pts)
(c) For this subtask, you are going to factorize n = 2773 using an elliptic curve.
Tasks to do: (4p)
i. Choose an Elliptic Curve E modulo n and a point A on the curve.
ii. Find the points 2A, 3A, 4A, ... on the curve until you can no longer find more points. Explain why you cannot proceed, and determine the prime factors of n as well.

4. Let E be the elliptic curve y^2 = x^3 + 2x + 3 (mod 19).
(a) Show that the point (1,5) lies on the curve. (3 pts)
(b) Find an integer k such that k(1,5) = (9,3). (3 pts)
(c) For this subtask, you are going to factorize n = 2773 using an elliptic curve.
Tasks to do: (4p)
i. Choose an Elliptic Curve E modulo n and a point A on the curve.
ii. Find the points 2A, 3A, 4A, ... on the curve until you can no longer find more points. Explain why you cannot proceed, and determine the prime factors of n as well.

Added by Leslie A.

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