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In the Elliptic Curve, y2= x3+x+6 mod 59, the point (2, 4) can generate a subgroup of order 17 as {(2, 4), (18, 29), (26,

In the Elliptic Curve, y2= x3+x+6 mod 59, the point (2, 4) can generate a subgroup of order 17 as {(2, 4), (18, 29), (26, 47), (38, 20), (9, 6), (24, 15), (48, 32), (29, 36), (29, 23), (48, 27), (24, 44), (9, 53), (38, 39), (26, 12), (18, 30), (2, 55), O}. Alice and Bob want to share a secret key using Diffie-Hellman algorithm. They decide to use the above Elliptic Curve and (2, 4) as the generator.

If Alice selects a one-time secret 13, what will be Alices public key? If Bob selects a one-time secret 9, what will be Bobs public key? What will be their shared secret key?

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