4.4 QUIZ 3 Elliptic Curve Groups over F2m For the following questions, assume the use of the field F23. The field is described here using polynomial representation with the irreducible polynomial x3 + x + 1. A generator for the field is g = (010), and the powers of g are: g1 = (010) g2 = (100) g3 = (011) g4 = (110) g5 = (111) g6 = (101) g7 = (001) = 1 1. Does the elliptic curve equation y2 + xy = x3 + g5x2 + 6 define a group over F23? 2. Do the points P(g3, g6) and Q(g5, g2) lie on the elliptic curve y2 + xy = x3 + g2x2 + g6 over F23? 3. What are the negatives of the following elliptic curve points over F23? P(g3,g6) Q(g,0) R(0,g3)
	4. In the elliptic curve group defined by y2 + xy = x3 + g2x2 + g6 over F23, what is P + Q if P = (g2,g6) and Q = (g5,g5)? 5. In the elliptic curve group defined by y2 + xy = x3 + g2x2 + g6 over F23, what is 2P if P = (g3, g4)? Click here for Solutions
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