1. What is the general equation for elliptic curve systems?

a) y^{3}+b_1 xy+b_2 y=x^{3}3+a_1 x^{2}+a_2 x+a_3

b) y^{3}+b_1 x+b_2 y=x^{2}+a_1 x^{2}+a_2 x+a_3

c) y^{2}+b_1 xy+b_2 y=x^{3}+a_1 x^{2}+a_2

d) y^{2}+b_1 xy+b_2 y=x^{3}+a_1 x^{2}+a_2 x+a_3

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^{2}+b_1 xy+b_2 y=x

^{3}+a_1 x

^{2}+a_2 x+a_3.

2. In Singular elliptic curve, the equation x^3+ax+b=0 does ____ roots.

a) does not have three distinct

b) has three distinct

c) has three unique

d) has three distinct unique

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3. How many real and imaginary roots does the equation y2=x3-1 have

a) 2 real, 1 imaginary

b) all real

c) all imaginary

d) 2 imaginary, 1 real

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4. How many real and imaginary roots does the equation y2=x3-4x have

a) 2 real, 1 imaginary

b) all real

c) all imaginary

d) 2 imaginary, 1 real

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5. In the elliptic curve group defined by y2= x3- 17x + 16 over real numbers, what is P + Q if P = (0,-4) and Q = (1, 0)?

a) (15, -56)

b) (-23, -43)

c) (69, 26)

d) (12, -86)

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6. In the elliptic curve group defined by y2= x3- 17x + 16 over real numbers, what is 2P if P = (4, 3.464)?

a) (12.022, -39.362)

b) (32.022, 42.249)

c) (11.694, -43.723)

d) (43.022, 39.362)

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7. “Elliptic curve cryptography follows the associative property.”

a) True

b) False

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8. “In ECC, the inverse of point P =(x1, y1) is Q = (-x1, y1). “

a) True

b) False