This set of Cryptography Multiple Choice Questions & Answers (MCQs) focuses on “Elliptic Curve Arithmetic/Cryptography”.

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

View Answer

Explanation: The general equations for an elliptic curve system is y

^{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

View Answer

Explanation: In Singular elliptic curve, the equation x^3+ax+b=0 does not have three distinct roots.

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

View Answer

Explanation: On solving the equation we get 2 imaginary and 1 real root.

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

View Answer

Explanation: On solving the equation we get all real roots.

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)

View Answer

Explanation: P=(x1, y1)= (0,-4)

Q=(x2, y2)= (1,0)

From the Addition formulae:

λ= (0-(-4)) / (1-0) = 4

x3= = 16 – 0 – 1 = 15 and

y3= 4(0 – 15) –(-4) = -56

Thus R=P + Q = (15, -56).

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)

View Answer

Explanation: From the Doubling formulae:

λ = (3*(4)2+ (-17)) / 2*(3.464) = 31 / 6.928 = 4.475

x3= (4.475)2- 2(4) = 20.022 – 8 = 12.022 and

y3= -3.464 + 4.475(4 – 12.022) = – 3.464 – 35.898 = -39.362

Thus 2P = (12.022, -39.362).

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

a) True

b) False

View Answer

Explanation: ECC does follow associative property.

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

a) True

b) False

View Answer

Explanation: The inverse of point P =(x1, y1) is Q =(x1, -y1).

**Sanfoundry Global Education & Learning Series – Cryptography and Network Security.**

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