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Cryptography Practice Test: Elliptic Curve Arithmetic/Cryptography
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Elliptic curve cryptography (ECC) is a public key encryption technique that uses elliptic curves to create cryptographic keys. ECC is considered one of the most powerful types of cryptography in use today. 

ECC is based on the assumption that it is difficult to find the discrete logarithm of a random number. ECC uses modular arithmetic and group theory to deal with elliptic curves over finite fields. A finite field is a set of a certain number of numbers, which also includes infinity. 
 

Cryptography Practice Test: Elliptic Curve Arithmetic/Cryptography
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16 Questions

1. P = C1 – (d x C2)
Is this above stated formula true with respect to ECC?
2. “Elliptic curve cryptography follows the associative property.”
3. How many real and imaginary roots does the equation y2=x3-4x have
4. If P = (1,4) in the elliptic curve E13(1, 1) , then 4P is
5. What is the general equation for elliptic curve systems?
6. Bob selects E67(2, 3) as the elliptic curve over GF(p). He selects e1 = (2, 22) and d = 4.
Then he calculates e2 = d × e1 and the publicly announces the tuple (E, e1, e2). Now, Alice wants to send the plaintext P = (24, 26) to Bob and she selects r = 2. What are C1 and C2?
7. P = C1 – (d x C2)
Is this above stated formula true with respect to ECC?
8. On adding the two points P (4,2) and Q (10, 6) in the elliptic curve E11(1,1) we get
9. 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)?
10. Multiply the point P=(8, 1) by a constant 3, thus find 3P, in the elliptic curve E13(1, 1)
11. On adding the two points P (4,2) and Q (10, 6) in the elliptic curve E11(1,1) we get
12. In Singular elliptic curve, the equation x^3+ax+b=0 does ____ roots.
13. For the point P (7, 0) defined in the curve E13(1, 1). What is –P?
14. For the point P (11, 2) defined in the curve E13(1, 1). What is –P?
15. In Singular elliptic curve, the equation x^3+ax+b=0 does ____ roots.
16. In the elliptic curve group defined by y2= x3- 17x + 16 over real numbers, what is 2P if P = (4, 3.464)?

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