Cryptography online quiz on “Elliptic Curve Arithmetic/Cryptography”.
1. On adding the two points P (4,2) and Q (10, 6) in the elliptic curve E11(1,1) we get
a) (9,3)
b) (6,4)
c) (7,5)
d) (2,8)
Answer: b
Clarification: Apply ECC to obtain P+Q=(6,4).
2. If P = (1,4) in the elliptic curve E13(1, 1) , then 4P is
a) (4, 2)
b) (7, 0)
c) (5, 1)
d) (8, 1)
Answer: d
Clarification: Apply ECC via adding P+P=2P then, 4P=2P+2P.
3. Multiply the point P=(8, 1) by a constant 3, thus find 3P, in the elliptic curve E13(1, 1)
a) (10,7)
b) (12,6)
c) (11,1)
d) (9,8)
Answer: a
Clarification: P+P=2P then, 3P=2P+P
Thus we get Q=3P = (10, 7).
4. 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 .What is the value of e2?
a) (23,49)
b) (16,55)
c) (12,19)
d) (13,45)
Answer: d
Clarification: e2 = d × e1 ; e2 =(13, 45).
5. 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?
a) C1=(35,1) ; C2 =(21,44)
b) C1=(44,21) ; C2 =(1,35)
c) C1=(44,21) ; C2 =(44,21)
d) C1=(21,44); C2 =(35,1)
Answer: a
Clarification: Alice finds the points C1= r × e1 ; C1= (35, 1),
C2=P + r × e2 ; C2= (21, 44).
6. P = C1 – (d x C2)
Is this above stated formula true with respect to ECC?
a) True
b) False
Answer: b
Clarification: P = C2 – (d x C1).
7. For the point P (11, 2) defined in the curve E13(1, 1). What is –P?
a) (12,4)
b) (10,7)
c) (11,11)
d) (11,12)
Answer: c
Clarification: The inverse of P(11,2) is (11,11) or (11,-2).
8. For the point P (7, 0) defined in the curve E13(1, 1). What is –P?
a) (7,1)
b) (8,12)
c) (8,1)
d) (7,0)
Answer: d
Clarification: The inverse of P(11,2) is (11,11) or (11,-2).