Question

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)

The question was posed to me in my homework.

This question is from Elliptic Curve Arithmetic/Cryptography in portion Other Public Key Cryptosystems and Cryptographic Hash Functions of Cryptograph & Network Security

Answer 1

Right choice is (a) (15, -56)

To explain: 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).