4. Complete the addition table below, where P = (2,4), and Q = (0,0) are points on the elliptic c...
Given an elliptic curve E mod p, where p is a prime, the number
of points on the curve is denoted as #E. Also, the ECDLP is
expressed as dP = T.
Which of these statements is TRUE? (select all that apply)
Incorrect 0/0.15 pts Question 18 The image below illustrates different elliptic curves. Elliptic curve cryptosystems rely on the hardness of the generalized discrete logarithm problem. ECDLP.png Given an elliptic curve E mod p, where p is a prime,...
Q4. Consider the elliptic curve E11(1,6); that is, the curve is defined by y2 = x + x +6 with a modulus of p = 11. a) Determine all of the points in E11(1,6). Hint: 0 5x<p and 0 sy<p, x and y are integers. Coding may be the easier way. b) For P(2,4), calculate 13P. c) For P(2,4) and Q(2,7), calculate P+Q. show your steps.
3. Let E be the elliptic curve y2-x3+x 6 over ZI1 1) Find all points on E by calculating the quadratic residues like the one demonstrated in the lecture 2) What is the order of the group? [Do not forget the identity element 0] 3) Given a point P - (2, 7), what is 2P? [point doubling] 4) Given another point Q (3, 6), what is PQ? [point addition]
3. Let E be the elliptic curve y2-x3+x 6 over ZI1...
Considering the ECDSA based on the elliptic curve E: y2 =x3+ax+b over GF(p) where 0<a,b<p, assume that the size of the elliptic curve group is 160 bits, then the size of an ECDSA is a 640 bits b 80 bits c 320 bits d 160 bits
List all points (x,y) in the elliptic curve y2≡ x3 + 2x - 9 (mod
19). (Hint: Corresponding to any given x , points (x,y) and (x,-y)
can exist on the elliptic curve only if y2≡ x3 + 2x - 9 (mod 19) is
a quadratic residue mod 19. Recall that a value v
∊ Zp is a quadratic residue modulo p only if v(p-1)/2≡ 1 (mod p).
If v is indeed a quadratic residue, we can calculate the two...
Let F = (P,Q) be the vector field defined by P(x,y) ity, (1, y) = (0,0) 10, (x,y) = (0,0) Q(x, y) = -Ity. (x, y) = (0,0) 10, (x, y) = (0,0). (a) (3 points) Show that F is a gradient vector field in RP \ {y = 0}. (b) (4 points) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx +Qdy in the counter-clockwise direction. (c) (1 point) Does your calculation in...
2. In R3 you are given the points P(0,0, 10) and Q(42, 70, 4), and R(42, 70,-4) (a) Find the equation of the linear motion which travels through P at time 0 and through R at time 7 (b) Describe the motion of the particle which travels via linear motion, passing through P at time 0, then bounces off of the ry-plane and continues via a linear motion, until it passes though Q at time 14. (Draw a sketch of...
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
2. (20 points) It the demand curve is Q(p) = pa (where αく0), what is the elasticity of demand? If the marginal cost is $2, and α--4, what is the profit-maximizing price?