Consider the elliptic curve group based on the equationwhere a = 10, b = 8, and p= 11.In this group, what is 2(2,5) = (2, 5) + (2, 5)?In this group, what is (2, 6) + (6, 3)?What is the inverse of (6, 8) (with entries in Z11)?y² = x³ + ax + bmod p

As per the question we are given the following elliptic curve : y2 = x3 + 10x + 8 mod 11 And we…

Answered: Consider the elliptic curve group based…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q3)Find the following: 1- 0={2,1}, J={1,2,4,6,5,3}, and , R={5,4,2},T={6,5,1}Prove (OUR)c = OcnRc. 2- Ln(LUT) is equal to 3- 0={2,1}, J={1,2,4,6,5,3}, and , R={5,4,2},T={6,5,1}Prove On(RUT) = (ONR)U(OnT). 4- Mn(NUM)c equals 5- K={x: x positive number multiple of 3 equal and less than 99}W={x: x prime number equal and less than 19}Find n(K)+n(W)
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Question 12 of 34 Evaluate x3 ( ²)zdx 4+x .2 OA) (4+x^2 )^(5/2) (5x^2-8))/35+C OB) I DONT KNOW O)(4+x^2 Y (5/2) (5x^2-8))45+C D) NONE OF THESE Previous
[Glc-1-P]eq + [Glc-6-P] éq = 1 M Kéq = [Glc-6-Pleq [Glc-1-Pléq = 18,78 from equation 1 and 2 can you exlain how we get the equation below : (18,78 + 1) [Glc-1-P]éq = 1 M [Glc-1-Pleq = 1 2 1 M 19,78 = 0,05056 M [Glc-6-P]eq = 1 M -0,05056 M = 0,94944 M
(3) Let the elliptic curve & be y² = x³ + x + 6 (mod 11). (a) Given the point a = (2,7) on the elliptic curve E, calculate 2a and 3a. (b) Consider the elliptic curve ElGamal cryptosystem. Let the private key be s = 7. (i) What is the public key? (Hint: You don't need to include the known information E, p, a in the public key, but have to calculate = sa. ) (ii) Encoding: Suppose the text has been converted to a point x = (10, 9) on E. Choose the random number k 3. What are the points (or numbers) to be transmitted? = (iii) Decoding: When receiving information from (ii), how to recover the original text?
(4 5 kuvvet serisinin yakınsaklık aralığgı aşagıdakilerden hangisidir? [0. ) (0, 2 0,2) (0,) (0,) b) Bos birak Kapat 1/70
Question 17 (Mandatory) (3.5 points) x3 = s² x1 x2 mod p and = Y3 : S(x1 − x3) — y₁ mod p where S= y2-y mod p; if P * Q (point addition) X2-X1 3x² + a 2yı = mod p if P Q (point doubling) (Show your work.) Consider the elliptic curve given by y² 3 x + 2x + 2 mod 17. The result of adding the points (9, 16) and (13, 7) is ○ a) (7,6) b) (7,11) c) (9,16) d) (16,4) Previous Page Next Page Page 17 of 30
Example 19-5. Use the method of separation of symbols to prove the following identities : (a) Uo + U1 + ... + U, = ( "i') Uo +( "2') auo +(") a²u, + .. n + 1 n + N + 1 3 + ( *:) a" n + 1 (b) Uz x + Uz x² + Uz x³ + .. x² %3D (1– x) U1 + (1 – x)2AU1 + (1 – x)34²U¡ + .. |
Let X be a uniform random variable on the interval [-1, 3] such that:u2 + 4Xu + 1 = 0.1. What is the probability that this equation has complex roots?2. What is the probability that this equation has real rootsdistinct roots?3. What is the probability that this equation has a double root?
1.1.2
19. Express in a + bi form: (5 – 6yi)(4 + 8i) – [(2 – 3yi) – 3(1 + 6i)] - |

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Consider the elliptic curve group based on the equation where a = 10, b = 8, and p = 11. In this group, what is 2(2, 5) = (2, 5) + (2, 5) ? In this group, what is (2, 6) + (6, 3)? What is the inverse of (6, 8) (with entries in Z11)? y² = x³ + ax + b mod P