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equation Consider the elliptic curve group based on the y² = x³ + ax + b where a = 2, b = 1, and p = 5. In this group, what is 2(0, 1) = (0, 1) + (0, 1)? mod p In this group, what is (0, 4) + (1, 2)? What is the inverse of (1, 3) (with entries in Z5)?

equation Consider the elliptic curve group based on the y² = x³ + ax + b where a = 2, b = 1, and p = 5. In this group, what is 2(0, 1) = (0, 1) + (0, 1)? mod p In this group, what is (0, 4) + (1, 2)? What is the inverse of (1, 3) (with entries in Z5)?

Advanced Engineering Mathematics
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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**Educational Content on Elliptic Curve Groups** Consider the elliptic curve group based on the equation: \[ y^2 \equiv x^3 + ax + b \mod p \] where \( a = 2 \), \( b = 1 \), and \( p = 5 \). 1. In this group, what is \( 2(0, 1) = (0, 1) + (0, 1) \)? **Answer:** [ ] 2. In this group, what is \( (0, 4) + (1, 2) \)? **Answer:** [ ] 3. What is the inverse of \( (1, 3) \) (with entries in \( \mathbb{Z}_5 \))? **Answer:** [ ] These questions explore operations within an elliptic curve group, specifically focusing on point doubling, addition, and finding inverses within a finite field.
Transcribed Image Text:**Educational Content on Elliptic Curve Groups** Consider the elliptic curve group based on the equation: \[ y^2 \equiv x^3 + ax + b \mod p \] where \( a = 2 \), \( b = 1 \), and \( p = 5 \). 1. In this group, what is \( 2(0, 1) = (0, 1) + (0, 1) \)? **Answer:** [ ] 2. In this group, what is \( (0, 4) + (1, 2) \)? **Answer:** [ ] 3. What is the inverse of \( (1, 3) \) (with entries in \( \mathbb{Z}_5 \))? **Answer:** [ ] These questions explore operations within an elliptic curve group, specifically focusing on point doubling, addition, and finding inverses within a finite field.
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