(6) Let P = (x, y) be a point on an elliptic curve E : y² = x³ + bx+c (mod p). The smallest positive integer n such that POPOOP: nP = ∞0. In times. is called the order of P. Compute the order of the point (3, 2) on the elliptic curve y² = x³ - 2 (mod 7).
(6) Let P = (x, y) be a point on an elliptic curve E : y² = x³ + bx+c (mod p). The smallest positive integer n such that POPOOP: nP = ∞0. In times. is called the order of P. Compute the order of the point (3, 2) on the elliptic curve y² = x³ - 2 (mod 7).
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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![(6) Let \( P = (x, y) \) be a point on an elliptic curve \( E: y^2 \equiv x^3 + bx + c \) (mod \( p \)).
The smallest positive integer \( n \) such that
\[
\underbrace{P \oplus P \oplus \cdots \oplus P}_{n \text{ times}} := nP = \infty.
\]
is called the order of \( P \). Compute the order of the point \( (3, 2) \) on the elliptic curve \( y^2 \equiv x^3 - 2 \) (mod 7).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb59f2b3-b797-4fcf-b1df-52d222f437c9%2F6b84ce69-c6b3-4d4c-a92a-5ab0423e850d%2Fmf2jv8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(6) Let \( P = (x, y) \) be a point on an elliptic curve \( E: y^2 \equiv x^3 + bx + c \) (mod \( p \)).
The smallest positive integer \( n \) such that
\[
\underbrace{P \oplus P \oplus \cdots \oplus P}_{n \text{ times}} := nP = \infty.
\]
is called the order of \( P \). Compute the order of the point \( (3, 2) \) on the elliptic curve \( y^2 \equiv x^3 - 2 \) (mod 7).
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