5. An elliptic curve is a curve of the form y² = x³ + ax +b for some constants a, b. These curves are extremely special addition given by the following picture: P R P+Q P Q R=0 Addition of distinct points P TOT=O that they admit an R ΡΘΡ Adding a point to itself Figure 1: Elliptic curve addition (Image from [Sil09]) In particular, as shown in the second image, adding a point P to itself requires finding the tangent line to the curve at P. (a) Verify that the point (-4,-3) lies on the curve y² = x³ + 73. (b) Compute the sum (−4, −3) & (−4, −3) using the description and picture above. Verify that this point is also on the curve.
5. An elliptic curve is a curve of the form y² = x³ + ax +b for some constants a, b. These curves are extremely special addition given by the following picture: P R P+Q P Q R=0 Addition of distinct points P TOT=O that they admit an R ΡΘΡ Adding a point to itself Figure 1: Elliptic curve addition (Image from [Sil09]) In particular, as shown in the second image, adding a point P to itself requires finding the tangent line to the curve at P. (a) Verify that the point (-4,-3) lies on the curve y² = x³ + 73. (b) Compute the sum (−4, −3) & (−4, −3) using the description and picture above. Verify that this point is also on the curve.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![5. An elliptic curve is a curve of the form
y² = x³ + ax + b
for some constants a, b. These curves are extremely special in that they admit an
addition given by the following picture:
P
R
P+Q
P Q R=0
Addition of distinct points
T
P
TOT=O
R
ΡΘΡ
Adding a point to itself
Figure 1: Elliptic curve addition (Image from [Sil09])
In particular, as shown in the second image, adding a point P to itself requires finding
the tangent line to the curve at P.
(a) Verify that the point (−4, −3) lies on the curve y² = x³ + 73.
(b) Compute the sum (−4, −3) + (−4, −3) using the description and picture above.
Verify that this point is also on the curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e5ea172-2838-4041-9e7f-74e8cb5bb4e3%2Ffae52831-8e4c-4871-b09b-0161832712ab%2F9mm749d_processed.png&w=3840&q=75)
Transcribed Image Text:5. An elliptic curve is a curve of the form
y² = x³ + ax + b
for some constants a, b. These curves are extremely special in that they admit an
addition given by the following picture:
P
R
P+Q
P Q R=0
Addition of distinct points
T
P
TOT=O
R
ΡΘΡ
Adding a point to itself
Figure 1: Elliptic curve addition (Image from [Sil09])
In particular, as shown in the second image, adding a point P to itself requires finding
the tangent line to the curve at P.
(a) Verify that the point (−4, −3) lies on the curve y² = x³ + 73.
(b) Compute the sum (−4, −3) + (−4, −3) using the description and picture above.
Verify that this point is also on the curve.
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