MHB How to Use Elliptic Curve Cryptography to Find Inverses and Points on the Curve?

AI Thread Summary
To solve the elliptic curve equations y² = x³ + x + 1 mod 17 and y² = x³ + 3x + 1 mod 13, one approach is to evaluate the equations for all integer values of x within the specified modulus. This method allows for the identification of all points on the curve. Once the points are determined, inverses can also be calculated based on the results. Additionally, visualizing the curves by plotting the points can enhance understanding of the relationships between them. This process aids in improving calculus skills related to elliptic curve cryptography.
vokoyo
Messages
9
Reaction score
0
May I know how to solve the equation as below:

(1) y2 = x3 + x + 1 mod 17

Finding Inverses
Finding Points on the Curve

(2) y2 = x3 + 3x + 1 mod 13

Finding Inverses
Finding Points on the Curve
 
Last edited by a moderator:
Mathematics news on Phys.org
vokoyo said:
May I know how to solve the equation as below:

(1) y2 = x3 + x + 1 mod 17

Finding Inverses
Finding Points on the Curve

Hi vokoyo,

How about filling in $x=0, ..., 16$.
Those are all the relevant possibilities for $x$.
After that the same results will appear periodically.

That way we find all the points on the curve.
And from the results we can also find all inverses, can't we?
 
Thank you very much for your advice and suggestion

Please show me your sample solution draft
so that I can improve my calculus skills

I fact I would like to draw the curve line or point by point
 
Last edited by a moderator:

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

A Finding Minimal Mean Distance Curves on the Unit Sphere
Replies
2
Views
2K
B Solving the Heart Curve Equation: 'y =
Replies
18
Views
4K
MHB Tell me, must I use m = (y2 - y1)/(x2 - x1), where m is 1/4?
Replies
12
Views
2K
How to Begin Solving a Basic Open B-Spline Curve with Given Control Points?
Replies
11
Views
6K
MHB How do I find the Euclidean Coordinate Functions of a parametrized curve?
Replies
1
Views
1K
MHB How to solve Chinese Remainder Theorem
Replies
11
Views
3K
B Are Inverse Problems More Complex Than Direct Problems in Mathematics?
Replies
13
Views
3K
MHB How Do I Find a Point on a Curve with a Specific Slope?
Replies
2
Views
1K
I Partial Differential Equation solved using Products
Replies
2
Views
2K
I Finding Perpendicular Spirals in a Family of Curves
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top