Based on your application, your task is to implement elliptic curve points over a finite field class. To get maximum points for this task you need:
- Implement point addition operation.
- Implement scalar multiplication for a given point.
- Function that finds order of the elliptic curve group
- Provide a basic documentation for the code or answer my questions about how code works in person.
https://cs-math-elliptic-curve-points.web.app
When user loads the program 2 graphs are generated with (function plotter) which have starting functions with initial values. Function parameters are configurable via UI which change variables that turn to math service for computation. Variables can be copied to allow sharing of settings.
Program code is designed to be slightly "dumb" - to not use overly clever syntax and keep code flow readable. Interesting part happens in math.service.ts, rest of the code is just semantics and UI stuff.
UI controls should be intuitive, follow color coding for lines and points.
Error level messages indicates errors that should not happen. Warning levels indicate something went wrong, but was corrected for the user. Information level messages are just informative that something special happened in background.
Flow: Element(UI input) <───> functionPlot(Fn)
└───────────────────┴─── variables <───> math.service.ts
Each element on a graph is a function (solving for y or cords etc.). Graph functions (lines, curves, points) ask computation from match service. Calculation is relative, meaning changes to parameters (e.q. P, Q) will reflect on R. Some edge cases are covered (stopping user going out of bounds for x, when Q=P, selecting closest x root etc.) Calculations are here:
Due to limitations of calculating from geometric method to algebraic method Accuracy on chart is around ~ > .0001 Computational and performance wise lower decimal points may be rounded for plotting which introduces errors. Hence, you may notice line thickening on graph that happens due to inaccuracy. Meaning R on the plotter is on Curve with 99.9999% accuracy (or better).
Cool implementation of custom method logger using decorator @Log()
- Plotter - https://mauriciopoppe.github.io/function-plot/
- Source - http://pi.math.cornell.edu/~dwh/courses/M403-S03/cubics.htm
- Source - http://www.math.utah.edu/~wortman/1060text-tcf.pdf
- Source - https://medium.com/understanding-ecc/understanding-the-ellyptic-curve-cryptography-d91c11e4e331
- Source - https://bearworks.missouristate.edu/cgi/viewcontent.cgi?article=4697&context=theses
- Funny - https://eprint.iacr.org/2013/635.pdf
[07:06:17.885] fnRecalculatePQ -> IN: {change: Array(2), prev: Array(2), curvePoints: Array(103)} OUT: (2) [31, 35]
[07:06:17.885] invert -> IN: {n: -31, k: 101} OUT: 13
[07:06:17.886] fnAddPoint -> IN: {p: Array(2), q: Array(2), k: 101, a: 10} OUT: (2) [45, 73]
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