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For K-12 Students · Elliptic Curve

Elliptic Curve for a hash collision

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a hash collision live below — adjust the inputs and watch it respond, right in your browser.

Elliptic Curve AdditionLive

the geometry behind ECC

Controls

Presets

Curve parameter a

Curve parameter b

Point P (x)

Point Q (x)

On an elliptic curve y² = x³ + ax + b, you "add" two points with a geometric rule: draw the line through P and Q, find where it meets the curve again, and reflect that point over the x-axis. Repeating this addition is easy, but reversing it — the elliptic-curve discrete log — is brutally hard, which is what makes ECC secure with far smaller keys than RSA.

▶ Run in Python

Data Inspector

Slope-0.14

P+Q (x)0.52

P+Q (y)-0.79

Governing equation

y^{2} = x^{3} - 1.0 x + 1.0, λ = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} = - 0.14

Reading this result: The secant through P and Q meets the curve at a third point; reflecting it across the x-axis gives P+Q. Repeating this is easy, but undoing it (the discrete log) is what secures ECC.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Elliptic Curve for a hash collision" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.