Elliptic Curve Point Calculator
Add two points on a small prime-field elliptic curve and inspect the result. An educational calculator, unsuitable for production cryptography.
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Elliptic Curve Point Calculator
Add two points on a small prime-field elliptic curve and inspect the result. An educational calculator, unsuitable for production cryptography.
Worked example
a = 2; p = 17; P = (5,1); Q = (6,3)
P + Q = (10, 6)
Input and calculation
Set curve coefficient a to 2 and prime modulus p to 17. Enter P as 5,1 and Q as 6,3. Each point uses integer coordinates separated by one comma.
Run point addition. Expect P + Q = (10, 6). For P = 5,1 and Q = 5,16, expect the point at infinity.
Limits
The curve is y² = x³ + ax + b modulo p; b is derived from P and Q must lie on that curve. Use an odd prime from 3 to 200,000. This is a teaching tool for one point addition, not key generation, signatures or production cryptography.
Enter comma- or whitespace-separated safe integers; decimals are not allowed. -9007199254740991 ≤ a, xP, yP, xQ, yQ ≤ 9007199254740991
a: 2; p: 17; P: 5,1; Q: 6,3; P + Q = (10,6)
4a³ + 27b² ≡ 0 (mod p): The curve is singular; elliptic-curve point addition is not supported.
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