Elliptic curve cryptography replaced RSA for nearly every modern protocol because it delivers the same security with a fraction of the key size and the compute. We walk what an elliptic curve actually is, why the discrete-log problem on a curve is hard, the genuine differences between P-256 and Curve25519 politically and technically, how signing differs from key exchange, and which curve belongs in which job in 2026.
Ed25519
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Elliptic Curve Cryptography for the Curious Engineer