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Foundations: Cryptography / Curves

What is X25519?X25519 is one of the most widely deployed ways to do modern Diffie–Hellman key exchange, but its importance is not just speed

What is X25519?X25519 is one of the most widely deployed ways to do modern Diffie–Hellman key exchange, but its importance is not just speed. It was designed so secure, constant-time implementations are much easier to get right, which is why it appears across TLS 1.3, Noise, WireGuard, and many cryptographic libraries.Mar 21, 202622 min read

What Is Elliptic Curve Cryptography?Elliptic Curve Cryptography lets modern systems get strong public-key security with much smaller keys than older designs

What Is Elliptic Curve Cryptography?Elliptic Curve Cryptography lets modern systems get strong public-key security with much smaller keys than older designs. Its power comes from a simple asymmetry: multiplying a curve point is easy, but reversing that multiplication appears hard — and that gap supports signatures, key exchange, and much of today’s wallet infrastructure.Mar 21, 202627 min read

What is secp256k1?secp256k1 is the elliptic curve behind Bitcoin keys, legacy Ethereum transaction signatures, and many other blockchain systems

What is secp256k1?secp256k1 is the elliptic curve behind Bitcoin keys, legacy Ethereum transaction signatures, and many other blockchain systems. Its importance is easy to underestimate: a short parameter list defines the exact mathematical world in which private keys, public keys, and signatures all have to agree.Mar 21, 202622 min read

What is Curve25519?Curve25519 matters because it made strong elliptic-curve cryptography easier to implement safely, not just faster

What is Curve25519?Curve25519 matters because it made strong elliptic-curve cryptography easier to implement safely, not just faster. Its design ties together a carefully chosen curve, a prime field that computers handle efficiently, and formulas that support constant-time key exchange in real protocols like TLS.Mar 21, 202622 min read