Category
9 articles in this category.
BLS signatures use a bilinear pairing on the curve BLS12-381 to make short, deterministic signatures that can be added together into one. Learn how a pairing works, how a message is hashed to a curve, how aggregation saves space, and how a rogue key attack is stopped.
39 min read
ECDH lets two parties agree on a shared secret using points on an elliptic curve. Learn how P-256, P-384, and secp256k1 define the group, how public keys are encoded and validated, why the secret is only an x coordinate, and how an invalid-curve attack works.
23 min read
ECDSA is the elliptic curve version of DSA, used to sign TLS handshakes and Bitcoin transactions. Learn how signing and verifying work, why a repeated nonce reveals the private key, how RFC 6979 removes that risk, and how a signature is encoded.
23 min read
Ed25519 is the EdDSA signature scheme on the Edwards curve of Curve25519, defined in RFC 8032. Learn how a 32-byte seed becomes a key, how a deterministic nonce replaces random numbers, how a signature is checked with the cofactor, and why the range check on S matters.
19 min read
Shamir's secret sharing splits a secret into shares so that any k of n shares rebuild it and fewer reveal nothing at all. Learn how a polynomial hides the secret, how Lagrange interpolation recovers it, why k minus one shares give no information, and how GF(256) makes the scheme work on bytes.
20 min read
X25519 is the Diffie-Hellman function on Curve25519, defined in RFC 7748. Learn how a 32-byte private key is clamped, how the Montgomery ladder multiplies a point using only its u coordinate, why the curve was chosen, and what the all-zero check protects against.
18 min read
ECC gets RSA-level security from far smaller keys. Here's the curve math behind it, and why it now powers most of the web.
13 min read
ElGamal turns Diffie-Hellman key exchange into full public-key encryption. Here's how the discrete-log problem protects every message it sends.
7 min read
EdDSA replaced random nonces with deterministic ones, closing off one of ECDSA's worst failure modes. Here's the math behind Ed25519.
8 min read
