Elliptic curves

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  • Elliptic Curves from Scratch: Group Law, Double-and-Add and a Toy ECDH

    Building elliptic-curve cryptography up from the chord-and-tangent rule to scalar multiplication and a working Diffie–Hellman exchange on a 103-point curve, then showing exactly why that curve is worthless.

    10 min read 1,848 words Category: Security Tags: cryptography, elliptic curves, python

  • CO: A Cubic Surface, a Hyperplane Section, and a Flag Collected One Small Prime at a Time

    A write-up of the crypto challenge CO from WannaGame Championship 2025, where the group lives on a cubic surface in projective 3-space, a hyperplane through the given points cuts it into an ordinary elliptic curve, and the same secret scalar reused across attacker-chosen primes falls to Pohlig-Hellman and the CRT.

    8 min read 1,528 words Category: Security Tags: ctf, cryptography, elliptic curves