About this episode

Brian and Rob recap their experiences in Vegas and discuss elliptic curve point operations in detail.

The Study guide: https://ecc-study-guide.magicinternetmath.com/guide.pdf In this episode, I (Brian) finally introduce myself properly and Rob and I kick off with a Vegas + Bitcoin++ recap before diving back into Chapter 6 of our elliptic curve study guide. We talk small, dev‑focused conferences versus mega‑cons, the Hoover Dam power-plant tour, and the standout conversations around quantum risk, BitVM, and Binohash. We also share plans to bring a math‑track BitDevs to Philly and to run a hands‑on Codex32 workshop soon. Then we slow things down to the math. Using the curve over the reals as a warmup, we revisit the group axioms that make elliptic curves useful for Bitcoin: identity (the point at infinity), inverses (reflect across the x‑axis), closure, and associativity. We sketch point addition and doubling, why doubling accelerates scalar multiplication, and how this geometry-algebra fusion underpins private→public key derivation. Along the way we touch BIP‑68 relative timelocks, why secp256k1’s simple y^2=x^3+7 form is performant, and where post‑quantum work like FROST and research at ZeroSync/Localhost is heading. 'Magic Internet Math (site)': https://magicinternetmath.com/…

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