clz - opcode to return number of leading 0s in a bit Before clz Binary search to find most and least significant bits With clz msb = 255 - clz(x) lsb = 255 - clz(x & -x) What's x & -x? See code comment Code github.com/t4sk/notes/blob/m… Binary examples github.com/Uniswap/v3-core/b…

Groth16 I will explain the complex equations in the future Notes github.com/t4sk/notes

Elliptic curve add, scalar mul and pair Solidity examples Operations are executed by calling precompiles Reverts if point are invalid (0, 0) is point at infinity Code github.com/t4sk/notes/blob/m…

EC pairing Notes github.com/t4sk/notes

Most digestable explanation of Groth16 soundness building-babylon.net/2026/08… Compares the coefficients for A, B and C and deduces that the ending equation is the Groth16 equation.

How to evaluate a polynomial at a point on a elliptic curve Notes github.com/t4sk/notes

Schwartz-Zippel Lemma explains why evaluating polynomials at a single random point is sufficient to conclude that polynomial identity u(x)v(x) = w(x) + h(x)t(x) is true for all x, with high probability Notes github.com/t4sk/notes

Groth16 QAP part 2

Groth16 QAP part 1 Notes github.com/t4sk/notes

ECDH - Elliptic Curve Diffie-Hellman Used to create a shared key for symmetric encryption Shared key [s] is never revealed over any communication channel More notes github.com/t4sk/notes