I firmly believe that designing custom silicon is currently needlessly difficult. I’m also an unabashed supporter of auditable, privacy-respecting silicon.

Lastly, I’m just another programmer with a fancy camera working for a startup. The date on a page is when it was first written, not when it was last edited. Find my archived content here

For quick reference, here is the yosys manual as of July 26, 2021.

# Rational Points on Elliptic Curves

Rational Points on Elliptic Curves How can we find all rational points on an elliptic curve? Knowns The Elliptic Curve(ECC) equation: $$y^2 = x^3 - 2x$$ A point on the ECC: $$P_0 : (x_0, y_0)$$ A Better Defined Problem Instead of trying to find all rational points on an ECC outright, how about we try to solve the following problem which appears to be better defined and might also give us the insight needed to find all rational points.…

# Succinct Trig-Free Parametric Circles

Introductory Remarks Recently, I've been studying asymmetric elliptic cryptography so that I can implement a bitcoin client that can read and engage with the bitcoin blockchain. I'm also studying ECC to better enable me to reason about an election system that uses public and private keys, and signs hashed votes with private keys. The Description I came across the following description of a circle when working through this material. $(\frac {1 - t^2}{1 + t^2}, \frac {2t}{1 + t^2})$…