## One Clock Cycle Polynomial Math

Error correction codes and cryptographic computations are most easily performed working with $GF(2^n)$  polynomials.  By using very special values of $n$ we can build circuits which multiply and square in one clock cycle on an FPGA. These circuits come about by flipping back and forth between a standard polynomial basis and a normal basis representation of elements in $GF(2^n)$.

A normal basis is yet another form of polynomial but instead of adding powers of $\beta$ we add...

## Elliptic Curve Cryptography

Secure online communications require encryption.  One standard is AES (Advanced Encryption Standard) from NIST.  But for this to work, both sides need the same key for encryption and decryption.  This is called Private Key encryption.  Public Key encryption is used to create a private key between two sides that have not previously communicated.  Compared to the history of encryption, Public Key methods are very recent having been started in the 1970's.  Elliptic...

## An absolute position encoder VHDL core

November 11, 2015
Introduction

Let's consider motorized systems controlled by electronics. A closed loop architecture looks like this:

The following components are involved:

• the motor itself (DC, stepper ...),
• the controller, in charge of computing position according to the whole system state,
• the driver board in charge of generating signals and power for the motor,
• the position encoder, the subject of this post.

Most of the time, there is a difference between the position the system...

## Helping New Bloggers to Break the Ice: A New Ipad Pro for the Author with the Best Article!

November 9, 2015

Breaking the ice can be tough.  Over the years, many individuals have asked to be given access to the blogging interface only to never post an article.  Maybe they underestimated the time it takes to write a decent article, or maybe they got cold feet. I don't blame or judge them at all - how many times in my life have I had the intention to do something but didn't follow through?  Once, maybe twice 😉 (don't worry if you don't...

## Polynomial Math

Elliptic Curve Cryptography is used as a public key infrastructure to secure credit cards, phones and communications links. All these devices use either FPGA's or embedded microprocessors to compute the algorithms that make the mathematics work. While the math is not hard, it can be confusing the first time you see it.  This blog is an introduction to the operations of squaring and computing an inverse over a finite field which are used in computing Elliptic Curve arithmetic. ...

## Welcoming MANY New Bloggers!

The response to the latest call for bloggers has been amazing and I am very grateful.

In this post I present to you the individuals who, so far (I am still receiving applications at an impressive rate and will update this page as more bloggers are added),  have been given access to the blogging interface.  I am very pleased with the positive response and I think the near future will see the publication of many great articles, given the quality of the...

## Recruiting New Bloggers!

Previous calls for bloggers have been very successful in recruiting some great communicators - Rick LyonsJason Sachs, Victor Yurkovsky, Mike Silva, Markus NentwigGene BrenimanStephen Friederichs,

## Summer of Gateware

September 18, 2015

This (last) summer the MyHDL project participated in the Google Summer of Code (GSoC) as a sub-organization under the Python Software Foundation (PSF). This was our first year participating - there was a lot for us to learn.  Overall it was a worthwhile and beneficial activity.

Being a first time sub-org we were limited to a maximum of two students.  We had nine students apply and twelve mentors volunteer.  Only being able to select two students...

In this article I will take a look at the wonderful MuPDF viewer and present a small modification that saves bookmarks alongside the pdf files, making it infinitely more useful.

Some days I sit down to work and wonder how anything ever gets done. A simple example.  When I work on an FPGA design, I wind up with 3 or 4 screens full of documentation, generally in PDF format.  There are the Xilinx manuals, the various tool manuals, language reference manuals, you name it.  While...

## Inside the Spartan-6: Using LUTs to optimize circuits

While building a small CPU on a Spartan-6 chip I came across the same old problem: my Verilog was mapping to a lot of slices . Way more then seems reasonable. So let's dig in and see what's really going on.

The J1 CPU (see Messing Around with a J1) is an amazingly streamlined design expressed in just over 100 lines of Verilog, and is reasonably compact at 150 Spartan-6 slices (half of that with the modifications described in the article).  But the Picoblaze is...

## MyHDL Resources and Projects

Last updated 07-Nov-2017

MyHDL Resources

If you want to dive into MyHDL (digital hardware description in Python) there are many resources available.  Below is a list of MyHDL resources, including some of the past blogs here on fpgarelated.

The MyHDL manual is a great (probably the best) place to get started.

The manual is an in-depth introduction to MyHDL.  The concepts are well explained and there are examples to test while working through the...

## Crowdfunding Articles?

Many of you have the knowledge and talent to write technical articles that would benefit the EE community.  What is missing for most of you though, and very understandably so, is the time and motivation to do it.

But what if you could make some money to compensate for your time spent on writing the article(s)?  Would some of you find the motivation and make the time?

I am thinking of implementing a system/mechanism that would allow the EE community to...

## Makefiles for Xilinx Tools

Building a bitstream from an HDL is a complicated process that requires the cooperation of a lot of tools.  You can hide behind an IDE or grow a pair and use command line tools and a makefile to tie your build process together.  I am not a huge fan of makefiles either (I believe a language should be expressive enough to automate the build process), but the alternatives are dismal.

Command-line driven workflow is easier on the hands and faster.  The example...

## FPGA Assemblers and Time Machines

September 2, 20121 comment

Flashback to 1986. A young man has a crazy idea - he wants to make a CPU all by himself. He is reading early Xilinx manuals cover to cover as if they were novels. Yes, you are quick - this is indeed a (mostly) true story about me and my dream, suddenly made possible by this new FPGA technology.

Sadly more than 20 years went by before my first CPU ran in a Xilinx FPGA. Why did it take so long? Every few years I set up the tools and every time I walked away, scared silly. As the years...

## Back from Embedded World 2019 - Funny Stories and Live-Streaming Woes

March 1, 20191 comment

When the idea of live-streaming parts of Embedded World came to me,  I got so excited that I knew I had to make it happen.  I perceived the opportunity as a win-win-win-win.

• win #1 - Engineers who could not make it to Embedded World would be able to sample the huge event,
• win #2 - The organisation behind EW would benefit from the extra exposure
• win #3 - Lecturers and vendors who would be live-streamed would reach a (much) larger audience
• win #4 - I would get...

## Back from ESC Boston

NOT going to ESC Boston would have allowed me to stay home, in my comfort zone.

NOT going to ESC Boston would have saved me from driving in the absolutely horrible & stressful Boston traffic1.

NOT going to ESC Boston would have saved me from having to go through a full search & questioning session at the Canada Customs on my return2.

2017/06/06 update: Videos are now up!

So two days...

## Data Types for Control & DSP

There's a lot of information out there on what data types to use for digital signal processing, but there's also a lot of confusion, so the topic bears repeating.

I recently posted an entry on PID control. In that article I glossed over the data types used by showing "double" in all of my example code.  Numerically, this should work for most control problems, but it can be an extravagant use of processor resources.  There ought to be a better way to determine what precision you need...

## binary hello world

Python + Ohio + MyHDL + FPGA

Recently I had the opportunity to coordinate a hands-on programmable hardware (FPGA) workshop (open-space) at a regional Python conference - @pyohio. The workshop was for those that had little to no exposure to programmable hardware. For this situation I used two basic examples: two versions of a binary hello world.

The binary hello world -- blinking an LED -- is a good starting point to introduce programmable hardware, hardware descriptions languages,...