Elliptic Curve Key Exchange
Elliptic Curve Cryptography is used to create a Public Key system that allows two people (or computers) to exchange public data so that both sides know a secret that no one else can find in a reasonable time. The simplest method uses a fixed public key for each person. Once cracked, every message ever sent with that key is open. More advanced key exchange systems have "perfect forward secrecy" which means that even if one message key is cracked, no other message will...
DiscreteTime PLLs, Part 1: Basics
Design Files: Part1.slx
Hi everyone,
In this series of tutorials on discretetime PLLs we will be focusing on PhaseLocked Loops that can be implemented in discretetime signal proessors such as FPGAs, DSPs and of course, MATLAB.
In the first part of the series, we will be reviewing the basics of continuoustime baseband PLLs and we will see some useful mathematics that will give us insight into the inners working of PLLs. In the second part, we will focus on...
Polynomial Inverse
One of the important steps of computing point addition over elliptic curves is a division of two polynomials. When working in $GF(2^n)$ we don't have large enough powers to actually do a division, so we compute the inverse of the denominator and then multiply. This is usually done using Euclid's method, but if squaring and multiplying are fast we can take advantage of these operations and compute the multiplicative inverse in just a few steps.
The first time I ran across this...
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
IntroductionLet'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!
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 Lyons, Jason Sachs, Victor Yurkovsky, Mike Silva, Markus Nentwig, Gene Breniman, Stephen Friederichs,
Feedback Controllers  Making Hardware with Firmware. Part I. Introduction
Introduction to the topicThis is the 1st in a series of articles looking at how we can use DSP and Feedback Control Sciences along with some mixedsignal electronics and numbercrunching capability (e.g. FPGA), to create arbitrary (within reason) Electrical/Electronic Circuits with realworld connectivity. Of equal importance will be the evaluation of the functionality and performance of a practical design made from modestlypriced state of the art devices.
 Part 1:
Live Streaming from Embedded World!
For those of you who won't be attending Embedded World this year, I will try to be your eyes and ears by video streaming live from the show floor.
I am not talking improvised streaming from a phone, but real, high quality HD streaming with a highend camera and a device that will bond three internet connections (one wifi and two cellular) to ensure a steady, and hopefully reliable, stream. All this to hopefully give those of you who cannot be there in person a virtual...
Went 280km/h (174mph) in a Porsche Panamera in Germany!
Those of you who've been following my blog lately already know that I am going through some sort of midlife crisis that involves going out there to meet people and make videos. It all started with Embedded World early this year, then continued at ESC Boston a couple of months ago and the latest chapter just concluded as I returned from Germany after spending a week at SEGGER's headquarters to produce a video to highlight their 25th anniversary.
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...
How to start in FPGA development?  Some tips
IntroductionThe aim of this tutorial is to show some useful tips for people like me that one day started from zero to work with FPGA's. Why FPGA's? Because they are easy to use and they are not too expensive, and they are usually used in lab courses to let students "play" with them.
1: How to choose the right FPGA?As you may know there are a lot of different FPGA's, brands and models. How to choose the right one? It's very difficult to say that before knowing which will be the...
VGA Output in 7 Slices. Really.
Ridiculous? Read on  I will show you how to generate VGA timing in seven XilinxR Spartan3R slices.Some time ago I needed to output video to a VGA monitor for my Apple ][ FPGA clone. Obviously (I thought), VGA's been done before and all I had to do was find some Verilog code and drop it into my design. As is often the case (with me anyway), the task proved to be very different from my imagined 'couple of hours to integrate the IP'.I found some example code for my board. I...
StrangeCPU #4. Microcode
Summary:Sliding windows containing runs of microcode.
Table of Contents:
Part 1: A new CPU  technology review, reexamination of the premises; StrangeCPU concepts; x86 notes.

Part 2: SlidingWindow Token Machines, an indepth exploration of this curious technology; ARM notes.
FPGA or DSP Processor  Parameters to Make the Right Choice
Introduction
Digital Signal Processing (DSP) has a huge global market that is growing fast day by day with rapidly evolving sophisticated modern electronics applications like 3G wireless, voice over internet protocol (VoIP), multimedia systems, radar and satellite systems, medical systems, imageprocessing applications and consumer electronics. These sophisticated DSP applications pose many conflicting challenges to system designers and application developers in terms of cost and...
Fit Sixteen (or more) Asynchronous Serial Receivers into the Area of a Standard UART Receiver
IntroductionThis article will describe a technique, available in many current FPGA architectures, to fit a large amount of logic into a small area. About ten years ago now (Feb/Mar 2005), I helped develop a multiline Caller ID product. The MultiChannel Asynchronous Receiver (MCAR) FPGA core developed for that product will be used to illustrate the technique(s) needed to fit a 16 channel MCAR into a single Spartan II XC2S305VQ100 FPGA.
To stay true to the original design, I...
Feedback Controllers  Making Hardware with Firmware. Part 7. Turbocharged DSP Oscillators
This article will look at some DSP Sinewave oscillators and will show how an FPGA with limited floatingpoint performance due to latency, can be persuaded to produce much higher samplerate sinewaves of high quality.Comparisons will be made between implementations on Intel Cyclone V and Cyclone 10 GX FPGAs. An Intel numerically controlled oscillator
FPGA Assemblers and Time Machines
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...
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...
MyHDL Resources and Projects
Last updated 07Nov2017
MyHDL ResourcesIf 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 indepth introduction to MyHDL. The concepts are well explained and there are examples to test while working through the...
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 + FPGARecently I had the opportunity to coordinate a handson programmable hardware (FPGA) workshop (openspace) 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,...
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.
Commandline driven workflow is easier on the hands and faster. The example...
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...
SEGGER's 25th Anniversary Video
Chances are you will find this video more interesting to watch if you take five minutes to first read the story of the week I spent at SEGGER's headquarters at the end of June.
The video is only a little more than 2 minutes long. If you decide to watch it, make sure to go full screen and I would really love to read your thoughts about it in the comments down bellow. Do you think a video like this succeeds in making the viewer want to learn more about the company?...
Running Average
The running average filter is a useful way to reduce noise in a system. One project I recently worked on required a 4 times frequency output from an encoder input. The problem was the encoder is mounted to the wheel of an old truck and bearing noise was making the original algorithm generate way too many pulses. The original algorithm worked, but the noise on the input made it useless.
I first implemented the moving average based on