## 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...

## Discrete-Time PLLs, Part 1: Basics

Design Files: Part1.slx

Hi everyone,

In this series of tutorials on discrete-time PLLs we will be focusing on Phase-Locked Loops that can be implemented in discrete-time signal proessors such as FPGAs, DSPs and of course, MATLAB.

In the first part of the series, we will be reviewing the basics of continuous-time 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,

## 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 multi-line Caller ID product. The Multi-Channel 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 XC2S30-5VQ100 FPGA.

To stay true to the original design, I...

## Feedback Controllers - Making Hardware with Firmware. Part 2. Ideal Model Examples

Developing and Validating Simulation ModelsThis article will describe models for simulating the systems and controllers for the hardware emulation application described in Part 1 of the series.

- Part 1: Introduction
- Part 2: Ideal Model Examples
- Part 3: Sampled Data Aspects
- Part 4: Engineering of Evaluation Hardware
- Part 5:

## 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 mixed-signal electronics and number-crunching capability (e.g. FPGA), to create arbitrary (within reason) Electrical/Electronic Circuits with real-world connectivity. Of equal importance will be the evaluation of the functionality and performance of a practical design made from modestly-priced state of the art devices.

- Part 1:

## 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...

## 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...

## Learning VHDL - Basics

Since FPGA are becoming more accessible to the hobbyist, learning how to use them can be really useful for certain applications, like DSP and video generation; moreover, engineers that are able to code in VHDL/Verilog are always requested on the job market.

In this tutorial I will cover the basics of Xilinx ISE and VHDL. I willl base my code on the Basys2 board from Digilent: it is really cheap (especially for students) and has a lot of features on board, as you can see from the picture...

## 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 high-end 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...

## 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...

## Feedback Controllers - Making Hardware with Firmware. Part 6. Self-Calibration Related.

This article will consider the engineering of a self-calibration & self-test capability to enable the project hardware to be configured and its basic performance evaluated and verified, ready for the development of the low-latency controller DSP firmware and closed-loop applications. Performance specifications will be documented in due course, on the project website here.

- Part 6: Self-Calibration, Measurements and Signalling (this part)
- Part 5:

## Feedback Controllers - Making Hardware with Firmware. Part 5. Some FPGA Aspects.

This part of the on-going series of articles looks at a variety of aspects concerning the FPGA device which provides the high-speed maths capability for the low-latency controller and the arbitrary circuit generator application. In due course a complete specification along with application examples will be maintained on the project website here.- Part 5: Some FPGA Aspects (this part)
- Part 4: Engineering of...

## Launch of Youtube Channel: My First Videos - Embedded World 2017

I went to Embedded World 2017 in Nuremberg with an ambitious plan; I would make video highlights of several exhibits (booths) to be presented to the *Related sites audience. I would try to make the vendors focus their pitch on the essential in order to produce a one to three minutes video per booth.

So far my experience with making videos was limited to family videos, so I knew I had lots of reading to do and lots of Youtube videos and tutorials to watch. Trade shows are...

## Use Microprogramming to Save Resources and Increase Functionality

IntroductionMicroprogramming is a design approach that every FPGA designer should have in their bag of tricks. I subscribe to the concept that microprogramming is a structured approach to the design of state machines. This is essentially the view of Maurice Wilkes when he first proposed microprogramming in 1951 as an alternative method for the implementation of the control section of a computer. Wilkes was interested in improving the reliability and reducing time needed to implement...

## 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...

## Designing Embedded System with FPGA - 1

With the introduction of soft processors and related tools (like EDK from Xilinx), implementation of basic embedded system in FPGA is made easy. This requires very little or almost no knowledge of VHDL programming. Actually that’s how I started. If user is interested in taking full advantage of FPGA and its parallel processing power, then yes, detail understanding of soft processor, its peripheral bus and VHDL programming is required.

I will start with...

## Already 3000+ Attendees Registered for the Upcoming Embedded Online Conference

Chances are you already know, through the newsletter or banners on the Related sites, about the upcoming Embedded Online Conference.

Chances are you also already know that you have until the end of the month of February to register for free.

And chances are that you are one of the more than 3000 pro-active engineers who have already registered.

But If you are like me and have a tendency to do tomorrow what can be done today, maybe you haven't registered yet. You may...

## Embedded World 2018 - More Videos!

After the interview videos last week, this week I am very happy to release two more videos taken at Embedded World 2018 and that I am proud of.

For both videos, I made extensive use of my two new toys, a Zhiyun Crane Gimbal and a Sony a6300 camera.

The use of a gimbal like the Zhiyun makes a big difference in terms of making the footage look much more stable and cinematographic.

As for the Sony camera, it takes fantastic slow-motion footage and...

## MyHDL Resources and Projects

Last updated 07-Nov-2017

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 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...

## 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

## 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...