Elliptic Curve Digital Signatures
A digital signature is used to prove a message is connected to a specific sender. The sender can not deny they sent that message once signed, and no one can modify the message and maintain the signature. The message itself is not necessarily secret. Certificates of authenticity, digital cash, and software distribution use digital signatures so recipients can verify they are getting what they paid for.
Since messages can be of any length and mathematical algorithms always use fixed...
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...
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.
MyHDL FPGA Tutorial II cont. (Echo, Audio Interface)
IntroductionTo demonstrate the echo on an FPGA board an interface to an audio ADC/DAC chip will be used. The following will explain the connection to the audio codec and the HDL module used to interface.
Audio Codec InterfaceI have two boards with TI AIC23b audio codecs. The AIC23 has a configuration interface (ability to program the registers) and a streaming audio interface. The SPI mode will be used to configure the codec and the I2S interface is used to send and...
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...
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...
Spline interpolation
A cookbook recipe for segmented y=f(x) 3rdorder polynomial interpolation based on arbitrary input data. Includes Octave/Matlab design script and Verilog implementation example. Keywords: Spline, interpolation, function modeling, fixed point approximation, data fitting, Matlab, RTL, Verilog
IntroductionSplines describe a smooth function with a small number of parameters. They are wellknown for example from vector drawing programs, or to define a "natural" movement path through given...
Introducing the VPCIe framework
IntroductionMy daily work involves platforms featuring an embedded CPU communcating with a FPGA device over a PCI Express link (PCIe for short). The main purpose of this link is for the CPU to convey configuration, control, and status commands to hardware slaves implemented in the FPGA. For data intensive applications (2D XRay detector readout backend), this link can also be used as a DMA channel to transfer data from the FPGA to the CPU memory. Finally, a slave can interrupt the CPU using...
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...
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
Two jobs
For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.
edit  video of the event:
I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...
Feedback Controllers  Making Hardware with Firmware. Part 9. Closing the lowlatency loop
It's time to put together the DSP and feedback control sciences, the evaluation electronics, the Intel Cyclone floatingpoint FPGA algorithms and the builtin control loop testbed and evaluate some example designs. We will be counting the nanoseconds and looking for textbook performance in the creation of emulated hardware circuits. Along the way, there is a printed circuit board (PCB) issue to solve using DSP.
Fig 1. The evaluation platform
Additional design...
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.
Commandline driven workflow is easier on the hands and faster. The example...
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...
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...
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...
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...
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 slowmotion footage and...
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
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...
Feedback Controllers  Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally
This article will look at a design approach for feedback controllers featuring lowlatency "irrational" characteristics to enable the creation of physical components such as transmission lines. Some thought will also be given as to the capabilities of the currently utilized Intel Cyclone V, the new Cyclone 10 GX and the upcoming Xilinx Versal floatingpoint FPGAs/ACAPs.
Fig 1. Making a Transmission Line, with the Circuit Emulator
Additional...