Elliptic Curve Cryptography - Extension Fields
An introduction to the pairing of points on elliptic curves. Point pairing normally requires curves over an extension field because the structure of an elliptic curve has two independent sets of points if it is large enough. The rules of pairings are described in a general way to show they can be useful for verification purposes.
Software is free and can right any wrong
Software changes are so much easier than hardware modifications, so the temptation is always to take this approach to fixing bugs. This may not always be a good idea.
Modern C++ in embedded development: Static Classes
There is a concept of static class in C#. It is a class that contains only static members and methods, and it can’t be instantiated. In C#, a static class is declared using the static keyword.
Static classes are used to group functions that belong to the same logical unit or software module and that may have a shared state (member variables).
Static class in C++The concept of a static class can be implemented in C++ as a class with all static methods and members and by deleting...
Creating a Hardware Abstraction Layer (HAL) in C
In my last post, C to C++: Using Abstract Interfaces to Create Hardware Abstraction Layers (HAL), I discussed how vital hardware abstraction layers are and how to use a C++ abstract interface to create them. You may be thinking, that’s great for C++, but I work in C! How do I create a HAL that can easily swap in and out different drivers? In today’s post, I will walk through exactly how to do that while using the I2C bus as an example.
Elliptic Curve Cryptography - Key Exchange and Signatures
Elliptic curve mathematics over finite fields helps solve the problem of exchanging secret keys for encrypted messages as well as proving a specific person signed a particular document. This article goes over simple algorithms for key exchange and digital signature using elliptic curve mathematics. These methods are the essence of elliptic curve cryptography (ECC) used in applications such as SSH, TLS and HTTPS.
What does it mean to be 'Turing complete'?
The term "Turing complete" describes all computers and even some things we don't expect to be as powerful as a typical computer. In this article, I describe what it means and discuss the implications of Turing completeness on projects that need just a little more power, on alternative processor designs, and even security.
Elliptic Curve Cryptography - Security Considerations
The security of elliptic curve cryptography is determined by the elliptic curve discrete log problem. This article explains what that means. A comparison with real number logarithm and modular arithmetic gives context for why it is called a log problem.
Handling Translations in an Embedded Project
A brief walkthrough on how to handle human language translations in a low level C application. Some options are listed, each with advantages and disadvantages laid out.
Elliptic Curve Cryptography - Basic Math
An introduction to the math of elliptic curves for cryptography. Covers the basic equations of points on an elliptic curve and the concept of point addition as well as multiplication.
Square root in fixed point VHDL
In this blog we will design and implement a fixed point square root function in VHDL. The algorithm is based on the recursive Newton Raphson inverse square root algorithm and the implementation offers parametrizable pipeline depth, word length and the algorithm is built with VHDL records and procedures for easy use.
Getting Started with NuttX RTOS on Three Low Cost Boards
If you are an embedded system developer chances are you already played with Linux on some embedded board and saw how it is powerful, right?
So, I have a good news: you can have same power using NuttX on some ultra low cost board powered by a microcontroller instead of microprocessor (that normally is way more expansive).
In fact many companies already realized it before me. It explains why NuttX is the kernel used by many IoT frameworks:
Another great news is that few days ago...
Help, My Serial Data Has Been Framed: How To Handle Packets When All You Have Are Streams
Today we're going to talk about data framing and something called COBS, which will make your life easier the next time you use serial communications on an embedded system -- but first, here's a quiz:
Quick Diversion, Part I: Which of the following is the toughest area of electrical engineering? analog circuit design digital circuit design power electronics communications radiofrequency (RF) circuit design electromagnetic...My Love-Hate Relationship with Stack Overflow: Arthur S., Arthur T., and the Soup Nazi
Warning: In the interest of maintaining a coherent stream of consciousness, I’m lowering the setting on my profanity filter for this post. Just wanted to let you know ahead of time.
I’ve been a user of Stack Overflow since December of 2008. And I say “user” both in the software sense, and in the drug-addict sense. I’m Jason S, user #44330, and I’m a programming addict. (Hi, Jason S.) The Gravatar, in case you were wondering, is a screen...
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Last time, we talked about error correction and detection, covering some basics like Hamming distance, CRCs, and Hamming codes. If you are new to this topic, I would strongly suggest going back to read that article before this one.
This time we are going to cover Reed-Solomon codes. (I had meant to cover this topic in Part XV, but the article was getting to be too long, so I’ve split it roughly in half.) These are one of the workhorses of error-correction, and they are used in...
VHDL tutorial - combining clocked and sequential logic
In an earlier article on VHDL programming ("VHDL tutorial" and "VHDL tutorial - part 2 - Testbench", I described a design for providing a programmable clock divider for a ADC sequencer. In this example, I showed how to generate a clock signal (ADCClk), that was to be programmable over a series of fixed rates (20MHz, 10MHz, 4MHz, 2MHz, 1MHz and 400KHz), given a master clock rate of 40MHz. A reader of that article had written to ask if it was possible to extend the design to...
C to C++: 5 Tips for Refactoring C Code into C++
The article titled "Simple Tips to Refactor C Code into C++: Improve Embedded Development" provides essential guidance for embedded developers transitioning from C to C++. The series covers fundamental details necessary for a seamless transition and emphasizes utilizing C++ as a better C rather than diving into complex language features. The article introduces five practical tips for refactoring C code into C++. Replace #define with constexpr and const: Discouraging the use of #define macros, the article advocates for safer alternatives like constexpr and const to improve type safety, debugging, namespaces, and compile-time computation. Use Namespaces: Demonstrating the benefits of organizing code into separate logical groupings through namespaces, the article explains how namespaces help avoid naming conflicts and improve code readability. Replace C-style Pointers with Smart Pointers and References: Emphasizing the significance of avoiding raw pointers, the article suggests replacing them with C++ smart pointers (unique_ptr, shared_ptr, weak_ptr) and using references
Zebras Hate You For No Reason: Why Amdahl's Law is Misleading in a World of Cats (And Maybe in Ours Too)
I’ve been wasting far too much of my free time lately on this stupid addicting game called the Kittens Game. It starts so innocently. You are a kitten in a catnip forest. Gather catnip.
And you click on Gather catnip and off you go. Soon you’re hunting unicorns and building Huts and studying Mathematics and Theology and so on. AND IT’S JUST A TEXT GAME! HTML and Javascript, that’s it, no pictures. It’s an example of an
Supply Chain Games: What Have We Learned From the Great Semiconductor Shortage of 2021? (Part 5)
In this article we’re going to take a look at cycle time, queues, and inventory. Cycle time is a manufacturing term — for anything, not just semiconductors — meaning how long it takes for an individual product to make its way through a manufacturing process, from start to finish. We’re going to try to understand how long it takes to manufacture semiconductors. In particular, we’re going to try to answer these questions:
- How long does it take...
Levitating Globe Teardown, Part 1
I've been kicking some ideas around for a long time for a simple and inexpensive platform I could use for control systems experimentation for the beginner. I want something that can be controlled easily in a basic fashion, yet that provides some depth: I want to be able to present ever-more challenging goals to the student, that can be attained by fancier control algorithms all on the same device.
I'm currently looking at magnetic levitation. It's fun, it has the potential to be...
MSP430 LaunchPad Tutorial - Part 4 - UART Transmission
Today we are going to learn how to communicate using UART with the Launchpad. For this purpose I will replace the default microcontroller that comes with the board with the MSP430G2553. It is the most powerful device in the MSP430 Value Line and it comes with an integrated hardware UART module, along with 16 Kb of Flash memory, 512 bytes of SRAM and an 8-channel, 10 bit ADC.
UART communication can be useful when dealing with sensors: as a basic example, we could...
Ten Little Algorithms, Part 4: Topological Sort
Other articles in this series:
- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford's Method (And Friends)
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection
Today we’re going to take a break from my usual focus on signal processing or numerical algorithms, and focus on...
Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date
Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies". Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits. Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...
Important Programming Concepts (Even on Embedded Systems) Part II: Immutability
Other articles in this series:
- Part I: Idempotence
- Part III: Volatility
- Part IV: Singletons
- Part V: State Machines
- Part VI: Abstraction
This article will discuss immutability, and some of its variations in the topic of functional programming.
There are a whole series of benefits to using program variables that… well, that aren’t actually variable, but instead are immutable. The impact of...
Slew Rate Limiters: Nonlinear and Proud of It!
I first learned about slew rate limits when I was in college. Usually the subject comes up when talking about the nonideal behavior of op-amps. In order for the op-amp output to swing up and down quickly, it has to charge up an internal capacitor with a transistor circuit that’s limited in its current capability. So the slew rate limit \( \frac{dV}{dt} = \frac{I_{\rm max}}{C} \). And as long as the amplitude and frequency aren’t too high, you won’t notice it. But try to...
Coding Step 1 - Hello World and Makefiles
Articles in this series:
- Coding Step 0 - Development Environments
- Coding Step 1 - Hello World and Makefiles
- Coding Step 2 - Source Control
- Coding Step 3 - High-Level Requirements
- Coding Step 4 - Design
Step 0 discussed how to install GCC and the make utility with the expectation of writing and compiling your first C program. In this article, I discuss how to use those tools we installed last time. Specifically, how to use GCC to compile a C program and...
How to use I2C devices in (Apache) NuttX: Scanning for Devices
Previously in this EmbeddedRelated article, we saw how to use Buttons Subsystem on NuttX using a RaspberryPi Pico board. Now we will change from user input device (buttons) for something more generic: I2C protocol. NuttX supports a lot of I2C devices (sensors, displays, EEPROMs, I/O Expanders, I2C multiplexers, and many more). And most important: because NuttX is a Linux-like RTOS you will find the very familiar i2ctool to search for devices in your I2C bus. So, lets to get...
Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
Today we will be drifting back into the topic of numerical methods, and look at an algorithm that takes in a series of discretely-sampled data points, and estimates the maximum value of the waveform they were sampled from.
From bare-metal to RTOS: 5 Reasons to use an RTOS
Developers can come up with amazing and convoluted reasons to not use an RTOS. I have heard excuses ranging from they are too expensive (despite open source solutions) all the way to they aren’t efficient and use too much memory. In some circumstances some excuses are justified but there are many reasons why a developer should look to an RTOS to help with their real-time scheduling needs.
From bare-metal to RTOS Quick LinksC Programming Techniques: Function Call Inlining
Introduction
Abstraction is a key to manage software systems as they increase in size and complexity. As shown in a previous post, abstraction requires a developper to clearly define a software interface for both data and functions, and eventually hide the underlying implementation.When using the C language, the interface is often exposed in a header '.h' file, while the implementation is put in one or more corresponding '.c' files.
First, separating an interface from its...
Oscilloscope Dreams
My coworkers and I recently needed a new oscilloscope. I thought I would share some of the features I look for when purchasing one.
When I was in college in the early 1990's, our oscilloscopes looked like this:
Now the cathode ray tubes have almost all been replaced by digital storage scopes with color LCD screens, and they look like these:
Oscilloscopes are basically just fancy expensive boxes for graphing voltage vs. time. They span a wide range of features and prices:...
