From Baremetal to RTOS: A review of scheduling techniques
Transitioning from bare-metal embedded software development to a real-time operating system (RTOS) can be a difficult endeavor. Many developers struggle with the question of whether they should use an RTOS or simply use a bare-metal scheduler. One of the goals of this series is to walk developers through the transition and decision making process of abandoning bare-metal thinking and getting up to speed quickly with RTOSes. Before diving into the details of RTOSes, the appropriate first step...
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...
Mathematics and Cryptography
The mathematics of number theory and elliptic curves can take a life time to learn because they are very deep subjects. As engineers we don't have time to earn PhD's in math along with all the things we have to learn just to make communications systems work. However, a little learning can go a long way to helping make our communications systems secure - we don't need to know everything. The following articles are broken down into two realms, number theory and elliptic...
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...
Polynomial Inverse
One of the important steps of computing point addition over elliptic curves is a division of two polynomials.
One Clock Cycle Polynomial Math
Error correction codes and cryptographic computations are most easily performed working with GF(2^n)
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.
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.
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. ...
Polynomial Inverse
One of the important steps of computing point addition over elliptic curves is a division of two polynomials.
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.
Elliptic Curve Cryptography - Multiple Signatures
The use of point pairing becomes very useful when many people are required to sign one document. This is typical in a contract situation when several people are agreeing to a set of requirements. If we used the method described in the blog on signatures, each person would sign the document, and then the verification process would require checking every single signature. By using pairings, only one check needs to be performed. The only requirement is the ability to verify the...
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...
Linear Feedback Shift Registers for the Uninitiated, Part XI: Pseudorandom Number Generation
Last time we looked at the use of LFSRs in counters and position encoders.
This time we’re going to look at pseudorandom number generation, and why you may — or may not — want to use LFSRs for this purpose.
But first — an aside:
Science Fair 1983When I was in fourth grade, my father bought a Timex/Sinclair 1000. This was one of several personal computers introduced in 1982, along with the Commodore 64. The...
Linear Regression with Evenly-Spaced Abscissae
What a boring title. I wish I could come up with something snazzier. One word I learned today is studentization, which is just the normalization of errors in a curve-fitting exercise by the sample standard deviation (e.g. point \( x_i \) is \( 0.3\hat{\sigma} \) from the best-fit linear curve, so \( \frac{x_i - \hat{x}_i}{\hat{\sigma}} = 0.3 \)) — Studentize me! would have been nice, but I couldn’t work it into the topic for today. Oh well.
I needed a little break from...
Linear Feedback Shift Registers for the Uninitiated, Part VI: Sing Along with the Berlekamp-Massey Algorithm
The last two articles were on discrete logarithms in finite fields — in practical terms, how to take the state \( S \) of an LFSR and its characteristic polynomial \( p(x) \) and figure out how many shift steps are required to go from the state 000...001 to \( S \). If we consider \( S \) as a polynomial bit vector such that \( S = x^k \bmod p(x) \), then this is equivalent to the task of figuring out \( k \) from \( S \) and \( p(x) \).
This time we’re tackling something...
Unraveling the Enigma: Object Detection in the World of Pixels
Exploring the realm of embedded systems co-design for object recognition, this blog navigates the convergence of hardware and software in revolutionizing industries. Delving into real-time image analysis and environmental sensing, the discussion highlights advanced object detection and image segmentation techniques. With insights into Convolutional Neural Networks (CNNs) decoding pixel data and autonomously extracting features, the blog emphasizes their pivotal role in modern computer vision. Practical examples, including digit classification using TensorFlow and Keras on the MNIST dataset, underscore the power of CNNs. Through industry insights and visualization aids, the blog unveils a tapestry of innovation, charting a course towards seamless interaction between intelligent embedded systems and the world.
One Clock Cycle Polynomial Math
Error correction codes and cryptographic computations are most easily performed working with GF(2^n)
Flood Fill, or: The Joy of Resource Constraints
When transferred from the PC world to a microcontroller, a famous, tried-and-true graphics algorithm is no longer viable. The challenge of creating an alternative under severe resource constraints is an intriguing puzzle, the kind that keeps embedded development fun and interesting.
Number Theory for Codes
Everything in the digital world is encoded. ASCII and Unicode are combinations of bits which have specific meanings to us. If we try to interpret a compiled program as Unicode, the result is a lot of garbage (and beeps!) To reduce errors in transmissions over radio links we use Error Correction Codes so that even when bits are lost we can recover the ASCII or Unicode original. To prevent anyone from understanding a transmission we can encrypt the raw data...
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...
You Don't Need an RTOS (Part 1)
In this first article, we'll compare our two contenders, the superloop and the RTOS. We'll define a few terms that help us describe exactly what functions a scheduler does and why an RTOS can help make certain systems work that wouldn't with a superloop. By the end of this article, you'll be able to: - Measure or calculate the deadlines, periods, and worst-case execution times for each task in your system, - Determine, using either a response-time analysis or a utilization test, if that set of tasks is schedulable using either a superloop or an RTOS, and - Assign RTOS task priorities optimally.
There's a State in This Machine!
An introduction to state machines and their implementation. Working from an intuitive definition of the state machine concept, we will start with a straightforward implementation then we evolve it into a more robust and engineered solution.
Polynomial Inverse
One of the important steps of computing point addition over elliptic curves is a division of two polynomials.
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.
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...
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. ...
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.
Ten Little Algorithms, Part 7: Continued Fraction Approximation
In this article we explore the use of continued fractions to approximate any particular real number, with practical applications.