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.
Bellegram, a wireless DIY doorbell that sends you a Telegram message
A wireless button that uses the M5 STAMP PICO and Mongoose to send a Telegram message when pressed. The code is written in C
STM32 B-CAMS-OMV Walkthrough
Want to prototype embedded vision quickly? This walkthrough shows how the STM32 B-CAMS-OMV camera module pairs with the STM32H747I-DISCO discovery kit and the FP-AI-VISION1 function pack to get you running in minutes. The video covers the camera connection interface, key software functions to control and process data, and the ISP features that let image processing run inside the camera. The STM32 H7 project with B-CAMS-OMV drivers is available on GitHub.
Designing Communication Protocols, Practical Aspects
When your MCU must talk to a PC or smartphone, a clear protocol saves time and headaches. This post gives practical guidance for fast bring-up: how to structure a compact header, keep payloads byte-aligned and debug-friendly, and reserve bits for future use. It also covers CRCs for integrity, timeout and retry strategies for resynchronisation, and the simple start code trick that makes debugging easier.
Public speaking
Presenting technical work is unavoidable for embedded engineers, but few get formal training on how to do it well. This post gives practical, low-overhead tactics: use a single person focus to steady nerves, build a bullet point memory palace to guide remarks, time your talk with about 100 words per minute, avoid reading slides, and rehearse on camera. These tips make talks clearer and less stressful.
Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC
Jason Sachs shows how to pry CRC parameters out of a black-box oracle and reimplement the checksum yourself. By canceling the affine offsets, probing single-bit basis messages, and treating per-bit outputs as LFSR sequences, you can recover the generator polynomial, bit and byte order, and init/final XOR values. The post includes working Python code, a 4-message shortcut, and real-world tests such as zlib CRC32.
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Jason Sachs demystifies Reed-Solomon codes with hands-on examples and pragmatic tips for embedded engineers. The article shows why RS encoding is just polynomial division in GF(2^m), why decoding is mathematically heavier, and how to implement encoders in Python and in C-friendly form using LFSRs and table-driven methods. Read this for working code, generator-polynomial examples, and an embedded-minded view of RS practicalities.
Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction
Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.
This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes.
Ernie, You Have a Banana in Your EarI have had a really really tough time writing this article. I like the...
Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes
Last time we looked at some techniques using LFSR output for system identification, making use of the peculiar autocorrelation properties of pseudorandom bit sequences (PRBS) derived from an LFSR.
This time we’re going to jump back to the field of communications, to look at an invention called Gold codes and why a single maximum-length PRBS isn’t enough to save the world using spread-spectrum technology. We have to cover two little side discussions before we can get into Gold...
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Jason Sachs shows why LFSR-generated pseudonoise is a natural fit for direct-sequence spread spectrum, then walks through Fourier basics, spectral plots, and runnable Python examples. The article demonstrates how DSSS multiplies a UART bitstream with a chipping sequence to spread energy, how despreading concentrates the desired signal while scrambling narrowband interference, and how multiple transmitters can share bandwidth when using uncorrelated sequences.
Number Theory for Codes
If CRCs have felt like black magic, this post peels back the curtain with basic number theory and polynomial arithmetic over GF(2). It shows how fixed-width processor arithmetic becomes arithmetic in a finite field, how bit sequences are treated as polynomials, and why primitive polynomials generate every nonzero element. You also get practical insights on CRC implementation with byte tables and LFSRs.
Getting Started With Zephyr: Bluetooth Low Energy
In this blog post, I show how to enable BLE support in a Zephyr application. First, I show the necessary configuration options in Kconfig. Then, I show how to use the Zephyr functions and macros to create a custom service and characteristic for a contrived application.
Designing Communication Protocols, Practical Aspects
When your MCU must talk to a PC or smartphone, a clear protocol saves time and headaches. This post gives practical guidance for fast bring-up: how to structure a compact header, keep payloads byte-aligned and debug-friendly, and reserve bits for future use. It also covers CRCs for integrity, timeout and retry strategies for resynchronisation, and the simple start code trick that makes debugging easier.
Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes
Last time we looked at some techniques using LFSR output for system identification, making use of the peculiar autocorrelation properties of pseudorandom bit sequences (PRBS) derived from an LFSR.
This time we’re going to jump back to the field of communications, to look at an invention called Gold codes and why a single maximum-length PRBS isn’t enough to save the world using spread-spectrum technology. We have to cover two little side discussions before we can get into Gold...
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.
How to Give Persistent Names To USB-Serial Devices on Ubuntu 14.04
When your dock reshuffles ttyUSB assignments, Tayyar shows how to bind USB-serial devices to persistent names on Ubuntu 14.04. The post walks through using dmesg and udevadm to locate unique attributes like KERNELS and ATTRS{serial}, creating /etc/udev/rules.d entries with NAME and SYMLINK, and applying rules with udevadm trigger. It includes common pitfalls and quick fixes to get minicom talking to the right port.
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Jason Sachs shows why LFSR-generated pseudonoise is a natural fit for direct-sequence spread spectrum, then walks through Fourier basics, spectral plots, and runnable Python examples. The article demonstrates how DSSS multiplies a UART bitstream with a chipping sequence to spread energy, how despreading concentrates the desired signal while scrambling narrowband interference, and how multiple transmitters can share bandwidth when using uncorrelated sequences.
STM32 B-CAMS-OMV Walkthrough
Want to prototype embedded vision quickly? This walkthrough shows how the STM32 B-CAMS-OMV camera module pairs with the STM32H747I-DISCO discovery kit and the FP-AI-VISION1 function pack to get you running in minutes. The video covers the camera connection interface, key software functions to control and process data, and the ISP features that let image processing run inside the camera. The STM32 H7 project with B-CAMS-OMV drivers is available on GitHub.
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.
Reverse engineering wireless wall outlets
Fabien Le Mentec reverse engineers a cheap set of wireless wall outlets to add them to his BANO home automation while avoiding uncertified mains hardware. He uses PCB inspection to identify a Holtek MCU and RF83C, captures 433.92 MHz OOK signals with an RTL-SDR and ookdump, then replays commands using an RFM22 in direct mode controlled by an ATmega328P. The post explains frame structure and links to a working GitHub implementation.
Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction
Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.
This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes.
Ernie, You Have a Banana in Your EarI have had a really really tough time writing this article. I like the...
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Jason Sachs shows why LFSR-generated pseudonoise is a natural fit for direct-sequence spread spectrum, then walks through Fourier basics, spectral plots, and runnable Python examples. The article demonstrates how DSSS multiplies a UART bitstream with a chipping sequence to spread energy, how despreading concentrates the desired signal while scrambling narrowband interference, and how multiple transmitters can share bandwidth when using uncorrelated sequences.
Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC
Jason Sachs shows how to pry CRC parameters out of a black-box oracle and reimplement the checksum yourself. By canceling the affine offsets, probing single-bit basis messages, and treating per-bit outputs as LFSR sequences, you can recover the generator polynomial, bit and byte order, and init/final XOR values. The post includes working Python code, a 4-message shortcut, and real-world tests such as zlib CRC32.
Reverse engineering wireless wall outlets
Fabien Le Mentec reverse engineers a cheap set of wireless wall outlets to add them to his BANO home automation while avoiding uncertified mains hardware. He uses PCB inspection to identify a Holtek MCU and RF83C, captures 433.92 MHz OOK signals with an RTL-SDR and ookdump, then replays commands using an RFM22 in direct mode controlled by an ATmega328P. The post explains frame structure and links to a working GitHub implementation.
Designing Communication Protocols, Practical Aspects
When your MCU must talk to a PC or smartphone, a clear protocol saves time and headaches. This post gives practical guidance for fast bring-up: how to structure a compact header, keep payloads byte-aligned and debug-friendly, and reserve bits for future use. It also covers CRCs for integrity, timeout and retry strategies for resynchronisation, and the simple start code trick that makes debugging easier.
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.
Mathematics and Cryptography
Cryptographic math can look intimidating, but this roundup trims it to what FPGA engineers actually need. It groups concise articles on number theory and elliptic curves, focusing on polynomial math over Galois fields, FPGA-friendly inversion and one-clock-cycle techniques, and elliptic-curve key exchange and digital signatures. Read this to learn which subroutines to implement first and how to turn math into Verilog or VHDL.
One Clock Cycle Polynomial Math
Error correction codes and cryptographic computations are most easily performed working with GF(2^n)
Number Theory for Codes
If CRCs have felt like black magic, this post peels back the curtain with basic number theory and polynomial arithmetic over GF(2). It shows how fixed-width processor arithmetic becomes arithmetic in a finite field, how bit sequences are treated as polynomials, and why primitive polynomials generate every nonzero element. You also get practical insights on CRC implementation with byte tables and LFSRs.
Polynomial Inverse
One of the important steps of computing point addition over elliptic curves is a division of two polynomials.
