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.
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.
Open-Source Licenses Made Easy with Buildroot and Yocto for Embedded Linux
In this article I will try to explain what are the copyrights/copyleft, what are the popular opensource software licenses, and how to make sure that your Embedded Linux system complies with them using popular build systems ; Buildroot or YOCTO projec
Are We Shooting Ourselves in the Foot with Stack Overflow?
Most traditional, beaten-path memory layouts allocate the stack space above the data sections in RAM, even though the stack grows “down” (towards the lower memory addresses) in most embedded processors. This arrangement puts your program data in the path of destruction of a stack overflow. In other words, you violate the first Gun Safety Rule (ALWAYS keep the gun pointed in a safe direction!) and you end up shooting yourself in the foot. This article shows how to locate the stack at the BEGINNING of RAM and thus point it in the "safe" direction.
nRF5 to nRF Connect SDK migration via DFU over BLE
This writeup contains some notes on how I was able to migrate one of my clients projects based on the nRF5 SDK, to nRF Connect SDK (NCS) based firmware, via a DFU to devices in the field over BLE.
New book on Elliptic Curve Cryptography
New book on Elliptic Curve Cryptography now online. Deep discount for early purchase. Will really appreciate comments on how to improve the book because physical printing won't happen for a few more months. Check it out here: http://mng.bz/D9NA
NULL pointer protection with ARM Cortex-M MPU
This post explains how you can set up the ARM Cortex-M MPU (Memory Protection Unit) to protect thy code from dragons, demons, core dumps, and numberless other foul creatures awaiting thee after thou dereference the NULL pointer.
Modern C++ in Embedded Development: (Don't Fear) The ++
While C is still the language of choice for embedded development, the adoption of C++ has grown steadily. Yet, reservations about dynamic memory allocation and fears of unnecessary code bloat have kept many in the C camp. This discourse aims to explore the intricacies of employing C++ in embedded systems, negotiating the issues of dynamic memory allocation, and exploiting the benefits of C++ offerings like std::array and constexpr. Moreover, it ventures into the details of the zero-overhead principle and the nuanced distinctions between C and C++. The takeaway? Armed with the right knowledge and a careful approach, C++ can indeed serve as a powerful, safer, and more efficient tool for embedded development.
Working with Strings in Embedded C++
This article discusses the use of strings in embedded systems. It explains how the need for and use of strings in embedded systems has changed with the advent of cheaper, full graphic displays and the growth of the ‘Internet of Things’ (IoT). The article also covers character literals, C-Strings and string literals, and the difference in memory models between them. It also highlights the safety and security issues that arise from using strings in embedded systems. Finally, it explains how C++11 introduced a Raw string literal type that is useful for storing file paths or regular expressions.
Learning Rust For Embedded Systems
Rust eliminates whole classes of memory and concurrency bugs, making it a compelling choice for embedded projects, and the author recommends it for the VolksEEG project after a rapid evaluation. The post connects Rust fundamentals such as ownership and borrowing, RAII, traits, and unsafe blocks to familiar embedded patterns. It also provides a curated on-ramp of videos, books, and tools like Cargo, RTIC, and probe-rs to get hands-on quickly.
Watchdog Timer Anti-patterns
A watchdog timer can be useless or even harmful when misused. This post catalogs the most common watchdog anti-patterns, including feeding the watchdog unconditionally from a timer ISR, suspending it during long operations, sprinkling resets across code, timeout auctions, incomplete reset trees, and treating process supervision as a substitute for hardware. It finishes with practical rules to design watchdogs that genuinely improve embedded system reliability.
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.
C++ Assertion? Well Yes, But Actually No.
Assertions are a double-edged sword - on one side you enforce program correctness catching bugs close to their origin, on the other your application is subject to run-time error, like any interpreted language. This article explores what C++ can offer to get the advantages of assertions, without risking the crashes by moving contract checking at compile time.
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.
Linear Feedback Shift Registers for the Uninitiated, Part V: Difficult Discrete Logarithms and Pollard's Kangaroo Method
Most discrete-log problems are hopeless by brute force, but clever algorithms cut that cost to feasible levels. This installment walks through baby-step giant-step, Pollard’s rho and kangaroo methods, and how Silver-Pohlig-Hellman and index calculus leverage group structure to speed attacks on GF(2^n) fields. Jason Sachs includes Python examples, heuristics, and complexity nuggets so you can see when each method is practical.
The three laws of safe embedded systems
This short article is part of an ongoing series in which I aim to explore some techniques that may be useful for developers and organisations that are beginning their first safety-related embedded project.
Open-Source Licenses Made Easy with Buildroot and Yocto for Embedded Linux
In this article I will try to explain what are the copyrights/copyleft, what are the popular opensource software licenses, and how to make sure that your Embedded Linux system complies with them using popular build systems ; Buildroot or YOCTO projec
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.
Never use Float or Integer
Ada treats numbers as more than just numbers, and that changes how embedded code fails. This post shows why you should avoid using Float and Integer directly, then demonstrates how distinct types, ranges, and subtypes let the compiler catch unit mix-ups and out-of-range values before runtime. It also shows the same code running on a Raspberry Pi Pico, and briefly introduces SPARK for proving correctness.
“Smarter” cars, unintended acceleration – and unintended consequences
Smarter cars are arriving fast, but the software tricks behind them may be creating new safety and compliance risks. This post connects Tesla’s autopilot, the VW emissions scandal, and a reported Porsche throttle-delay case to ask whether automotive standards and regulations are keeping pace with increasingly intelligent vehicle control systems.
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.
Linear Feedback Shift Registers for the Uninitiated
Jason Sachs assembled an eighteen-part deep dive into linear feedback shift registers, connecting the simple shift-register circuit to finite-field algebra and practical tools. The series walks through primitive polynomials, Berlekamp-Massey state recovery, libgf2-based analysis, discrete-log methods, and real-world uses from PRNGs and Gold codes to Reed-Solomon and CRC reverse-engineering. It’s a single reference for engineers who want both theory and working code.
Linear Feedback Shift Registers for the Uninitiated, Part IV: Easy Discrete Logarithms and the Silver-Pohlig-Hellman Algorithm
Discrete logarithms can be either trivial or infeasible depending on how group elements are represented, and Jason Sachs shows a practical route when they are intentionally easy. This article walks through using LFSRs as fast counters, why a smooth group order matters, and how the Silver-Pohlig-Hellman algorithm plus the Chinese Remainder Theorem recovers exponents in GF(2) with small prime factors.
New book on Elliptic Curve Cryptography
New book on Elliptic Curve Cryptography now online. Deep discount for early purchase. Will really appreciate comments on how to improve the book because physical printing won't happen for a few more months. Check it out here: http://mng.bz/D9NA
Working with Strings in Embedded C++
This article discusses the use of strings in embedded systems. It explains how the need for and use of strings in embedded systems has changed with the advent of cheaper, full graphic displays and the growth of the ‘Internet of Things’ (IoT). The article also covers character literals, C-Strings and string literals, and the difference in memory models between them. It also highlights the safety and security issues that arise from using strings in embedded systems. Finally, it explains how C++11 introduced a Raw string literal type that is useful for storing file paths or regular expressions.
NULL pointer protection with ARM Cortex-M MPU
This post explains how you can set up the ARM Cortex-M MPU (Memory Protection Unit) to protect thy code from dragons, demons, core dumps, and numberless other foul creatures awaiting thee after thou dereference the NULL pointer.
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.
nRF5 to nRF Connect SDK migration via DFU over BLE
This writeup contains some notes on how I was able to migrate one of my clients projects based on the nRF5 SDK, to nRF Connect SDK (NCS) based firmware, via a DFU to devices in the field over BLE.
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.
Breaking AES with an Oscilloscope
AES is a powerful encryption algorithm that protects some our most important secrets. But did you know that many devices are inadvertently leaking the value of their private key through their power pins?! Join me in this special preview of my upcoming workshop at the Embedded Systems Summit (14-16 October 2025 in San Jose, CA) as we explore the world of hardware security and discover just how easy it could be to break AES encryption with only an oscilloscope and some math.
