## 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.

## 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. ...

## 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...

## The CRC Wild Goose Chase: PPP Does What?!?!?!

I got a bad feeling yesterday when I had to include reference information about a 16-bit CRC in a serial protocol document I was writing. And I knew it wasn’t going to end well.

The last time I looked into CRC algorithms was about five years ago. And the time before that… sometime back in 2004 or 2005? It seems like it comes up periodically, like the seventeen-year locust or sunspots or El Niño,...

## Reverse engineering wireless wall outlets

IntroductionI am improving the domotics framework that I described in a previous article://www.embeddedrelated.com/showarticle/605.php

I want to support wireless wall outlets, allowing me to switch devices power from a remote location over HTTP.

To do so, I could design my own wireless wall outlets and use a hardware similar to the previous one, based on the NRF905 chipset. The problem is that such a product would not be certified, and that would be an issue regarding the home insurance,...

## Using a RTLSDR dongle to validate NRF905 configuration

I am currently working on a system to monitor the garage door status from my flat. Both places are 7 floors apart, and I need to send the data wirelessly. I chose to operate on the 433MHz carrier, and I ordered 2 PTR8000 modules: http://www.electrodragon.com/w/NRF905_Transceiver_433MHz-Wireless_ModuleThe PTR8000 is based on the dual band sub 1GHz NRF905 chipset from NORDICSEMI: http://www.nordicsemi.com/eng/Products/Sub-1-GHz-RF/nRF905I...## When a Mongoose met a MicroPython, part I

This is more a framework than an actual application, with it you can integrate MicroPython and Cesanta's Mongoose.

Mongoose runs when called by MicroPython and is able to run Python functions as callbacks for the events you decide in your event handler. The code is completely written in C, except for the example Python callback functions, of course. To try it, you can just build this example on a Linux machine, and, with just a small tweak, you can also run it on any ESP32 board.

## 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...

## Using a RTLSDR dongle to validate NRF905 configuration

I am currently working on a system to monitor the garage door status from my flat. Both places are 7 floors apart, and I need to send the data wirelessly. I chose to operate on the 433MHz carrier, and I ordered 2 PTR8000 modules: http://www.electrodragon.com/w/NRF905_Transceiver_433MHz-Wireless_ModuleThe PTR8000 is based on the dual band sub 1GHz NRF905 chipset from NORDICSEMI: http://www.nordicsemi.com/eng/Products/Sub-1-GHz-RF/nRF905I...## STM32 B-CAMS-OMV Walkthrough

The STM32 B-CAMS-OMV camera module offers an accessible way to get started with embedded vision. Coupled with the STM32H747I-DISCO discovery kit and the FP-AI-VISION1 function pack, it's possible to be up and running in minutes.

This video describes the camera connection interface to the discovery kit and the key software functions required to control the camera and process its data. We review the ISP (Image Signal Processor) interface with examples of image processing...

## 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.

## The CRC Wild Goose Chase: PPP Does What?!?!?!

I got a bad feeling yesterday when I had to include reference information about a 16-bit CRC in a serial protocol document I was writing. And I knew it wasn’t going to end well.

The last time I looked into CRC algorithms was about five years ago. And the time before that… sometime back in 2004 or 2005? It seems like it comes up periodically, like the seventeen-year locust or sunspots or El Niño,...

## Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals

Last time we looked at the use of LFSRs for pseudorandom number generation, or PRNG, and saw two things:

- the use of LFSR state for PRNG has undesirable serial correlation and frequency-domain properties
- the use of single bits of LFSR output has good frequency-domain properties, and its autocorrelation values are so close to zero that they are actually better than a statistically random bit stream

The unusually-good correlation properties...

## Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC

Last time, we continued a discussion about error detection and correction by covering Reed-Solomon encoding. I was going to move on to another topic, but then there was this post on Reddit asking how to determine unknown CRC parameters:

I am seeking to reverse engineer an 8-bit CRC. I don’t know the generator code that’s used, but can lay my hands on any number of output sequences given an input sequence.

This is something I call the “unknown oracle”...

## The Asimov Protocol

While the Internet is choke-full of explanations of basic data communication protocols, very little is said about the higher levels of packing, formatting, and exchanging information in a useful and practical way. This less-charted land is still fraught with strange problems, whose solutions may be found in strange places – in this example, a very short, 60 years old Science Fiction story.

## 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

## 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.

## 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.

## When a Mongoose met a MicroPython, part I

This is more a framework than an actual application, with it you can integrate MicroPython and Cesanta's Mongoose.

Mongoose runs when called by MicroPython and is able to run Python functions as callbacks for the events you decide in your event handler. The code is completely written in C, except for the example Python callback functions, of course. To try it, you can just build this example on a Linux machine, and, with just a small tweak, you can also run it on any ESP32 board.

## 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.

## 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

## When a Mongoose met a MicroPython, part II

In the first part of this blog, we introduced this little framework to integrate MicroPython and Cesanta's Mongoose; where Mongoose runs when called by MicroPython and is able to run Python functions as callbacks for the events you decide in your event handler. Now we add MQTT to the equation, so we can subscribe to topics and publish messages right from MicroPython.

## Public speaking

Public Speaking: This common task goes with embedded system engineering. Pitching a project. Presenting at a conference. Delivering a status report. Teaching. All part of the job.

Stephane Boucher did a v-blog post here last week and is naturally apprehensive about how he did.

If you have not seen it you can catch it here:

First - Stephane - You did fine!

I spent some time (5 quarters, 3 classes a day, computer technology in a tech school) in a classroom and am comfortable in front of a...

## The Asimov Protocol

While the Internet is choke-full of explanations of basic data communication protocols, very little is said about the higher levels of packing, formatting, and exchanging information in a useful and practical way. This less-charted land is still fraught with strange problems, whose solutions may be found in strange places – in this example, a very short, 60 years old Science Fiction story.