To recap the basic math, an elliptic curve over a finite field has points $(x, y)$ which satisfy the equation $$y^2 = x^3 + a x + b \text{ mod } q.$$When points are added to themselves multiple times we write the multiplication as $$Y = k P$$where $k$ is an integer. Since the number of points is finite, after a while we get to a value of $k = n$ such that $$\mathscr O = n P ..read more

Cryptographic security has a lot of components. The simple stuff is the mathematics which is what I want to talk about. The hard stuff is preventing people from giving away things that should be secret (Loose lips sink ships still holds today!). The cryptographic security I want to talk about here comes from solving a mathematical problem to find a secret. The assumption is the ..read more

Cryptography is the art of hiding messages, NOT writing on graves, which is a direct translation a friend of mine once asked. I should have said "that's engraving!", but I was a week late. The main engine of encrypting a message uses a single key and a fast algorithm. The NIST standard is AES which can use key sizes of 128 bits, 192 bits, or 256 bits. Each of these is considered a ..read more

The most common math algorithms that are needed when we deal with numbers in embedded systems are sum/subtraction, multiplication, division. When we move from scalar to vector quantities and complex numbers, we invariably run into square root when we operate with lengths of vectors. Square root also comes up as the geometric mean of numbers as well as different energy and rms calculations ..read more

In today's rapidly evolving technology landscape, engineers seeking to remain competitive and in demand must focus on mastering modern FPGA (field programmable gate array) skills. This article explores how a comprehensive understanding of FPGA technology can unlock your engineering potential. FPGA Architecture A solid grasp of FPGA architecture is fundamental for engineers working with these ..read more

With the ever increasing number of applications involving video processing, AI or edge computing the appetite for suitably skilled FPGA Engineers has never been higher from the market which is expected to grow to $15 billion USD by 2027! In terms of industries opportunities can be typically found within: Automotive Aerospace Defense Data Processing However this list is ..read more

I’ve had microcontrollers (MCU) in my pocket for a few decades now. They have always been much more accessible than field programmable gate arrays (FPGA) but within the last few years, that has started to change. Quite a number of companies have developed sub \$100 FPGA experimenter boards (some quite a bit sub \$100). The major vendors have low or no cost versions of their tool chains and ..read more

Are you a microcontroller expert beckoned by the siren song of the FPGA? Not long ago, that was me. FPGA-expert friends of mine regularly extolled the virtues of these mysterious components and I wanted in. When I made the leap, I found a world seemingly very familiar, but in reality, vastly different. My years of C programming and microcontroller use often gave pre preconceived ..read more

Some years ago, when I went to the University, I bought some development boards based on different microcontrollers, and I remember that, although development boards were not expensive, I had to add to the price of the board, the shipping costs and the taxes, which were more than the 50% of the price of the board, but there are no option if I wanted to test that microcontroller. When I wanted ..read more

We are delighted to announce the launch of the very first new Related site in 15 years!  The new site will be dedicated to the trendy and quickly growing field of Machine Learning and will be called - drum roll please - MLRelated.com. We think MLRelated fits perfectly well within the “Related” family, with: the fast growth of TinyML, which is a topic of great interest to the ..read more