Ohm? Don’t Forget Kirchhoff!

It is hard to get very far into electronics without knowing Ohm’s law. Named after [Georg Ohm] it describes current and voltage relationships in linear circuits. However, there are two laws that are even more basic that don’t get nearly the respect that Ohm’s law gets. Those are Kirchhoff’s laws.

In simple terms, Kirchhoff’s laws are really an expression of conservation of energy. Kirchhoff’s current law (KCL) says that the current going into a single point (a node) has to have exactly the same amount of current going out of it. If you are more mathematical, you can say that the sum of the current going in and the current going out will always be zero, since the current going out will have a negative sign compared to the current going in.

You know the current in a series circuit is always the same, right? For example, in a circuit with a battery, an LED,¬†and a resistor, the LED and the resistor will have the same current in them. That’s KCL. The current going into the resistor better be the same as the current going out of it and into the LED.

This is mostly interesting when there are more than two wires going into one point. If a battery drives 3 magically-identical light bulbs, for instance, then each bulb will get one-third of the total current. The node where the battery’s wire joins with the leads to the 3 bulbs is the node. All the current coming in, has to equal all the current going out. Even if the bulbs are not identical, the totals will still be equal. So if you know any three values, you can compute the fourth.

If you want to play with it yourself, you can simulate the circuit below.

The current from the battery has to equal the current going into the battery. The two resistors at the extreme left and right have the same current through them (1.56 mA). Within rounding error of the simulator, each branch of the split has its share of the total (note the bottom leg has 3K total resistance and, thus, carries less current).

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NIST Helps You With Cryptography

Getting cryptography right isn’t easy, and it’s a lot worse on constrained devices like microcontrollers. RAM is usually the bottleneck — you will smash your stack computing a SHA-2 hash on an AVR — but other resources like computing power and flash code storage space are also at a premium. Trimming down a standard algorithm to work within these constraints opens up the Pandora’s box of implementation-specific flaws.

NIST stepped up to the plate, starting a lightweight cryptography project in 2013 which has now come out with a first report, and here it is as a PDF. The project is ongoing, so don’t expect a how-to guide. Indeed, most of the report is a description of the problems with crypto on small devices. Given the state of IoT security, just defining the problem is a huge contribution.

Still, there are some concrete recommendations. Here are some spoilers. For encryption, they recommend a trimmed-down version of AES-128, which is a well-tested block cipher on the big machines. For message authentication, they’re happy with Galois/Counter Mode and AES-128.

I was most interested in hashing, and came away disappointed; the conclusion is that the SHA-2 and SHA-3 families simply require too much state (and RAM) and they make no recommendation, leaving you to pick among less-known functions: check out PHOTON or SPONGENT, and they’re still being actively researched.

If you think small-device security is easy, read through the 22-question checklist that starts on page twelve. And if you’re looking for a good starting point to read up on the state of the art, the bibliography is extensive.

Your tax dollars at work. Thanks, NIST!

And thanks [acs] for the tip!

These Engineering Ed Projects Are Our Kind Of Hacks

Highly polished all-in-one gear for teaching STEM is one way to approach the problem. But for some, they can be intimidating and the up-front expenditure can be a barrier to just trying something before you’re certain you want to commit. [Miranda] is taking a different approach with the aim of making engineering education possible with junk you have around the house. The point is to play around with engineering concepts with having to worry about doing it exactly right, or with exactly the right materials. You know… hacking!

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