OK, we want to sketch out an authentication system which is sufficiently secure against common attacks even if all the details of the system are known to the attacker. Let's start with a simple system, take a look at what its vulnerabilities are, and...

A poster to one of the Joel On Software fora the other day asked what a "salt" was (in the cryptographic sense, not the chemical sense!) and why it's OK to make salts public knowledge. I thought I might talk about that a bit over the next few entries...

One more thing -- I said earlier that the VBScript float-to-string algorithm was a little bit different than the JScript algorithm. We can demonstrate quite easily by comparing the outputs of two nigh-identical programs: ' VBScript print 9.2 * 100.0 <...

Here's some fun for a Friday. A few years back a bunch of my coworkers and I got to discussing the space program over lunch. Someone asked why it is that we continue to launch devices into orbit by strapping a big old tank full of liquid oxygen to the...

I went to Joel Spolsky's geek dinner at Crossroads the other night, which was a lot of fun. I didn't get much of a chance to chat with Joel, as he was surrounded by a cadre of adoring fans three deep the whole time. I mostly hung out with KC and Larry...

A reader also asked the other day why it is that in VBScript, CSng(0.1) = CDbl(0.1) is False . Forget about binary floating point for a moment. Suppose that we had two fixed-point decimal systems, say one with five digits after the decimal place and one...

I've been getting lots of mail, questions and pointers to interesting articles on some of the trials and tribulations of using floating point arithmetic correctly. Please do keep it coming! Though I am certainly no expert in this area, I'm happy to take...

One of the truly great things about working here is that Distinguished Engineers take time out of their busy schedules to answer random questions . Many thanks to Anders and Scott for sharing their insights. Incidentally, as I've mentioned before , I...

A number of readers asked for an explanation of my offhand comment that Benford's Law can be used to show that binary is the best base for doing floating point math. One of the desired properties of a floating point system is that the "representation...

While I was poking through my old numeric analysis textbooks to refresh my memory for this series on floating point arithmetic, I came across one of my favourite weird facts about math. A nonzero base-ten integer starts with some digit other than zero...

I was pleased to learn earlier today that Scott Wiltamuth, one of the designers of C#, has started blogging . I'm looking forward to seeing what Scott has to say about the past, present, and future of language design for .NET. I first encountered Scott...

A month ago I was discussing some of the issues in integer arithmetic , and I said that issues in floating point arithmetic were a good subject for another day. Over the weekend I got some questions from a reader about floating point arithmetic, so this...

Happy New Year everyone! Let's start 2005 off with another episode of Riddle Me This, Google. Yes, once more, I've looked through the 43500 google queries that have resulted in page hits on my blog in the last six months. (Over 200 a day!) For most...