September 2008 – Good Math Bad Math

How Mortgages Turned into a Trillion Dollar Disaster

MarkCC September 25, 2008 Bad Economics

Ok, another batch of questions have come in, all variants on
the same theme.

The question is, if mortgages are at the root of the current economic disaster, how can it possibly result in close to a trillion dollars worth of losses?

It definitely seems strange, on two different levels. On an absolute scale, it’s hard to see how mortgage losses could add up to a trillion dollars. And on a relative scale, it’s hard to see how the foreclosures could really overwhelm the lenders when even an extremely high foreclosure rate represents a fairly modest loss considered as a percentage.

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Bad Probability and Economic Disaster; or How Ignoring Bayes Theorem Caused the Mess

MarkCC September 23, 2008 Bad Economics

There is at least a little bit of interesting bath math
to learn from in the whole financial mess going on now. A couple
of commenters beat me to it, but I’ll go ahead and write about
it anyway.

One of the big questions that comes up again and again is: how did they get away with this? How could they find any way of
taking things that were worthless, and turn them into something that could be represented as safe?

The answer is that they cheated in the math.

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Economic Disasters and Stupid Evil People

MarkCC September 22, 2008 Bad Economics

With the insanity that’s been going on in the financial world
lately, a bunch of people have asked me to post a followup to my
earlier posts on the whole mortgage disaster, to try to explain
what’s going on lately.

As I keep saying when people ask me things like this, I’m not an economist. I don’t know much about economics, and what little I do know, I tend to find terribly boring. And in this case, the discussion inevitably gets political, so I’m expecting lots of nasty email.

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Screwing Up Modes of Operation: Counter done right

MarkCC September 15, 2008 Encryption

So, as it turned out, I made a major screwup in my post earlier today on modes of operation. Rather than just edit the post, I'm adding a new post…

Modes of Operation in Block Cryptography

MarkCC September 15, 2008 Encryption

Sorry for the slow pace of the blog lately. I’ve been sick with a horrible
sinus infection for the last month, and I’ve also been particularly busy with work, which have left me with neither the time nor the energy to do the research necessary to put together a decent blog post. After seeing an ENT a couple of days ago, I’m on a batch of new antibiotics plus some steroids, and together, those should knock the infection out.

With that out of the way: we’re going to look at how to get from simple block ciphers to stream ciphers, using the oh-so-imaginatively named modes of operation!

As a quick refresher, block encryption specifies an encryption scheme that operates on fixed-size blocks of bits. In the case of DES, that’s 64 bits. In the
real world, that’s not terribly useful on its own. What we want is something called
a stream cipher: a cipher that’s usable for messages with arbitrary lengths. The way to get from a block cipher to a stream cipher is by defining
some mechanism for taking an arbitrary-sized message, and describing how to break it into blocks, and how to connect those blocks together.

Modes of operation are formal descriptions of the way that you
use block encryption on a message that’s larger than a single block. Modes of operation (MOOs) are critical in making effective use of a block cipher. Of course, there’s always a tradeoff in things like this: you have to choose what properties of your encrypted communication you want to protect. Particularly for DES encryption, the standard MOOs can provide confidentiality (making sure that no one can read your encrypted communication), or integrity (making sure that your communication isn’t altered during transmission), but not both.

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Friday Random 10, Sept 12

MarkCC September 12, 2008 Music

My apologies for how slow the blog has been lately. I've been sick with a horrible sinus infection for the last month. I saw an ENT on wednesday, and with…

Suddenly, I feel… coordinated

MarkCC September 11, 2008 Humor

This is about as off-topic as it gets, but I can't resist posting. Y'see, I'm a spectacularly uncoordinated person. I can trip over nothing. If you throw me a ball,…

DES Encryption Part 1: Encrypting the Blocks

MarkCC September 8, 2008 Encryption

As promised, now we’re going to look at the first major block
cipher: the DES. DES stands for “data encryption standard”; DES was the first encryption system standardized by the US government for official use. It’s an excellent example of a strong encryption system; to this day, while there are several theoretical attacks, there’s no feasible attack on a single DES-encrypted message that’s better than brute force. The main problem with DES is the shortness of its key: only 56 bits, which makes it downright practical to implement brute-force attacks against it using today’s hardware.

DES works with 64 bit blocks, and a 56 bit key. As an interesting aside, there are some serious questions about just why the standard key was 56 bits. Officially, the key length is 64 bits, but during the standardization process, the key was modified at the request of the NSA so that 8 of the bits were used as parity checks – that is, as extra bits that could be used for checking the validity of a key. 8 bits for parity checking on a 56 bit key is really overkill – in fact, putting parity checks into the key at all is really rather questionable. There’s been a lot of speculation that either
the NSA knew some kind of trick that could be used against a 56 bit key, or that 56 bits put the encryption within the range of what they could crack using a brute force attack. But no one has ever admitted to either solution, and as far as I know, no one knows of any way that a 56 bit key could have been feasibly cracked using brute force with the technology of the time.

Anyway – getting past the politics of it, it’s still a really interesting
system. It’s a rather elegant combination of simplicity and complexity. It’s got a simple repetitive structure based on lookup tables, which gives it its deceptive simplicity; but those lookup tables are actually an implementation of a very complex non-linear discrete mathematical system.

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Introduction to Block Ciphers

MarkCC September 4, 2008 Encryption

Where encryption starts getting really interesting, in my opinion, is
block ciphers. Block ciphers are a general category of ciphers that
are sort of a combination of substitution and transposition ciphers, and
sort of something entirely different. They’re really fascinating
things, but they’re pretty complicated.

The basic core of block ciphers is encryption of blocks. A block is
a fixed-length series of bits. The basic cipher is a pair of functions (E,E^-1), where E (the encryption function) takes a block B and a key K, and generates a new block B’=E(K,B), which is the encrypted form of the block; and E^-1 (the decryption function) takes a key and an encrypted block, and returns the original plaintext block: B=E^-1(K,B’).

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