Computers are fast, and they work far faster than humans can follow. But, as we all know, the time it takes a computer to perform a task depends on the size of the task: Creating 20 database records takes approximately twice as long as creating 10. So, in theory at least, if we could measure computer time precisely, and we could control other things being done in the computer, we could infer the size of the computer's input. In most situations size is relatively uninteresting to the attacker. But in cryptography, even the smallest bit of information can be significant.
Brumley and Boneh investigated a program that does RSA encryption for web sites. The authors try to derive the key by successive guesses of increasing value as possibilities for the key. Although the details of the attack are beyond the scope of this book, the idea is to use a trick in the optimization of RSA encryption. Grossly oversimplified, encryption with numbers less than the key take successively longer amounts of time as the numbers get closer to the key, but then the time to encrypt drops sharply once the key value is passed. Brute force guessing is prohibitive in time. But the authors show that you don't have to try all values. You infer the key a few bits at a time from the left (most significant bit). So you might try 00xxx, 01xxx, 10xxx, and 11xxx, noticing that the time to compute rises from 00xxx to 01xxx, rises from 01xxx to 10xxx, and falls between 10xxx and 11xxx. This tells you the key value is between 10xxx and 11xxx. The attack works with much longer keys (on the order of 1000 bits) and the authors use about a million possibilities for the xxx portion. Still, this technique allows the authors to infer the key a bit at a time, all based on the amount of time the encryption takes. The authors performed their experiments on a network, not with precise local timing instruments, and still they were able to deduce keys.
Cryptography is the primary area in which speed and size are information that should not be revealed. But you should be aware that malicious code can perform similar attacks undetected.