Difficult: First off, they do not explain, but it seems that must stand for concatonation? Possibly this was in a section that was not assigned yet, or maybe I just forgot the notation from an earlier assignment. The Birthday attack seems very interesting, especially the paradox part (that you can find two matching birthdays with high probability but not match a given one). It looks like they violate this paradox with the birthday attack on discrete logarithms, however. I understand how they are using the matching of two different groups instead of trying to match a single value, but I do not understand why a similar method cannot be used in many other situations where you want to match a given value.
Reflective: Frequent discussions of how we cannot truly create a random sequence without natural phenomena has lead me to wonder if they have been working on this problem in a manner besides trying to find more and more random mathematical functions. Most of the natural phenomena mentioned as random are inherently slow (such as flipping coins or counting clicks in a second). However, there are many random natural phenomena that occur quickly that can be read with modern machinery. For example, I seem to remember from my chemistry classes that vibrations in a crystal lattice are random, but happen many times in a millisecond. We can "read" these vibrations even in a small sample of crystal, so why could we not use this as a speedy random sequence generator. If the number of vibrations in a millisecond (or less if you need) is even, you get a 0, odd you get a 1. Small crystals and the equipment to read their vibrations could then be installed in your desktop. I may be wrong with the specific example, but I am sure there are many random, small scale, fast phenomena that we know about now.
No comments:
Post a Comment