I have been working off and on for some time on a one-time pad application (that I will release next week). Since the success of an OTP is dependent on having a good source of random numbers, I have kept my eyes open for any information related to random numbers, and their generation. Conventional wisdom has it that the best way to generate random numbers is to measure some physical phenomenon such as radioactive decay, and use these measurements to form your "random" number sequence. Recently, I came across an interesting article in the "New Scientist" (May 8, 1993) entitled "The half Life of a Dirty Book". This article indicates that phenomena-based measurements may have some interesting properties. A number of years ago, when people used log tables (any of you remember the CRC tables?), some astute observers noticed that the front section of the log tables were more heavily used than the back section. This seemed odd, since it would seem reasonable that all portions of the table should have an equal chance of being examined. In 1938, the physicist Frank Benford made a study of numerous measurements based on natural phenomena. He looked at surface areas of lakes, molecular weights of compounds etc. He discovered that the first digit of any such measurement was most likely to be a one, and least likely to be a nine. The probability that this digit takes a given value decreases in a regular manner as the digits increase from one to nine. This is called Benford's Law. Later, a report in the European Journal for Physics (vol 14, page 59) showed that that alpha decay half lives, both predicted and observed, followed Benford's law. What was also interesting was that Benford's law is scale- invariant. According to the article: "The same law applies whether you measure the areas of lakes in hectares or square yards, whether you multiply house numbers by seven or 93, or whether you count the half-lives of alpha particles in seconds or centuries". The article concludes that Benford's law may actually be a part of chaos theory. Fractals, they also point out, are scale - invariant. All this may indicate that random number produced from observations of physical phenomena may have characteristics that set them apart from software-derived random numbers. Does this give a tool for breaking random number based encryption? I can't see how, since you still can't figure out the exact sequence. But it perhaps means there may be fractal patterns there, at least for numbers derived from physical phenomena. Interesting. Of course, with an 8 bit random number sequence (with a maximum number of 255), it would be hard to generate a number sequence that did not follow Benford's law.. You would have to throw in a lot of 9's , and 99's to get as as many numbers begining with '9' as you do that begin with a '1' (1, 10-19,100-199). So let's see..... first we had flat distributions vs. normal distributions, now Benford vs. non Benford..... Jim Pinson Confused in Galapagos.