Differences between version 6 and predecessor to the previous major change of RandomNumberGenerator.
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| Newer page: | version 6 | Last edited on Thursday, March 25, 2004 2:15:01 pm | by AristotlePagaltzis | Revert |
| Older page: | version 5 | Last edited on Thursday, March 25, 2004 2:04:11 pm | by AristotlePagaltzis | Revert |
@@ -5,15 +5,21 @@
These __must__ be hardware by definition. A variety of approaches for their design exist, but listening to white noise or radioactive decay seem to be the most popular ones. There are a number of publicly queriable true random number generators on the web, such as [http://www.random.org/] and [http://www.fourmilab.ch/hotbits/].
!!! Pseudorandom number generators
-A pseudo random number generator such as offered by the random(3) and rand(3) functions of the standard [C] library generates numbers using mathematical [Algorithm]s. Such a generator has a "period", which means that it produces a repeating sequence of numbers. With a good algorithm, the period length can well reach billions of numbers
.
+A pseudo random number generator such as offered by the random(3) and rand(3) functions of the standard [C] library generates numbers using mathematical [Algorithm]s.
-However
, designing such an algorithm is difficult terrain which requires thorough understanding
of statistics and very sharp math skills. __Do not attempt to roll your own.__ Most naive attempts at handrolled pseudorandom number generators have alarmingly short period lengths. Often
, hapless programmers will try to make
a "better" generator by lumping together two different algorithms with decent period lengths each
-- but the result is almost inevitably a generator with a ''shorter'' period!
+;: ''Anyone attempting to produce random numbers by purely arithmetic means is
, of course
, in
a state of sin.''
--JohnVonNeumann
-Note
that true randomness is not always desirable. Random number sequences often have certain specific characteristics which make them better suited as input to certain kinds of statistical algorithm, because they cause a far faster convergence toward the same final result than truly random numbers could. Truly random numbers also make debugging much harder for obvious reasons; if you want to verify an algorithm, you want to be able to replay "random" number sequences as necessary. On the other hand, you will usually need a statistically decently random sequence to examine the longterm behaviour of the algorithm, so just using a sequence with regular characteristics wouldn't work.
+An inevitable consequence is that such a generator has a "period", which means that it produces a repeating sequence of numbers. With a good algorithm though, the period length can well reach billions of numbers.
+
+However, designing such an algorithm is difficult terrain which requires thorough understanding of statistics and very sharp math skills. __Do not attempt to roll your own.__ Most naive attempts at handrolled pseudorandom number generators have alarmingly short period lengths. Often, hapless programmers will try to make a "better" generator by lumping together two different algorithms with decent period lengths each -- but the result is almost invariably a generator with a ''shorter'' period!
+
+Another problem in cryptographical applications of pseudorandom numbers is that the algorithm is known. If you know a long enough sequence of generated numbers, you can simply solve the resulting equations yourself and then predict the numbers the generator will be producing next. There is an obvious solution: the algorithm must include enough hidden state so that a solvable set of equations cannot be formulated just by looking at a number sequence it generated.
+
+But note
that true randomness still
is not always desirable. Random number sequences often have certain specific characteristics which make them better suited as input to certain kinds of statistical algorithm, because they cause a far faster convergence toward the same final result than truly random numbers could. Truly random numbers also make debugging much harder for obvious reasons; if you want to verify an algorithm, you want to be able to replay "random" number sequences as necessary. On the other hand, you will usually need a statistically decently random sequence to examine the longterm behaviour of the algorithm, so just using a sequence with regular characteristics wouldn't work.
So there are many areas where pseudorandom numbers are actually more desirable than truly random ones.
!!! Hybrids
In [Unix] systems, there's commonly a __/dev/random__ device to access a pseudorandom number generator. This generator however includes a twist that lets it generate higher quality random numbers than otherwise expected: its seed is periodically perturbed using using low-level timing information from the network, mouse, keyboard, and possibly other entropy sources, which only the [Kernel] has proper access to. It is generally considered a sufficiently good generator for everything except the random numbers to be used in cryptographic suituations PublicKey generation.
