Question

A series of 3-dimensional points are produced using a 64-bit LCG, how many hpyerplanes do these numbers lie on? Research and describe in your own words, the Mersenne Twister and Truecrypt algorithms.

Answer 1

LCG is used to
choose points in an n-dimensional space, the points will lie on, at most, m^1/n hyper
planes

64^1/3 = 4 hyperplanes present

Mersenne Twister algorithm:
Mersenne Twister is today's most popular pseudorandom number generator. It is used by every widely distributed mathematical software package. It has been available as an option in MATLAB since it was invented and has been the default for almost a decade.
Mersenne primes
Mersenne primes are primes of the form 2^p - 1 where p itself is prime. They are named after a French friar who studied them in the early 17th century. We learn from Wikipedia that the largest known prime number is the Mersenne prime with p equal to 57,885,161. The Mersenne Twister has p equal to 19937. This is tiny as far as Mersenne primes go, but huge as far as random number generators are concerned.

Truecrypt algorithm:
TrueCrypt is a software system for establishing and maintaining an on-the-fly-encrypted volume
(data storage device). On-the-fly encryption means that data is automatically encrypted right before
it is saved and decrypted right after it is loaded, without any user intervention. No data stored on an
encrypted volume can be read (decrypted) without using the correct password/keyfile(s) or correct
encryption keys. Entire file system is encrypted.