The article explains how the Mersenne Twister pseudorandom number generator, despite its period of 2^19937-1, can be reverse-engineered using linear algebra. By observing 624 consecutive outputs, one can set up a system of linear equations over GF(2) to recover the internal state and predict future outputs.
The Mersenne Twister (MT) is a random number generator with strong statistical but weak cryptographic properties. This post demonstrates how to recover the internal state of an MT generator from its output using linear algebra, contrasting this approach with the usual bit twiddling method.
The post explains how to recover the internal state of the lehmer64 random number generator from its outputs, following a similar approach to a previous article on hacking the Mersenne Twister. The lehmer64 generator is noted for its simple implementation and high speed.
The article discusses the probability that a random n × n binary matrix (filled with 0s and 1s) is invertible, exploring different approaches to calculating this probability depending on the underlying assumptions about the entries.
A blog post discusses the probability that a random matrix over a finite field is invertible, noting that this probability converges quickly as the matrix dimension n increases.