The post discusses Euler's function within the framework of q-series and integer partitions, exploring how the product form of Euler's function relates to generating functions for partitions and its connections to combinatorial identities.
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.