翻訳言語

q級数と分割におけるオイラー関数

オイラー関数は、数論においてオイラーのトーシェント関数とは異なる概念であり、q級数や整数の分割理論において重要な役割を果たす。この記事では、オイラー関数の定義と基本的な性質、そして分割関数との関係について解説する。

Reverse engineering Mersenne Twister with Linear Algebra
3.0
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.
Hacking the lehmer64 RNG
2.0
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.
Probability that a random binary matrix is invertible
1.5
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.
Euler function
1.0
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.

翻訳言語

Reverse engineering Mersenne Twister with Linear Algebra
3.0
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.
Hacking the lehmer64 RNG
2.0
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.
Probability that a random binary matrix is invertible
1.5
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.
Euler function
1.0
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.

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