p-adic Chaos and Random Number Generation

p-adic Chaos and Random Number Generation

Pseudorandom number generation by $p$-adic ergodic transformations

The paper study counter-dependent pseudorandom generators; the latter are generators such that their state transition function (and output function) is being modified dynamically while working: For such a generator the recurrence sequence of states satisfies a congruence xi+1 ≡ fi(xi) (mod 2), while its output sequence is of the form zi = Fi(ui). The paper introduces techniques and construction...

Pseudorandom number generation by p-adic ergodic transformations: an addendum

The paper study counter-dependent pseudorandom number generators based on m-variate (m > 1) ergodic mappings of the space of 2-adic integers Z2. The sequence of internal states of these generators is defined by the recurrence law xi+1 = H B i (xi) mod 2 n, whereas their output sequence is zi = F B i (xi) mod 2 n; here xj , zj are m-dimensional vectors over Z2. It is shown how the results obtain...

p-adic Verification of Class Number Computations

Random numbers and random matrices: Quantum chaos meets number theory

The statistical analysis of the eigenvalues of quantum systems has become an important tool in understanding the connections between classical and quantum physics. The statistical properties of the eigenvalues of a quantum system whose classical counterpart is integrable match those of random numbers. The eigenvalues of a chaotic classical system have statistical properties like those of the ei...