Generation of nonrecursive n -bit pseudorandom numbers by two times ( n -bit) × ( n -bit) multiplication ( n = 64, 128, 192, …, 16384 )
Year: 2026
Type: article
Abstract: In this paper, we show that we can generate nonrecursive n -bit pseudorandom numbers by two times ( n -bit) × \,{\times} ( n -bit) multiplication and succeeding extraction of an n -bit integer from the result of multiplication. The algorithm, which we call MmS, is described using the functions defined by T 2 k ( X , Y ) = 2 k X Y - ⌊ 2 k X Y ⌋ + 1 {T_{2^{k}}(X,Y)=2^{k}XY-\lfloor 2^{k}XY\rfloor+1} , X , Y ∈ [ 1 , 2 ) {X,Y\in[1,2)} , and T ˇ 2 k ( X ) ≡ T 2 k ( X , X ) {\check{T}_{2^{k}}(X)\equiv T_{2^{k}}(X,X)} . We observe and consider mathematically the condition that T 2 k ( X , Y ) {T_{2^{k}}(X,Y)} and succeeding repetition of T ˇ 2 k ( X )
Author: Hirotake Yaguchi
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7130927140