arXiv subjects

Michael A. Idowu

Publications and source records attributed to Michael A. Idowu.

8 recordsLinked to original sources

arXiv2025

Deterministic Cryptographic Seed Generation via Cyclic Modular Inversion over $\mathbb{Z}/3^p\mathbb{Z}$

We present a deterministic framework for cryptographic seed generation based on cyclic modular inversion over $\mathbb{Z}/3^p\mathbb{Z}$. The method enforces algebraic admissibility on seed inputs via the identity $d_k \equiv -\left(2^{k-1}\right)^{-1} \bmod 3^p$, thereby producing structured and invertible residue sequences. This mapping yields entropy-rich, cycle-complete seeds well-suited for cryptographic primitives such as DRBGs, KDFs, and post-quantum schemes. To assess the quality of randomness, we introduce the Entropy Confidence Score (ECS), a composite metric reflecting coverage, uniformity, and modular bias. Although not a cryptographic PRNG in itself, the framework serves as a deterministic entropy filter that conditions and validates seed inputs prior to their use by conventional generators. Empirical and hardware-based results confirm constant-time execution, minimal side-channel leakage, and lightweight feasibility for embedded applications. The framework complements existing cryptographic stacks by acting as an algebraically verifiable entropy filter, thereby enhancing structural soundness and auditability.

cs.CR↗

arXiv2025

Symbolic Generation and Modular Embedding of High-Quality abc-Triples

We present a symbolic identity for generating integer triples $(a, b, c)$ satisfying $a + b = c$, inspired by structural features of the \emph{abc conjecture}. The construction uses powers of $2$ and $3$ in combination with modular inversion in $\mathbb{Z}/3^p\mathbb{Z}$, leading to a parametric identity with residue constraints that yield abc-triples exhibiting low radical values. Through affine transformations, these symbolic triples are embedded into a broader space of high-quality examples, optimised for the ratio $\log c / \log \operatorname{rad}(abc)$. Computational results demonstrate the emergence of structured, radical-minimising candidates, including both known and novel triples. These methods provide a symbolic and algebraic framework for controlled triple generation, and suggest exploratory implications for symbolic entropy filtering in cryptographic pre-processing.

cs.CR↗

arXiv2015

Instantaneous Modelling and Reverse Engineering of DataConsistent Prime Models in Seconds!

A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of new reverse engineering and dynamic methods for automated systems modelling of complex systems, including complex biological, financial, control, and artificial neural network systems. The systems/model theory behind the invention has been formalised as a new, effective and robust system identification strategy complementary to process-based modelling. The proposed dynamic modelling and network inference solutions often involve tackling extremely difficult parameter estimation challenges, inferring unknown underlying network structures, and unsupervised formulation and construction of smart and intelligent ODE models of complex systems. In underdetermined conditions, i.e., cases of dealing with how best to instantaneously and rapidly construct data-consistent prime models of unknown (or well-studied) complex system from small-sized time series data, inference of unknown underlying network of interaction is more challenging. This article reports a robust step-by-step mathematical and computational analysis of the entire prime model construction process that determines a model from data in less than a minute.

q-bio.QM↗

arXiv2015

On the Foundations of the Theory of a new Collatz Based Number System

Set out here are some fundamental theories that may be regarded as newly discovered metamathematics of the odd integers in relation to the Collatz conjecture (also called the 3x+1 problem). Originally motivated by the requirement to invent a new optimised integer factorisation method, this foundational paper primarily focuses on the foundation, formalisation and presentation of a new theoretical framework (schema or blueprint) of a Collatz based number system. The proposed framework is based on metamathematical theories meticulously derived through iterative analyses and reverse engineering (i.e., by hand and mathematical computations) of many large subsets of integers. A collation of the fundamental results from these analytical attempts has led to the establishment of a completely deterministic model of a generalised Collatz based number system that is fundamentally and strangely associated with nonchaotic patterns. The proposed Collatz based number schema comprises of both visual and theoretical representations of many hidden patterns in Collatz sequences yet to be reported in literature. This novel theoretical approach may be viewed as a new method to contemporary Collatz conjecture research which may be connected to the proofs of many other mathematical theorems in number theory and discrete mathematics.

math.GM↗

arXiv2014

Zeta Functional Analysis

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $ζ(2n+1)$ in terms of zeta at other fractional points. This paper also establishes and presents new expository notes and perspectives on zeta function theory and functional analysis. In addition, a new fundamental result, in form of a new function called omega $Ω(s)$, is introduced to analytic number theory for the first time. This new function together with some of its most fundamental properties and other related identities are here disclosed and presented as a new approach to the analysis of sums of generalised harmonic series, related alternating series and polygamma functions associated with Riemann zeta function.

math.GM↗

arXiv2012

A closed-form expression for zeta(2n+1) reveals a self-recursive function

Euler discovered a formula for expressing the value of the Riemann zeta function for all even positive integer arguments. A closed-form expression for the Riemann zeta function for all odd integer arguments, based on the values of the Dirichlet beta function, euler numbers and pi, reveals a new evidence about the self-recursive nature of Riemann zeta function at odd integers. We demonstrate for the first time that the Riemann zeta function at odd integers always produces a recurrence relation that is self-recursive.

math.NT↗

arXiv2012

Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function for positive integers

A new definition for the Dirichlet beta function for positive integer arguments is discovered and presented for the first time. This redefinition of the Dirichlet beta function, based on the polygamma function for some special values, provides a general method for obtaining all special constants associated with Dirichlet beta function. We also show various new and fundamental relations between the polygamma function, Riemann zeta, the even-indexed euler numbers, the Dirichlet beta functions in a way never seen or imagined before.

math.NT↗

arXiv2012

Elegant expressions and generic formulas for the Riemann zeta function for integer arguments

A new definition for the Riemann zeta function for all positive integer number s > 1 is presented. We discover a most elegant expression and easy method for calculating the Riemann zeta function for small even integer values. Through this new reformulation we provide a one-line proof of the value of zeta(2) and demonstrate that zeta(2s) may be calculated by hand using only the cotangent function when the magnitude of the integer s is small.

math.NT↗