Oportunidade Estratégica IPT-Holosystems em Criptografia Pós-Quântica para Defesa Nacional

Published by Rāmānujan Institute for the Development of Prodigious Young Mathematicians on

Abstract

Este documento apresenta um framework matemático rigoroso para Arquitetura Zero Trust Pós-Quântica, desenvolvido integralmente em ambiente teórico (in silico), com implicações práticas diretas para defesa nacional, segurança pública e controle aeroespacial.

A proposta aborda um dos maiores desafios da criptografia pós-quântica contemporânea: como garantir segurança contra adversários quânticos sem paralisar infraestruturas existentes, elevar custos operacionais ou comprometer desempenho em sistemas críticos. O framework unifica protocolos clássicos e pós-quânticos por meio de teoria das categorias, reticulados e álgebra funcional, permitindo interoperabilidade segura, autenticação em tempo real e proteção contra ataques quânticos e clássicos.

Além da base matemática profunda, o trabalho descreve aplicações concretas em comunicações táticas, sistemas de comando e controle, segurança pública, inteligência e aviação, demonstrando ganhos expressivos de latência, eficiência energética e viabilidade de adoção gradual. O documento posiciona a matemática abstrata como motor central para uma nova geração de sistemas criptográficos resilientes em um mundo pós-quântico.

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Rāmānujan Institute for the Development of Prodigious Young Mathematicians

I am the founder of the Rāmānujan Institute for the Development of Prodigious Young Mathematicians, which aims to foster the education and growth of children and young people aged 2 to 16 who demonstrate exceptional mathematical abilities. Our institute is dedicated to providing an advanced and challenging curriculum that not only prepares students for prestigious competitions, such as the International Mathematical Olympiad (IMO), but also supports their overall development. We focus on nurturing mathematical talent while ensuring that our students develop the skills necessary for success in academic and professional environments. Through mentorship programs and a commitment to inclusivity, we strive to create a community where young mathematicians can thrive and make significant contributions to the field. I am also Marcos Eduardo Elias, an engineer and mathematician. My academic journey began with a Bachelor’s degree in Mechatronic Engineering from the Polytechnic School of the University of São Paulo (USP). My education culminated in a Doctorate in Mathematics from St. Petersburg State University, specializing in Real, Complex, and Functional Analysis. I have held teaching positions at institutions such as Ibmec, Insper, and FGV-SP. I am also a member of the Brazilian Mathematical Society. In the financial sector, I founded several institutions, including GAS Investimentos (later Vinci Partners), Empiricus Research, Turing High Frequency Trading, Modena Capital and Guiar Investments. In the financial markets, I am known as the Volatility Hunter, and - in the last 30 years, I have been relentlessly searching for highly asymmetric upside risk (I am on the right side of the barbell). I have been contributing to the MIT Sloan Management Review, primarily on topics related to risk management. My current research interests include real, complex, and functional analysis, linear algebra for quantum algorithmics, Feigenbaum-Coullet-Tresser universality, stochastic calculus, and Grothendieck's Standard Conjectures on Algebraic Cycles.

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