Hi, I'm

Zeel Gajjar.

Cryptography Researcher · Quantum Computing · Cybersecurity

I build cryptographic tools, explore quantum computing, and research the mathematics behind secure systems. Currently pursuing BTech in Cybersecurity at M.B. Institute of Technology.

01. About Me

I'm a cybersecurity student with a deep interest in the mathematics behind cryptographic systems. My work spans cryptography, quantum computing, and algebraic topology areas where abstract mathematics directly impacts real world security.

I've self studied quantum physics principles to understand quantum measurement concepts for cryptographic applications. I'm passionate about making cryptography and security concepts accessible to everyone.

Outside of research, I compete in CTF challenges on PicoCTF and OverTheWire, working through problems in web exploitation, binary exploitation, and cryptography.

Education BTech in Cybersecurity M.B. Institute of Technology · Class of 2029
Focus Areas Cryptography · Quantum Computing · Topology
Interests CTFs · Research · Open Source

02. Research

In Progress

Topological Characterization of Access Structures in Secret Sharing via Simplicial Homology

Zeel Gajjar, Dhruvi Jamnapara

This paper establishes a rigorous topological framework for analyzing secret sharing schemes by modeling unauthorized coalitions as simplicial complexes and applying simplicial homology to derive lower bounds on share size. We demonstrate that non trivial homology groups correspond directly to structural obstructions preventing efficient scheme construction.

Through matroid theory, we classify access structures by representability and show that topological invariants Betti numbers and the Euler characteristic serve as computable predictors of scheme complexity. Results are validated with explicit computations on access structures involving up to seven participants using SageMath.

Secret Sharing Simplicial Homology Betti Numbers Matroid Theory SageMath
View Repository →
In Progress

Entanglement Detection via Binary Tree of Bloch Sphere Visualization and CNN Classification

Zeel Gajjar, Yasmin Sekh

We present a machine learning approach to quantum entanglement detection using Binary Tree of Bloch Sphere (BTBS) visualization for n-qubit systems. A convolutional neural network classifies quantum states as entangled or separable directly from BTBS image representations.

The BTBS representation preserves entanglement structure visually ,product states display identical subtrees while entangled states produce distinct patterns across subtrees. Preliminary results demonstrate comparable accuracy to analytical methods with potential computational advantages over traditional von Neumann entropy calculation.

Quantum Entanglement Bloch Sphere CNN Machine Learning Quantum Computing

03. Projects

Quantum-Inspired Cryptographic Key Generator

GitHub →

A dual-mode cryptographic key generation system that harvests entropy from webcam pixel noise, system randomness, and high-precision temporal sources. The standard mode extracts visual entropy through dynamic geometric measurement overlays with Shannon entropy calculation and HKDF-SHA512 key derivation. The cryptographic-grade mode applies multi-stage Von Neumann debiasing, quintuple hash whitening cascades (SHA-512, SHA-256, Blake2b), and triple entropy source pooling with enforced temporal de-correlation. Validated against the NIST SP 800-22 Statistical Test Suite with a 100% pass rate across all 16 tests for 2000+ generated keys.

Python OpenCV HKDF-SHA512 NIST SP 800-22

Cryptographic Key Statistical Test Suite

GitHub →

A comprehensive statistical analysis tool that evaluates cryptographic key quality through 34 randomness tests. Implements the complete NIST SP 800-22 Rev. 1a suite (15 tests) alongside 16 supplementary tests including autocorrelation, Shannon entropy, chi-square uniformity, avalanche effect, strict avalanche criterion, Lempel-Ziv complexity, and birthday spacing analysis. Features intelligent test skipping for insufficient bit-length scenarios, automated p-value computation at configurable significance levels, and generates detailed CSV reports with visualization plots for each analyzed key.

Python NumPy SciPy Matplotlib Pandas

Topological Secret Sharing Analysis Pipeline

GitHub →

A diagnostic pipeline for evaluating the feasibility and efficiency of secret sharing access structures using algebraic topology. Given an access structure, the system constructs its unauthorized simplicial complex, computes topological invariants (Betti numbers, Euler characteristic, simplicial homology groups), identifies critical participants through vertex analysis, and estimates information-theoretic share size lower bounds. Includes matroid-based representability checking for ideal scheme detection and batch processing across datasets of access structures with export to CSV, JSON, and LaTeX.

Python SageMath LaTeX Jupyter

Quantum Computing Experiments

GitHub →

A collection of quantum algorithm implementations exploring fundamental quantum computing concepts. Includes the Deutsch-Jozsa algorithm demonstrating quantum advantage through single-query function classification, a quantum coin simulation examining superposition and measurement collapse, and random circuit generation for analyzing gate combinations and quantum state evolution. Each implementation serves as both a functional demonstration and an educational reference for quantum circuit design principles.

Python JavaScript HTML CSS

04. Skills & Tools

Languages

Python C C++ Julia JavaScript Bash

Security Tools

Burp Suite Wireshark Nmap

Frameworks & Libraries

OpenCV Pandas Matplotlib NumPy SciPy Fernet PyGame Electron.js SageMath

Domains

Cryptography Cryptanalysis Network Security Web Exploitation Binary Exploitation Statistical Testing Cyber Forensics Quantum Computing

05. Achievements

1st Place — College Ideathon

Designed and pitched an IoT encryption system for smart home devices using camera-based entropy generation, hardware entropy, and thermal noise. The system enables edge devices to generate their own cryptographic keys without relying on external random number services.

Independent Research

Authored a research paper on cryptographic key generation combining visual entropy from webcam photon noise with system entropy sources. Validated the dual-source architecture with a 100% pass rate across all 16 NIST SP 800-22 Statistical Tests for over 2000 generated keys.

CTF Competitions

Active participant in PicoCTF and OverTheWire wargames, solving challenges across web exploitation, binary exploitation, and cryptography categories. Focused on applying theoretical knowledge to practical offensive security scenarios.

06. Get In Touch

I'm open to research collaborations, discussions about cryptography, or anything quantum computing. Feel free to reach out.