Cryptography
The Fragility of Raw RSA: From Mathematical Elegance to Existential Forgery
Why textbook RSA preserves multiplicative structure and enables existential forgery, and how hash-then-sign and padding schemes like RSA-PSS close the gap.
Articles, notes, and lecture follow-ups.
Articles on cryptography, software verification, machine learning, and the supporting math.
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Cryptography
The Architecture of Trust: A Comparative Analysis of Group Structures in Cryptography
How Lagrange and Cauchy shape real-world DH and ECC groups, why nearly-prime cofactor curves trade purity for performance, and what Secure Scuttlebutt teaches about validation.
Cryptography
The Hidden Geometry of Trust: Subgroups, Cofactors, and Scalar Efficiency in ECC
From Weierstrass curves and double-and-add to cofactor attacks and Dual_EC_DRBG—how subgroup geometry and implementation choices determine ECC trust boundaries.
Cryptography
Vulnerability Assessment Report: Nonce Leakage and Implementation Risks in (EC)DSA
A structured look at HNP-based key recovery, BIGNUM representation leaks, lazy resizing CVEs, and protocol-level subgroup failures in modern signature stacks.
Cryptography
Engineering Protocol-Secure and Side-Channel Resistant Cryptography: From Theory to Implementation
Bridging prime-order proofs with cofactor reality: small-subgroup attacks, BIGNUM leaks, twist security, and a practical mitigation checklist for protocol engineers.
Cryptography
The Great Cryptographic Shift: From Classical Diffie-Hellman to Elliptic Curves
Why finite-field DLP hits a scalability wall, how ECC and Pollard rho change the cost curve, and a worked finite-field point arithmetic example on F23.
Cryptography
Cracking the Code: A Review of Cryptographic Failures in Peer-to-Peer and Wireless Protocols
From Tamarin’s prime-order ideal to Scuttlebutt, Bluetooth P-256 invalid-point attacks, and OpenSSL lazy resize—how symbolic proofs miss implementation and protocol reality.
Cryptography
The Perfection Paradox: Why the World's Only Unbreakable Code is a Logistical Nightmare
Discover the only mathematically unbreakable encryption method—and why its perfection makes it practically useless.
Cryptography
The One-Time Pad: When Math Guarantees Absolute Security
Discover the only encryption method proven to be mathematically unbreakable—and why its implementation is far more dangerous than it appears.
Cryptography
Why Natural Numbers Fail the Security Test: The Zero Divisor Trap
Explore why the natural numbers we use everyday are fundamentally unsuitable for encryption, and the mathematical traps that await those who don't understand fields.
Cryptography
Malleability and the Block Cipher: Why Encryption Isn't Enough
Learn why encrypted data can still be tampered with and how block ciphers attempt to solve the fundamental problems of encryption.
Cryptography
The Linearity Trap: Why Your Algebra Teacher is an Accidental Hacker
Explore how the Hill Cipher's reliance on linear algebra made it vulnerable to high school math—and why pattern repetition destroyed the unbreakable Vigenère cipher.
Cryptography
The Secret Architecture of Security: Groups Aren't Just for Numbers
Discover how the Symmetric Group—where elements are actions rather than numbers—forms the foundation of modern cryptographic security.
Cryptography
From DES to AES: The Mathematical Evolution of Modern Ciphers
Trace the journey from the broken DES standard to the ironclad AES, and discover the algebraic foundations that make modern encryption possible.
Cryptography
The Binary Secret: How AES Uses Polynomials to Secure the Internet
Discover how the simplest mathematical field Z_2 with just 0 and 1 becomes the foundation for AES encryption through extension fields and irreducible polynomials.
Software Verification and Validation
Software Verification – Upcoming Topic (see Canvas Modules)
Placeholder draft for a later lecture; the exact topic and structure will be filled in once the corresponding Canvas module is available.
Cryptography
Cryptography – Upcoming Topic (see Canvas Modules)
Placeholder draft for a later lecture whose precise topic will be aligned with the Canvas modules and updated once materials are posted.
Software Verification and Validation
Software Verification – LangSmith Experiments and Observability
Stub post expanding the LangSmith hands-on work into a discussion of experiment design, observability, and how tooling supports verification efforts.
Cryptography
Cryptography – Public-Key Cryptography Overview
Stub lecture post introducing the core ideas of public-key cryptography, setting up later deep dives into RSA and related schemes.
Software Verification and Validation
Software Verification – Introduction to Formal Methods
Stub post introducing formal methods in , connecting mathematical reasoning to practical verification of real systems.
Cryptography
Cryptography – Attack Models and Security Goals
Stub lecture post on formalizing security goals and attack models in cryptography, bridging intuitive threats to precise definitions.
Software Verification and Validation
Software Verification – LangSmith Tutorial and Hands-On Setup
Stub post capturing the LangSmith tutorial and hands-on setup work from the modules, focusing on tooling for testing and observability.
Cryptography
Cryptography – Block Ciphers and Modes of Operation
Stub for a lecture post on block ciphers and common modes of operation, building on earlier symmetric encryption basics.
Software Verification and Validation
Software Verification – Specifications and Requirements
Stub post on writing precise specifications and requirements, a key prerequisite for formal verification and systematic testing.
Cryptography
Cryptography – Number Theory Prerequisites
Stub post for the mathematical foundations of modern cryptography, focusing on number theory concepts used later for public-key systems.
Software Verification and Validation
Software Verification – Testing Strategies and Test Design
A stub post on core testing strategies in , from black-box and white-box testing to basic coverage criteria and test design heuristics.
Cryptography
Cryptography – Symmetric Encryption Basics
A stub for the first deep-dive into symmetric encryption in , focusing on block ciphers, modes of operation, and basic threat models.
Software Verification and Validation
Software Verification – Introduction to Testing
An overview of software testing in , covering why testing matters, core terminology, and how testing fits into the broader picture of verification and validation.
Cryptography
Cryptography – Course Overview and Foundations
Course overview for Cryptography, outlining goals, logistics, and the foundational security concepts that will shape the rest of the semester.
Software Verification and Validation
Unit Testing Strategies: Writing Effective Test Cases
Comprehensive guide to unit testing strategies, covering test case design, coverage metrics, mocking techniques, and best practices for writing maintainable test suites.
Cryptography
Symmetric Encryption Algorithms: Understanding Block and Stream Ciphers
A deep dive into symmetric encryption algorithms, including block ciphers like AES and DES, stream ciphers, and their applications in modern cryptography.
General
Spring 2026 Semester Overview: Cryptography and Software Verification
An overview of Spring 2026 coursework in Cryptography and Software Verification and Validation: goals, themes, and how this blog supports the semester.
Software Verification and Validation
Software Verification and Testing: Building Reliable Systems
Exploring the fundamentals of software verification and validation, covering testing strategies, quality assurance techniques, and methods for building reliable software systems.
Cryptography
Public Key Cryptography: Understanding RSA and Key Exchange
Exploring public key cryptography systems, including the RSA algorithm, Diffie-Hellman key exchange, and how asymmetric encryption enables secure communication without shared secrets.
Software Verification and Validation
Integration Testing and Continuous Verification
Exploring integration testing methodologies and continuous verification practices, including test automation, CI/CD pipelines, and strategies for maintaining software quality throughout development.
Software Verification and Validation
Formal Methods in Software Verification: Mathematical Approaches to Correctness
An introduction to formal methods for software verification, including model checking, theorem proving, and mathematical techniques for proving program correctness.
Cryptography
Cryptography Fundamentals: An Introduction to Secure Communication
An introduction to the fundamental concepts of cryptography, exploring how secure communication systems work and why they are essential in modern computing.
Cryptography
Cryptographic Hash Functions: Ensuring Data Integrity
Understanding cryptographic hash functions, their properties, applications in data integrity verification, digital signatures, and password storage systems.
Logic for Computer Scientists
Homework 3 Guide: Quantifier Scope, Proofs, and CNF
Worked guide for Logic for Computer Scientists Homework 3: scoping, inference proofs, CNF transformations, and predicate encodings.
Software Verification and Validation
Research Model Checking with SPIN and Promela
A deep dive into SPIN model checker and Promela modeling language for verifying concurrent systems, with practical examples and verification workflows.
Cryptography
Research Zero-Knowledge Proofs: The SNARK Revolution
Exploring the theoretical foundations and practical implementation of zk-SNARKs—the cryptographic primitives enabling succinct, non-interactive proofs that verify computations without revealing inputs.
Software Verification and Validation
Symbolic Execution with KLEE: Automated Test Generation and Bug Finding
Introduction
Logic for Computer Scientists
Model Checking and Logic Review: Validating Systems and Concepts
A comprehensive review of advanced logic concepts including Hilbert Systems, the Tableaux Method, and Herbrand Semantics, showing how they feed into model checking with concrete transition-system examples.
Intelligent Systems
Logistic Regression and Softmax: Probabilistic Linear Models for Classification
Upgrade the perceptron into a calibrated probabilistic classifier with logistic regression and its multiclass softmax extension, unpacking the sigmoid link, cross-entropy loss, gradient descent, and the bridge to mode...
Logic for Computer Scientists
Linear Temporal Logic: Specification and Verification of Reactive Systems
Master Linear Temporal Logic (LTL) for specifying and verifying time-dependent properties of reactive systems, from safety invariants to liveness guarantees.
Intelligent Systems
The Perceptron Algorithm: Introduction to Linear Classifiers and Neural Networks
Transition from probabilistic to discriminative models with the Perceptron algorithm, learning how linear classifiers use weighted features to make predictions and laying the foundation for neural networks.
Logic for Computer Scientists
Negation and Non-Monotonic Reasoning: When New Information Invalidates Old Conclusions
Explore non-monotonic reasoning systems where new information can invalidate previous conclusions, from the classic Tweety the bird example to stable models in logic programming.
Intelligent Systems
Laplace Smoothing and Maximum Likelihood Estimation in Naive Bayes
Learn how to handle zero-frequency problems and overfitting in Naive Bayes through Laplace smoothing and understand the theoretical foundations of maximum likelihood estimation.
Logic for Computer Scientists
Herbrand Logic and Semantics: Simplifying First-Order Interpretations
Learn how Herbrand semantics reduce the infinite complexity of first-order logic interpretations to finite, manageable models through ground atoms and the Herbrand base.
Intelligent Systems
Naive Bayes Classification: From Bayesian Networks to Supervised Learning
Learn how Naive Bayes bridges probabilistic reasoning and machine learning, using conditional independence assumptions to build powerful classifiers for spam detection, digit recognition, and more.
Intelligent Systems
Variable Elimination: Efficient Probabilistic Inference in Bayesian Networks
Learn how variable elimination dramatically reduces computational complexity in Bayesian network inference through strategic factor manipulation and elimination ordering.
Intelligent Systems
Bayesian Networks: D-Separation and Probabilistic Inference
Master d-separation algorithms for determining conditional independence in Bayesian networks and understand the foundation of probabilistic inference.
Logic for Computer Scientists
Hilbert Proof Systems and Herbrand Logic: Foundations of Automated Theorem Proving
An in-depth exploration of Hilbert proof systems and the Tableaux method for predicate logic, with detailed examples on quantifier manipulation and step-by-step proof construction.
Logic for Computer Scientists
The Unification Algorithm: Finding Most General Unifiers in First-Order Logic
Learn how the unification algorithm finds the most general unifier (MGU) that makes two terms identical, a fundamental operation in automated reasoning and logic programming.
Theory of Automata
Thompson's Construction: From Regex to NFA
Explore Thompson's Construction algorithm, the elegant method for converting regular expressions to NFAs that revolutionized pattern matching and influenced decades of Unix tools.
Intelligent Systems
Reinforcement Learning: An Introduction to Learning from Rewards
Discover reinforcement learning—the paradigm where agents learn to maximize expected rewards through experience, from robot locomotion to DeepRacer vehicles.
Logic for Computer Scientists
Propositional Logic II: Truth Tables and Formation Trees
Learn to analyze propositional formulas using truth tables and formation trees—essential tools for understanding logical structure and validity.
Logic for Computer Scientists
Propositional Logic Basics: Building the Foundation for Logical Reasoning
Master the fundamental building blocks of logical reasoning: propositions, truth values, and logical connectives that form the bedrock of computer science applications.
Logic for Computer Scientists
Introduction to Logic for Computer Scientists
Discover how logic—the study of reasoning—forms the invisible foundation of every computer program, database query, and artificial intelligence system you build.
General
Welcome to My Blog
An introduction to this blog and what I plan to share about my journey in computer science and machine learning research.
Logic for Computer Scientists
Prolog Programming Fundamentals: Logic Programming for Beginners
An introduction to Prolog's unique declarative paradigm, exploring facts, rules, queries, and how logic programming differs from imperative approaches.
Theory of Automata
Understanding the Master's Theorem: A Practical Guide
A comprehensive guide to understanding and applying the Master's Theorem for analyzing divide-and-conquer algorithms.
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