Daminha Blog

An introduction to the Learning With Errors (LWE) problem, its lattice structure, hardness reduction from BDD and SVP, and its computational variants: DLWE and ss-LWE. [Read More]

In this 9th installment of the Cryptography series, we explore the powerful applications of lattice reduction in both algebra and cryptanalysis. Specifically, we demonstrate how modeling problems as finding short vectors in a lattice allows us to efficiently solve the Minimal Polynomial reconstruction, Coppersmith’s method for finding small roots, Low-density Subset Sum problems (Knapsack), and the Hidden Number Problem (HNP). [Read More]

This post, Part 8 of the Cryptography series, dives into the foundations of lattice-based cryptography. We begin by defining lattices, their bases, and crucial invariant properties like the determinant and successive minima. The post also analyzes the core NP-Hard computational problems on lattices, including the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP). Finally, we explore the LLL (Lenstra–Lenstra–Lovász) algorithm, a foundational basis reduction algorithm that finds approximate solutions to these problems in polynomial time. [Read More]

This blog lays the essential mathematical groundwork for understanding modern cryptography. We begin with Group Theory, exploring the definitions of a group, its order, and subgroups—abstract concepts that form the backbone of many public-key cryptosystems. The post then transitions to Vector Spaces and core linear algebra concepts like basis, linear independence, and orthogonality. Finally, we delve into the Gram–Schmidt algorithm, a powerful tool for constructing orthogonal bases, paving the way for more advanced cryptographic topics. [Read More]

This sixth blog in the Cryptography Series explores two fundamental ideas regarding Pseudorandom Generators (PRGs). First, we will learn about the Blum-Micali method, an intelligent sequential construction that allows us to build a PRG capable of extending its output to an arbitrary length from a base PRG that only stretches its input slightly. Next, the post introduces a core security standard: next-bit unpredictability. The highlight of this post is the proof of a classic and surprising result: a PRG is considered secure (indistinguishable from a truly random sequence) if and only if no adversary can efficiently predict its next bit. This provides a solid bridge between statistical theory and practical predictability. [Read More]

This blog delves into two critical aspects of stream ciphers and pseudorandom generators (PRGs). The first part exposes severe vulnerabilities that arise from the misuse of stream ciphers, focusing on two classic attacks: the “two-time pad” flaw, where key reuse leads to complete plaintext disclosure, and “malleability,” which allows an attacker to modify message content undetectably. The second part shifts from attacks to constructions, introducing a method for combining secure PRGs to create a new one with a longer output. The centerpiece of this section is the detailed presentation of the “hybrid argument,” a fundamental and powerful proof technique widely used in modern cryptography to demonstrate the security of protocols. [Read More]

This post explores the stream cipher, a practical solution to the long-key problem of the One-Time Pad. We delve into how a “pseudo-random generator” (PRG) can “stretch” a short key (seed) into a long keystream for encryption. The blog’s core focuses on the formal security definition of a PRG—the concept of “computational indistinguishability”—and presents a detailed proof demonstrating that a secure PRG leads to a semantically secure stream cipher. [Read More]

This blog delves deeper into the meaning and consequences of semantic security, one of the foundational concepts of modern cryptography. We will begin by proving that a semantically secure encryption scheme does not allow an adversary to deduce even the smallest piece of partial information about the original message, such as its parity. Next, through the example of an Internet roulette game, the blog will illustrate how the definition of semantic security is applied to analyze the security of real-world applications. Finally, we will become acquainted with another, equivalent interpretation of semantic security—the bit-guessing game—a powerful and convenient tool commonly used in cryptographic proofs. [Read More]

A deep-dive into advanced process injection techniques, demonstrating how to bypass Windows’ Protected Process Light (PPL) security mechanism. The post covers the journey from classic DLL injection to exploiting the KnownDlls TOCTOU vulnerability in CSRSS, and finally using Shellcode Reflective DLL Injection (sRDI) to achieve code execution in a PPL process. [Read More]

This blog is a detailed technical guide on how to perform session hijacking by extracting, decrypting, and transferring encrypted Google Chrome cookies from one computer to another. It delves into Chrome’s security mechanisms, explaining how cookies are encrypted using the AES-256-GCM algorithm and how the encryption key is protected by Windows’ Data Protection API (DPAPI). The blog specifically highlights the complexities involved in handling the newer version 20 (v20) cookies, which are protected by App-Bound Encryption and require SYSTEM-level privileges to decrypt. By following the instructions provided, readers will be able to clone a login session and potentially bypass even two-factor authentication (2FA) mechanisms. [Read More]