KRYPTOG Logs

Roughly $10^{20}$ (a hundred quintillion) symmetric keys — an astronomically impractical number. * At IoT scale, pairwise symmetric keys reach $\sim 10^{20}$ - impossible to manage. * The calculation: ~30 billion ($3 \times 10^{10}$) smart devices connected by end of 2020 If "e...

Quiz: KRYPTOG / Introduction to Cryptology | updated: Oct 26, 2026

A collision attack finds ANY two different messages with the same hash (attacker controls both), while a pre-image attack must match a specific given hash. * The attacker crafts both messages; the birthday paradox cuts the work to $\sim 2^{n/2}$. * Collision attack: Find $m_1 \n...

Quiz: KRYPTOG / Fundamentals of Cryptography | updated: Oct 26, 2026

Stream ciphers provide confidentiality only — they do NOT provide integrity or authenticity. Provides: Confidentiality — the plaintext is hidden from eavesdroppers Does NOT provide: Integrity — an attacker can flip bits in the ciphertext, and the corresponding plaintext bits w...

Quiz: KRYPTOG / Symmetric Cryptography | updated: Oct 26, 2026

Using the same key for encryption and MAC can lead to attacks where the attacker exploits the relationship between the two operations to forge messages or recover plaintext. The deeper rule is domain separation: a key proven safe for one job carries no guarantee when reused for a...

Quiz: KRYPTOG / Symmetric Cryptography | updated: Oct 26, 2026

The signer raises the message to the secret exponent, $s = m^d \bmod N$; anyone verifies by raising the signature to the public exponent and checking $s^e \bmod N = m$. It is the same modular exponentiation run with opposite keys. * Signing and verifying are the same exponentiat...

Quiz: KRYPTOG / Digital Signatures and Advanced Public Key Techniques | updated: Oct 26, 2026

With only 23 people in a room, there's a >50% chance two share a birthday — and with $\sqrt{n}$ elements, you expect a collision in a space of size $n$. * The curve crosses 50% at 23 and ~90% at 40 — collisions appear far sooner than intuition expects. * The math for birthdays:...

Quiz: KRYPTOG / One-Way and Hash Functions | updated: Oct 26, 2026

Because key length is not the security margin: real attacks shave the effective bit count. A time-memory tradeoff can need only about ⅔ of the bits, quantum search (Grover) halves them, and a conservative worst case is the cube root — 256/3 ≈ 85 bits is still hopeless, but 128/3...

Quiz: KRYPTOG / Key Sizes and Conclusion | updated: Oct 26, 2026

Quantum computers reduce block cipher brute-force from $2^n$ to $2^{n/2}$ (Grover's algorithm), which is serious but manageable — just double the key size. Asymmetric crypto is much harder hit. * Effective security of AES-128 under each attack — the theoretical classical TMTO ($...

Quiz: KRYPTOG / Cryptanalysis | updated: Oct 26, 2026

In modular arithmetic, $a \cdot b \equiv 0 \mod N$ does NOT mean that $a = 0$ or $b = 0$ — there can be "zero divisors," which is fundamentally different from real numbers. For real numbers: $a \cdot b = 0 \Leftrightarrow a = 0$ or $b = 0$ (zero-product property) For modular arit...

Quiz: KRYPTOG / Mathematics for Asymmetric Cryptography | updated: Oct 26, 2026

A group $\langle G, * \rangle$ is a set $G$ with an operation $*$ that satisfies closure, associativity, has a neutral element, and every element has an inverse. The four group axioms: Property Requirement Closure $a * b \in G$ for all $a, b \in G$ Associativity $a * (b...

Quiz: KRYPTOG / Mathematics for Asymmetric Cryptography | updated: Oct 26, 2026