Question 1

Offline Attacks

Accepted Answer

occur when an adversary has stolen the database of hashed passwords and can use their own high-powered hardware to guess passwords as fast as their machines allow, without interacting with the victim's server. Online Attacks occur when an adversary must guess the password directly through a website's login portal. Online attacks are inherently constrained by network latency, rate limiting, and account lockouts. Finally, Key Stretching is a defensive technique used by modern hash functions (like PBKDF2, bcrypt, or Argon2) that intentionally slows down the hashing process. By forcing the computer to perform thousands of mathematical iterations for a single guess, key stretching drastically reduces the number of guesses an attacker can make per second, effectively increasing the survival time of a password with lower entropy.

Question 2

Scenario 2: The Average Consumer.

Accepted Answer

Consider an everyday user, John, setting up a master password for his password manager. John needs a secret that is highly secure but memorable enough that he will not lock himself out of his digital life. He decides to use the EFF Diceware wordlist. He rolls physical dice to randomly select five words, resulting in the phrase velvet-sunset-guitar-ocean-biscuit. The entropy calculation is $5 	imes 12.92 = 64.6$ bits. While 64.6 bits is lower than the 128 bits used by the hospital, the password manager's software utilizes the PBKDF2 hash function with 600,000 iterations (severe key stretching). Even if John's encrypted vault is stolen, the key stretching limits the attacker to perhaps 1,000 guesses per second. At that speed, cracking his 64.6-bit passphrase would take an average of 438,000 years. John's practical security is absolute, balanced perfectly with human usability.

Question 3

Scenario 3: Legacy Banking Systems.

Accepted Answer

Many legacy financial mainframes were built in the 1980s and still restrict users to 8-character passwords using only uppercase letters and numbers (a pool of 36 characters). An 8-character alphanumeric password has an absolute maximum entropy of $8 	imes \log_2(36) = 41.3$ bits. Because banks cannot easily overhaul these multi-billion-dollar legacy systems, they are mathematically vulnerable to rapid brute-force attacks if the hashes were ever leaked. To compensate for this low mathematical entropy, the banks apply massive compensating controls. They enforce strict online-only authentication, locking the account after three failed attempts. They implement mandatory multi-factor authentication (MFA) via SMS or hardware tokens. The low entropy of the password is offset by ensuring the attacker is never allowed to utilize their hardware speed to guess the combinations.

Question 4

What is considered a "good" entropy score for a password?

Accepted Answer

For an online account protected by rate-limiting and account lockouts (like a standard web forum), 40 to 50 bits of entropy is generally sufficient. For a critical online account, such as a primary email or banking portal, you should aim for 60 to 80 bits. For passwords that protect offline data—such as the master password to a password manager, a cryptocurrency wallet, or a computer's full-disk encryption—a minimum of 80 bits is highly recommended, with 100+ bits being ideal to withstand dedicated GPU brute-force attacks over many years.

Question 5

Does using special characters actually increase entropy?

Accepted Answer

Yes, but only if they are used randomly. Adding symbols increases the character pool ($N$) from 62 (alphanumeric) to 94 (full keyboard). In the formula $E = L 	imes \log_2(N)$, increasing $N$ increases the entropy per character from roughly 5.9 bits to 6.5 bits. However, if you simply append an exclamation point to the end of a recognizable word (e.g., Summer2024!), the increase in practical entropy is negligible because attackers program their software to guess that exact pattern. Length is almost always a more reliable way to increase entropy than forcing special characters.

Question 6

How do quantum computers threaten password entropy?

Accepted Answer

Quantum computers utilize a concept called Grover's Algorithm, which can search an unsorted database much faster than classical computers. In cryptographic terms, Grover's Algorithm effectively halves the bit-strength of symmetric keys and hashes. Therefore, a password or key that currently has 128 bits of entropy against classical computers would only offer 64 bits of security against a sufficiently powerful quantum computer. To maintain current security levels in a post-quantum world, security architects are planning to double key sizes, moving from 128-bit standards to 256-bit standards.

Question 7

What is the difference between entropy and a hash function?

Accepted Answer

Entropy is the measure of how unpredictable the raw, plain-text password is. A hash function is the mathematical algorithm used to scramble that plain-text password into a fixed-length string of gibberish before it is stored in a database. If a password has low entropy (like password123), even the strongest hash function can be cracked because the attacker can simply hash password123 on their own machine and see that the outputs match. High entropy ensures the attacker cannot guess the input, while a strong hash function ensures they cannot reverse the output.

Question 8

What are "salt" and "pepper" in password security?

Accepted Answer

A "salt" is a unique, random string of characters generated by the server and added to your password before it is hashed and stored. Salting prevents attackers from using pre-computed "Rainbow Tables" (massive databases of pre-hashed common passwords) because the unique salt changes the resulting hash entirely. A "pepper" is similar to a salt, but it is a secret value kept separate from the database (often hardcoded into the application server). While salts and peppers protect the database at rest, they do not increase the intrinsic entropy of the user's chosen password against a dedicated brute-force attack once the salt is known.

Question 9

Why do some calculators give different entropy scores for the same password?

Accepted Answer

Different calculators use different underlying models. A pure Shannon entropy calculator strictly uses the $E = L 	imes \log_2(N)$ formula, assuming perfect randomness. If you type 12345678, it will calculate the entropy of an 8-digit number (about 26 bits). However, an advanced, heuristic-based calculator (like zxcvbn) checks dictionaries and common patterns. It will recognize 12345678 as a highly predictable sequence and award it 0 bits of practical entropy. Always trust heuristic calculators for human-created passwords, and Shannon calculators for machine-generated random strings.

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