Quantum computers do not impact the entropy provided by key-stretching algorithms.A 20-word passphrase with 2 256 bit entropy today, yields 128-bit post-quantum protection.For example, the cost of searching for the right 2 128 passphrase drops to (very) roughly ~2 64. Grover’s quantum search algorithm halves the key search space, so all entropy values in the table above are halved on quantum computers.10-word diceware passphrases provide 128 bits of entropy.7-word diceware passphrases are recommended, yielding ~90 bits of entropy against classical computing attacks.Classical vs Quantum Computing Classical Computing Attack Which is then divided by 31536000 seconds / year to get the number of years. To gauge strength against adversary capabilities, an example 80-bit password versus an adversary capable of 1 trillion or (2 40 guesses per second): Lower bound - Doubling every 24 months 2013-2025: It is expected that Moore's Law ends by 2025 because of physical constraints of silicon.ġ trillion guesses in 2013 = 2 40 operations. Other estimates by the industry put that at 18 months. Moore's Law predicts the doubling of number of on-die transistors every 24 months (two years). Table: Diceware Password Strength Word TotalĮstimated Brute-force Time (Classical Computing) The relationship between entropy and the length of the diceware password is outlined below. Log (62) / log (2) = 5.95 bits per character Log (32) / log (2) = 5 bits per characterĪlternatively, an alphanumeric string using lower/uppercase will have 62 characters in the set: There are 32 special characters on a standard U.S. Įntropy per word is calculated by dividing log of number of words in list by log 2. This in practice is extremely unlikely and is detectable by the user and in the latter case a recommended number of words is advised to mitigate this risk. The concept of Min-entropy measures the worst case lower bound of passphrase entropy in case of diceware generating words that have semantic meaning as a sentence or short passphrases whose character length can be easily brute-forced. The entropy type referred to throughout this page is Shannon Entropy. As will be explained later, one can deviate from this rule to have a shorter password while still having a realistically strong protection level. When determining appropriate password length, ideally it should have at least as much entropy as the bit length of the symmetric key that is derived from it. This relies on the fact that the time taken to try all possible combinations would be infeasibly large, even for a well-equipped adversary. Passwords that are long enough should be safe for millions or billions of years, even if the list chosen is known to the attacker. Instead of generating a random sequence containing alphanumerical and special characters, Diceware selects a sequence of words equiprobably from a list containing several thousand that have been curated for their memorability, length and profanity. To generate strong passwords that are both easy to remember and have an easily calculatable large entropy, it is advised to use the Diceware package. Generating Unbreakable Passwords Introduction Key-stretching measures which help to make password length manageable in a post-quantum world and.Estimating the brute force time for passwords of different length.How to calculate entropy for both pre-quantum and post-quantum strength.This method is very fast for short and/or non-random passwords. If weak passwords (passphrases) are used, they will be easily discovered by trying every possible character combination in reasonable time through brute-force attacks. Considering Moore's Law it could have only improved since. Warning: In 2013, nation-state adversaries were supposedly capable of one trillion guesses per second when attempting to brute-force passwords.
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