Password strength

 ( Cryptography ) 

The strength of random passwords depends on the actual entropy of the underlying number generator; however, these are often not truly random, but pseudorandom. Many publicly available password generators use random number generators found in programming libraries that offer limited entropy. However, most modern operating systems offer cryptographically strong random number generators that are suitable for password generation. It is also possible to use ordinary dice to generate random passwords . Random password programs often can ensure that the resulting password complies with a local password policy; for instance, by always producing a mix of letters, numbers, and special characters.

For passwords generated by a process that randomly selects a string of symbols of length, L, from a set of N possible symbols, the number of possible passwords can be found by raising the number of symbols to the power L, i.e. N ^L. Increasing either L or N will strengthen the generated password. The strength of a random password as measured by the information entropy is just the binary logarithm or log₂ of the number of possible passwords, assuming each symbol in the password is produced independently. Thus a random password's information entropy, H, is given by the formula:

where N is the number of possible symbols and L is the number of symbols in the password. H is measured in .Schneier, B: Applied Cryptography, 2e, page 233 ff. John Wiley and Sons. In the last expression, log can be to any base.

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+ Entropy per symbol for different symbol sets ! Symbol set	Entropy per symbol H
bits
4.000 bits
bits
bits
bits
bits
bits
bits
bits
bits
bits
bits per word
bits
bits

A binary number byte is usually expressed using two hexadecimal characters.

To find the length, L, needed to achieve a desired strength H, with a password drawn randomly from a set of N symbols, one computes:

$L\; =\; \{\backslash left\; \backslash lceil\; \backslash frac\; \{H\}\{\backslash log\_2\; N\}\; \backslash right\; \backslash rceil\}$

where $\backslash left\; \backslash lceil\; \backslash \; \backslash right\; \backslash rceil$ denotes the mathematical ceiling function, i.e. rounding up to the next largest natural number.

The following table uses this formula to show the required lengths of truly randomly generated passwords to achieve desired password entropies for common symbol sets:

+ Lengths L of truly randomly generated passwords required to achieve a desired password entropy H for symbol sets containing N symbols

1 word

3 words

4 words

5 words

7 words

8 words

10 words

13 words

15 words

18 words

20 words

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Human-generated passwords

People are notoriously poor at achieving sufficient entropy to produce satisfactory passwords. According to one study involving half a million users, the average password entropy was estimated at 40.54 bits.

(2007). 9781595936547 ISBN 9781595936547

Thus, in one analysis of over 3 million eight-character passwords, the letter "e" was used over 1.5 million times, while the letter "f" was used only 250,000 times. A uniform distribution would have had each character being used about 900,000 times. The most common number used is "1", whereas the most common letters are a, e, o, and r.

Users rarely make full use of larger character sets in forming passwords. For example, hacking results obtained from a MySpace phishing scheme in 2006 revealed 34,000 passwords, of which only 8.3% used mixed case, numbers, and symbols.

The full strength associated with using the entire ASCII character set (numerals, mixed case letters, and special characters) is only achieved if each possible password is equally likely. This seems to suggest that all passwords must contain characters from each of several character classes, perhaps upper and lower-case letters, numbers, and non-alphanumeric characters. Such a requirement is a pattern in password choice and can be expected to reduce an attacker's "work factor" (in Claude Shannon's terms). This is a reduction in password "strength". A better requirement would be to require a password not to contain any word in an online dictionary, or list of names, or any license plate pattern from any state (in the US) or country (as in the EU). If patterned choices are required, humans are likely to use them in predictable ways, such as capitalizing a letter, adding one or two numbers, and a special character. This predictability means that the increase in password strength is minor when compared to random passwords.

Password Safety Awareness Projects

Google developed Interland teach the kid internet audience safety on internet. On the chapter called Tower Of Tresure it is advised to use unusual names paired with characters like (₺&@#%) with a game.

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NIST Special Publication 800-63-2

NIST Special Publication 800-63 of June 2004 (revision two) suggested a scheme to approximate the entropy of human-generated passwords:

Using this scheme, an eight-character human-selected password without uppercase characters and non-alphabetic characters OR with either but of the two character sets is estimated to have eighteen bits of entropy. The NIST publication concedes that at the time of development, little information was available on the real-world selection of passwords. Later research into human-selected password entropy using newly available real-world data has demonstrated that the NIST scheme does not provide a valid metric for entropy estimation of human-selected passwords. The June 2017 revision of SP 800-63 (Revision three) drops this approach.

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Usability and implementation considerations

Because national keyboard implementations vary, not all 94 ASCII printable characters can be used everywhere. This can present a problem to an international traveler who wished to log into a remote system using a keyboard on a local computer . Many handheld devices, such as and , require complex shift sequences or keyboard app swapping to enter special characters.

Authentication programs can vary as to the list of allowable password characters. Some do not recognize case differences (e.g., the upper-case "E" is considered equivalent to the lower-case "e"), and others prohibit some of the other symbols. In the past few decades, systems have permitted more characters in passwords, but limitations still exist. Systems also vary as to the maximum length of passwords allowed.

As a practical matter, passwords must be both reasonable and functional for the end user as well as strong enough for the intended purpose. Passwords that are too difficult to remember may be forgotten and so are more likely to be written on paper, which some consider a security risk. In contrast, others argue that forcing users to remember passwords without assistance can only accommodate weak passwords, and thus poses a greater security risk. According to Bruce Schneier, most people are good at securing their wallets or purses, which is a "great place" to store a written password.

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Required bits of entropy

The minimum number of bits of entropy needed for a password depends on the threat model for the given application. If key stretching is not used, passwords with more entropy are needed. RFC 4086, "Randomness Requirements for Security", published June 2005, presents some example threat models and how to calculate the entropy desired for each one. Their answers vary between 29 bits of entropy needed if only online attacks are expected, and up to 96 bits of entropy needed for important cryptographic keys used in applications like encryption where the password or key needs to be secure for a long period and stretching isn't applicable. A 2010 Georgia Tech Research Institute study based on unstretched keys recommended a 12-character random password but as a minimum length requirement. It pays to bear in mind that since computing power continually grows, to prevent offline attacks the required number of bits of entropy should also increase over time.

The upper end is related to the stringent requirements of choosing keys used in encryption. In 1999, an Electronic Frontier Foundation project broke 56-bit DES encryption in less than a day using specially designed hardware. In 2002, distributed.net cracked a 64-bit key in 4 years, 9 months, and 23 days. As of October 12, 2011, distributed.net estimates that cracking a 72-bit key using current hardware will take about 45,579 days or 124.8 years. Due to currently understood limitations from fundamental physics, there is no expectation that any digital computer (or combination) will be capable of breaking 256-bit encryption via a brute-force attack. Whether or not quantum computers will be able to do so in practice is still unknown, though theoretical analysis suggests such possibilities.

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Guidelines for strong passwords

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Common guidelines

Guidelines for choosing good passwords are typically designed to make passwords harder to discover by intelligent guessing. Common guidelines advocated by proponents of software system security have included:Microsoft Corporation, Strong passwords: How to create and use them Bruce Schneier, Choosing Secure Passwords Google, Inc., How safe is your password? University of Maryland, Choosing a Good Password

Teri Bidwell (2025). 9781931836517, Syngress Publishing. . ISBN 9781931836517

• Consider a minimum password length of 8 characters as a general guide. Both the US and UK cyber security departments recommend long and easily memorable passwords over short complex ones.
• Generate passwords randomly where feasible.
• Avoid using the same password twice (e.g. across multiple user accounts and/or software systems).
• Avoid character repetition, keyboard patterns, dictionary words, and sequential letters or numbers.
• Avoid using information that is or might become publicly associated with the user or the account, such as the user name, ancestors' names, or dates.
• Avoid using information that the user's colleagues and/or acquaintances might know to be associated with the user, such as relatives or pet names, romantic links (current or past), and biographical information (e.g. ID numbers, ancestors' names or dates).
• Do not use passwords that consist wholly of any simple combination of the aforementioned weak components.

Forcing the inclusion of lowercase letters, uppercase letters, numbers, and symbols in passwords was a common policy but has been found to decrease security, by making it easier to crack. Research has shown how predictable the common use of such symbols are, and the US and UK government cyber security departments advise against forcing their inclusion in password policy. Complex symbols also make remembering passwords much harder, which increases writing down, password resets, and password reuse – all of which lower rather than improve password security. The original author of password complexity rules, Bill Burr, has apologized and admits they decrease security, as research has found; this was widely reported in the media in 2017. Online security researchers and consultants are also supportive of the change in best practice advice on passwords. Despite this, such complexity requirements in password policies remain common - a 2023 study of 20,000 websites found that about 20% still require passwords to contain characters from at least one character class.

Some guidelines advise against writing passwords down, while others, noting the large numbers of password-protected systems users must access, encourage writing down passwords as long as the written password lists are kept in a safe place, not attached to a monitor or in an unlocked desk drawer. Use of a password manager is recommended by the NCSC.

The possible character set for a password can be constrained by different websites or by the range of keyboards on which the password must be entered.e.g. for a keyboard with only 17 nonalphanumeric characters, see one for a BlackBerry phone in an enlarged image in support of Sandy Berger, BlackBerry Tour 9630 (Verizon) Cell Phone Review, in Hardware Secrets (August 31, 2009) , both as accessed January 19, 2010. That some websites don’t allow nonalphanumerics is indicated by Kanhef, Idiots, For Different Reasons (June 30, 2009) (topic post) , as accessed January 20, 2010.

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Examples of weak passwords

As with any security measure, passwords vary in strength; some are weaker than others. For example, the difference in strength between a dictionary word and a word with obfuscation (e.g. letters in the password are substituted by, say, numbers — a common approach) may cost a password-cracking device a few more seconds; this adds little strength. The examples below illustrate various ways weak passwords might be constructed, all of which are based on simple patterns which result in extremely low entropy, allowing them to be tested automatically at high speeds.:

Mark Burnett (2025). 9781597490412, Syngress Publishing. ISBN 9781597490412

• (as supplied by the system vendor and meant to be changed at installation time): password, default, admin, guest, etc. Lists of default passwords are widely available on the internet.
• Reused passwords: Passwords should be unique to a particular account. Altering reused passwords, such as changing a few letters or numbers, does not provide sufficient security.
• Dictionary words: chameleon, RedSox, sandbags, bunnyhop!, IntenseCrabtree, etc., including words in non-English dictionaries.
• Words with numbers appended: password1, deer2000, john1234, etc., can be easily tested automatically with little lost time.
• (words with simple obfuscation): p@ssw0rd, l33th4x0r, g0ldf1sh, etc., can be tested automatically with little additional effort. For example, a domain administrator password compromised in the DigiNotar attack was reportedly Pr0d@dm1n.
• Doubled words: crabcrab, stopstop, treetree, passpass, etc.
• Common sequences from a keyboard row: qwerty, 123456, asdfgh, etc. including diagonal or backward sequences (qazplm, ytrewq, etc).
• Numeric sequences based on well known numbers such as 911 ^{(9-1-1, 9/11)}, 314159... ^(pi), 27182... ^(e), 112 ^(1-1-2), etc.
• Identifiers: jsmith123, 1/1/1970, 555–1234, one's username, etc.
• Weak passwords in non-English languages, such as contraseña (Spanish) and ji32k7au4a83 (bopomofo keyboard encoding from Chinese)
• Anything personally related to an individual: license plate number, Social Security number, current or past telephone numbers, student ID, current address, previous addresses, birthday, sports team, relative's or pet's names/nicknames/birthdays/initials, etc., can easily be tested automatically after a simple investigation of a person's details.
• Dates: dates follow a pattern and make your password weak.
• Names of well-known locations: New York, Texas, China, London, etc.
• Names of brands, celebrities, sports teams, musical groups, TV shows, movies, etc.
• Short passwords: Even if a password doesn't have any of the weaknesses listed above, if it is too short, it can be easily cracked.

There are many other ways a password can be weak,Bidwell, p. 87 corresponding to the strengths of various attack schemes; the core principle is that a password should have high entropy (usually taken to be equivalent to randomness) and not be readily derivable by any "clever" pattern, nor should passwords be mixed with information identifying the user. Online services often provide a restore password function that a hacker can figure out and by doing so bypass a password.

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Rethinking password change guidelines

In the landscape of 2012, as delineated by William Cheswick in an article for ACM magazine, password security predominantly emphasized an alpha-numeric password of eight characters or more. Such a password, it was deduced, could resist ten million attempts per second for a duration of 252 days. However, with the assistance of contemporary GPUs at the time, this period was truncated to just about 9 hours, given a cracking rate of 7 billion attempts per second. A 13-character password was estimated to withstand GPU-computed attempts for over 900,000 years.

In the context of 2023 hardware technology, the 2012 standard of an eight-character alpha-numeric password has become vulnerable, succumbing in a few hours. The time needed to crack a 13-character password is reduced to a few years. The current emphasis, thus, has shifted. Password strength is now gauged not just by its complexity but its length, with recommendations leaning towards passwords comprising at least 13-16 characters. This era has also seen the rise of Multi-Factor Authentication (MFA) as a crucial fortification measure. The advent and widespread adoption of password managers have further aided users in cultivating and maintaining an array of strong, unique passwords.

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Password policy

A password policy is a guide to choosing satisfactory passwords. It is intended to:

• assist users in choosing strong passwords
• ensure the passwords are suited to the target population
• Provide recommendations for users concerning the handling of their passwords
• impose a recommendation to change any password which has been lost or suspected of compromise
• use a password blacklist to block the use of weak or easily guessed passwords.

Previous password policies used to prescribe the characters which passwords must contain, such as numbers, symbols, or upper/lower case. While this is still in use, it has been debunked as less secure by university research, by the original instigator of this policy, and by the cyber security departments (and other related government security bodies) of USA and UK. Password complexity rules of enforced symbols were previously used by major platforms such as Google and Facebook, but these have removed the requirement following the discovery that they actually reduced security. This is because the human element is a far greater risk than cracking, and enforced complexity leads most users to highly predictable patterns (number at the end, swap 3 for E, etc.) which helps crack passwords. So password simplicity and length (passphrases) are the new best practice and complexity is discouraged. Forced complexity rules also increase support costs, and user friction and discourage user signups.

Password expiration was in some older password policies but has been debunked as best practice and is not supported by USA or UK governments, or Microsoft which removed the password expiry feature. Password expiration was previously trying to serve two purposes:

• If the time to crack a password is estimated to be 100 days, password expiration times fewer than 100 days may help ensure insufficient time for an attacker.
• If a password has been compromised, requiring it to be changed regularly may limit the access time for the attacker.

However, password expiration has its drawbacks:

• Asking users to change passwords frequently encourages simple, weak passwords.
• If one has a truly strong password, there is little point in changing it. Changing passwords that are already strong introduces a risk that the new password may be less strong.
• A compromised password is likely to be used immediately by an attacker to install a backdoor, often via privilege escalation. Once this is accomplished, password changes won't prevent future attackers from accessing them.
• Moving from never changing one's password to changing the password on every authenticate attempt (pass or fail attempts) only doubles the number of attempts the attacker must make on average before guessing the password in a brute force attack. One gains much more security by just increasing the password length by one character than changing the password on every use.

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Creating and handling passwords

The hardest passwords to crack, for a given length and character set, are random character strings; if long enough they resist brute force attacks (because there are many characters) and guessing attacks (due to high entropy). However, such passwords are typically the hardest to remember. The imposition of a requirement for such passwords in a password policy may encourage users to write them down, store them in , or share them with others as a safeguard against memory failure. While some people consider each of these user resorts to increase security risks, others suggest the absurdity of expecting users to remember distinct complex passwords for each of the dozens of accounts they access. For example, in 2005, security expert Bruce Schneier recommended writing down one's password:

The following measures may increase acceptance of strong password requirements if carefully used:

• a training program. Also, updated training for those who fail to follow the password policy (lost passwords, inadequate passwords, etc.).
• rewarding strong password users by reducing the rate, or eliminating, the need for password changes (password expiration). The strength of user-chosen passwords can be estimated by automatic programs which inspect and evaluate proposed passwords when setting or changing a password.
• displaying to each user the last login date and time in the hope that the user may notice unauthorized access, suggesting a compromised password.
• allowing users to reset their passwords via an automatic system, which reduces help desk call volume. However, some systems are themselves insecure; for instance, easily guessed or researched answers to password reset questions bypass the advantages of a strong password system.
• using randomly generated passwords that do not allow users to choose their passwords, or at least offering randomly generated passwords as an option.

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Memory techniques

Password policies sometimes suggest memory techniques to assist remembering passwords:

• mnemonic passwords: Some users develop mnemonic phrases and use them to generate more or less random passwords which are nevertheless relatively easy for the user to remember. For instance, the first letter of each word in a memorable phrase. Research estimates the password strength of such passwords to be about 3.7 bits per character, compared to the 6.6 bits for random passwords from ASCII printable characters. Silly ones are possibly more memorable. Mnemonic Devices (Indianapolis, Ind.: Bepko Learning Ctr., University College), as accessed January 19, 2010 Another way to make random-appearing passwords more memorable is to use random words (see diceware) or syllables instead of randomly chosen letters.
• after-the-fact mnemonics: After the password has been established, invent a mnemonic that fits. Remembering Passwords (ChangingMinds.org) , as accessed January 19, 2010 It does not have to be reasonable or sensible, only memorable. This allows passwords to be random.
• visual representations of passwords: a password is memorized based on a sequence of keys pressed, not the values of the keys themselves, e.g. a sequence !qAsdE#2 represents a rhomboid on a US keyboard. The method to produce such passwords is called PsychoPass. Passwords produced by this method are much weaker than their length suggests, since successive keys are not independent and common keyboard sequences are included in password dictionaries. But some improvements can be made.
• password patterns: Any pattern in a password makes guessing (automated or not) easier and reduces an attacker's work factor.
• For example, passwords of the following case-insensitive form: consonant, vowel, consonant, consonant, vowel, consonant, number, number (for example pinray45) are called Environ passwords. The pattern of alternating vowel and consonant characters was intended to make passwords more likely to be pronounceable and thus more memorable. Such patterns severely reduce the password's information entropy, making brute force password attacks considerably more efficient. In the UK in October 2005, employees of the British government were advised to use passwords in this form.

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Password managers

A reasonable compromise for using large numbers of passwords is to record them in a password manager program, which include stand-alone applications, web browser extensions, or a manager built into the operating system. A password manager allows the user to use hundreds of different passwords, and only have to remember a single password, the one which opens the encrypted password database. Needless to say, this single password should be strong and well-protected (not recorded anywhere). Most password managers can automatically create strong passwords using a cryptographically secure random password generator, as well as calculating the entropy of the generated password. A good password manager will provide resistance against attacks such as key logging, clipboard logging and various other memory spying techniques.

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See also

• Keystroke logging
• Passphrase
• Phishing
• Vulnerability (computing)

6 Types of Password Attacks & How to Stop Them | OneLogin. (n.d.). Retrieved April 24, 2024, from https://www.google.com/

Franchi, E., Poggi, A., & Tomaiuolo, M. (2015). Information and Password Attacks on Social Networks: An Argument for Cryptography. Journal of Information Technology Research, 8(1), 25–42. https://doi.org/10.4018/JITR.2015010103

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External links

• RFC 4086: Randomness Requirements for Security
• Password Patterns:The next generation dictionary attacks

Categories: Cryptography, Password Authentication