Memorized secrets that are randomly chosen by the CSP (e.g., at enrollment) or by the verifier (e.g., when a user requests a new PIN) SHALL be at least 6 characters in length and SHALL be generated using an approved random bit generator [SP 800-90Ar1].
In addition, verifiers SHOULD perform an additional iteration of a key derivation function using a salt value that is secret and known only to the verifier. This salt value, if used, SHALL be generated by an approved random bit generator [SP 800-90Ar1] and provide at least the minimum security strength specified in the latest revision of SP 800-131A (112 bits as of the date of this publication). The secret salt value SHALL be stored separately from the hashed memorized secrets (e.g., in a specialized device like a hardware security module). With this additional iteration, brute-force attacks on the hashed memorized secrets are impractical as long as the secret salt value remains secret.
CSPs creating look-up secret authenticators SHALL use an approved random bit generator [SP 800-90Ar1] to generate the list of secrets and SHALL deliver the authenticator securely to the subscriber. Look-up secrets SHALL have at least 20 bits of entropy.
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To attack the schneier construction. We estimate the entropy for the first letter of a previous word given the previous first letter of the previous word. Normal letters have only about 1.2 bits or so of entropy. First letters are higher in entropy, but no where near 3 bits per character of s/key. In addition, this entropy measure is very suspect and it is an average figure.
Ignoring the usability problem, Base85 is even denser with 32-bits per five characters which allows a secure 15 char password. Ironically even this rarely works. 15 characters is sometimes too long for the system and this presumes no case folding and no characters in b85 are prohibited by the system.
With upper case, lower case, numbers, and basic special characters you have 85 printable characters (including space, but not tab) on a standard US keyboard, which is approximately 6.409 bits per character of entropy for a random password, so with 20 random characters you have the equivalent of a 128-bit key.
For non-memorized passwords (something you must write down and physically secure), you are not optimizing for memorability. In this case, you can use your favored random-generator of choice, but choose an encoding that eliminates visual duplicates such as lowercase-L, uppercase-I, zero, uppercase-O and so on. You also should think about portability since one problem created by password policies is that they make it impossible for a user to use a single generation method (when, for example, one policy requires special-characters, while another prohibits them).
Selecting letters and numbers completely at random is 6 bits per character. Adding punctuation at the end is three bits. So 10 completely random letters and numbers, plus a punctuation mark, is 63 bits.
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. See stronger methods. Random password programs often have the ability to ensure that the resulting password complies with a local password policy; for instance, by always producing a mix of letters, numbers and special characters.
Using this scheme, an eight-character human-selected password without upper case 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.
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 of time 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. Keep in mind that computing power continues to grow, so to prevent offline attacks the required bits of entropy should also increase over time. 153554b96e