Ch. 10 Identification and Entity Authentication
communication efficiency. This includes the number of passes (message exchanges) and the bandwidth required (total number of bits transmitted).
More subtle properties include:
real-time involvement of a third party (if any). Examples of third parties include an on-line trusted third party to distribute common symmetric keys to communicating entities for authentication purposes; and an on-line (untrusted) directory service for distributing public-key certificates, supported by an off-line certification authority (see Chapter 13).
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nature of trust required in a third party (if any). Examples include trusting a third party to correctly authenticate and bind an entity’s name to a public key; and trusting a third party with knowledge of an entity’s private key.
nature of security guarantees. Examples include provable security and zero-know- ledge properties (see §10.4.1).
storage of secrets. This includes the location and method used (e.g., software only, local disks, hardware tokens, etc.) to store critical keying material.
Relation between identification and signature schemes
Identification schemes are closely related to, but simpler than, digital signature schemes, which involve a variable message and typically provide a non-repudiation feature allowing disputes to be resolved by judges after the fact. For identification schemes, the semantics of the message are essentially fixed – a claimed identity at the current instant in time. The claim is either corroborated or rejected immediately, with associated privileges or access either granted or denied in real time. Identifications do not have “lifetimes” as signatures do1 – disputes need not typically be resolved afterwards regarding a prior identification, and attacks which may become feasible in the future do not affect the validity of a prior identification. In some cases, identification schemes may also be converted to signature schemes using a standard technique (see Note 10.30).
10.2 Passwords (weak authentication)
Conventional password schemes involve time-invariant passwords, which provide so-call- ed weak authentication. The basic idea is as follows. A password, associated with each user (entity), is typically a string of 6 to 10 or more characters the user is capable of com- mitting to memory. This serves as a shared secret between the user and system. (Conven- tional password schemes thus fall under the category of symmetric-key techniques provid- ing unilateral authentication.) To gain access to a system resource (e.g., computer account, printer, or software application), the user enters a (userid, password) pair, and explicitly or implicitly specifies a resource; here userid is a claim of identity, and password is the evi- dence supporting the claim. The system checks that the password matches corresponding data it holds for that userid, and that the stated identity is authorized to access the resource. Demonstration of knowledge of this secret (by revealing the password itself) is accepted by the system as corroboration of the entity’s identity.
Various password schemes are distinguished by the means by which information al- lowing password verification is stored within the system, and the method of verification. The collection of ideas presented in the following sections motivate the design decisions
1Some identification techniques involve, as a by-product, the granting of tickets which provide time-limited access to specified resources (see Chapter 13).
§10.2 Passwords (weak authentication) 389
made in typical password schemes. A subsequent section summarizes the standard attacks these designs counteract. Threats which must be guarded against include: password dis- closure (outside of the system) and line eavesdropping (within the system), both of which allow subsequent replay; and password guessing, including dictionary attacks.
10.2.1 Fixed password schemes: techniques (i) Stored password files
The most obvious approach is for the system to store user passwords cleartext in a system password file, which is both read- and write-protected (e.g., via operating system access control privileges). Upon password entry by a user, the system compares the entered pass- word to the password file entry for the corresponding userid; employing no secret keys or cryptographic primitives such as encryption, this is classified as a non-cryptographic tech- nique. A drawback of this method is that it provides no protection against privileged in- siders or superusers (special userids which have full access privileges to system files and resources). Storage of the password file on backup media is also a security concern, since the file contains cleartext passwords.
(ii) “Encrypted” password files
Rather than storing a cleartext user password in a (read- and write-protected) password file, a one-way function of each user password is stored in place of the password itself (see Fig- ure 10.1). To verify a user-entered password, the system computes the one-way function of the entered password, and compares this to the stored entry for the stated userid. To pre- clude attacks suggested in the preceding paragraph, the password file need now only be write-protected.
10.3 Remark (one-way function vs. encryption) For the purpose of protecting password files, the use of a one-way function is generally preferable to reversible encryption; reasons in- clude those related to export restrictions, and the need for keying material. However, in both cases, for historical reasons, the resulting values are typically referred to as “encrypted” passwords. Protecting passwords by either method before transmission over public com- munications lines addresses the threat of compromise of the password itself, but alone does not preclude disclosure or replay of the transmission (cf. Protocol 10.6).
(iii) Password rules
Since dictionary attacks (see §10.2.2(iii)) are successful against predictable passwords, some systems impose “password rules” to discourage or prevent users from using “weak” passwords. Typical password rules include a lower bound on the password length (e.g., 8 or 12 characters); a requirement for each password to contain at least one character from each of a set of categories (e.g., uppercase, numeric, non-alphanumeric); or checks that candi- date passwords are not found in on-line or available dictionaries, and are not composed of account-related information such as userids or substrings thereof.
Knowing which rules are in effect, an adversary may use a modified dictionary attack strategy taking into account the rules, and targeting the weakest form of passwords which nonetheless satisfy the rules. The objective of password rules is to increase the entropy (rather than just the length) of user passwords beyond the reach of dictionary and exhaus- tive search attacks. Entropy here refers to the uncertainty in a password (cf. §2.2.1); if all passwords are equally probable, then the entropy is maximal and equals the base-2 loga- rithm of the number of possible passwords.
Ch. 10 Identification and Entity Authentication
Claimant A
Verifier (system) B Password table
h(passwordA )
password, A
h(passwordA )
h(password) no REJECT
Figure 10.1: Use of one-way function for password-checking.
Another procedural technique intended to improve password security is password ag- ing. A time period is defined limiting the lifetime of each particular password (e.g., 30 or 90 days). This requires that passwords be changed periodically.
(iv) Slowing down the password mapping
To slow down attacks which involve testing a large number of trial passwords (see §10.2.2), the password verification function (e.g., one-way function) may be made more computa- tionally intensive, for example, by iterating a simpler function t > 1 times, with the output of iteration i used as the input for iteration i + 1. The total number of iterations must be restricted so as not to impose a noticeable or unreasonable delay for legitimate users. Also, the iterated function should be such that the iterated mapping does not result in a final range space whose entropy is significantly decimated.
(v) Salting passwords
To make dictionary attacks less effective, each password, upon initial entry, may be aug- mented with a t-bit random string called a salt (it alters the “flavor” of the password; cf. §10.2.3) before applying the one-way function. Both the hashed password and the salt are recorded in the password file. When the user subsequently enters a password, the system looks up the salt, and applies the one-way function to the entered password, as altered or augmented by the salt. The difficulty of exhaustive search on any particular user’s pass- word is unchanged by salting (since the salt is given in cleartext in the password file); how- ever, salting increases the complexity of a dictionary attack against a large set of passwords simultaneously, by requiring the dictionary to contain 2t variations of each trial password, implying a larger memory requirement for storing an encrypted dictionary, and correspond- ingly more time for its preparation. Note that with salting, two users who choose the same password have different entries in the system password file. In some systems, it may be appropriate to use an entity’s userid itself as salt.
(vi) Passphrases
To allow greater entropy without stepping beyond the memory capacity of human users, passwords may be extended to passphrases; in this case, the user types in a phrase or sen- tence rather than a short “word”. The passphrase is hashed down to a fixed-size value, which plays the same role as a password; here, it is important that the passphrase is not simply trun-
§10.2 Passwords (weak authentication) 391
cated by the system, as passwords are in some systems. The idea is that users can remember phrases easier than random character sequences. If passwords resemble English text, then since each character contains only about 1.5 bits of entropy (Fact 7.67), a passphrase pro- vides greater security through increased entropy than a short password. One drawback is the additional typing requirement.
10.2.2 Fixed password schemes: attacks (i) Replay of fixed passwords
A weakness of schemes using fixed, reusable passwords (i.e., the basic scheme of §10.2), is the possibility that an adversary learns a user’s password by observing it as it is typed in (or from where it may be written down). A second security concern is that user-entered passwords (or one-way hashes thereof) are transmitted in cleartext over the communications line between the user and the system, and are also available in cleartext temporarily during system verification. An eavesdropping adversary may record this data, allowing subsequent impersonation.
Fixed password schemes are thus of use when the password is transmitted over trusted communications lines safe from monitoring, but are not suitable in the case that passwords are transmitted over open communications networks. For example, in Figure 10.1, the claimant A may be a user logging in from home over a telephone modem, to a remote office site B two (or two thousand) miles away; the cleartext password might then travel over an unsecured telephone network (including possibly a wireless link), subject to eavesdropping.
In the case that remote identity verification is used for access to a local resource, e.g., an automated cash dispenser with on-line identity verification, the system response (ac- cept/reject) must be protected in addition to the submitted password, and must include vari- ability to prevent trivial replay of a time-invariant accept response.
(ii) Exhaustive password search
A very naive attack involves an adversary simply (randomly or systematically) trying pass- words, one at a time, on the actual verifier, in hope that the correct password is found. This may be countered by ensuring passwords are chosen from a sufficiently large space, limit- ing the number of invalid (on-line) attempts allowed within fixed time periods, and slowing down the password mapping or login-process itself as in §10.2.1(iv). Off-line attacks, in- volving a (typically large) computation which does not require interacting with the actual verifier until a final stage, are of greater concern; these are now considered.
Given a password file containing one-way hashes of user passwords, an adversary may attempt to defeat the system by testing passwords one at a time, and comparing the one-way hash of each to passwords in the encrypted password file (see §10.2.1(ii)). This is theoreti- cally possible since both the one-way mapping and the (guessed) plaintext are known. (This could be precluded by keeping any or all of the details of the one-way mapping or the pass- word file itself secret, but it is not considered prudent to base the security of the system on the assumption that such details remain secret forever.) The feasibility of the attack depends on the number of passwords that need be checked before a match is expected (which itself depends on the number of possible passwords), and the time required to test each (see Ex- ample 10.4, Table 10.1, and Table 10.2). The latter depends on the password mapping used, its implementation, the instruction execution time of the host processor, and the number of processors available (note exhaustive search is parallelizable). The time required to actu- ally compare the image of each trial password to all passwords in a password file is typically negligible.
392 Ch. 10 Identification and Entity Authentication
10.4 Example (password entropy) Suppose passwords consist of strings of 7-bit ASCII char- acters. Each has a numeric value in the range 0-127. (When 8-bit characters are used, val- ues 128-255 compose the extended character set, generally inaccessible from standard key- boards.) ASCII codes 0-31 are reserved for control characters; 32 is a space character; 33- 126 are keyboard-accessible printable characters; and 127 is a special character. Table 10.1 gives the number of distinct n-character passwords composed of typical combinations of characters, indicating an upper bound on the security of such password spaces.
(lowercase)
36 (lowercase alphanumeric)
62 (mixed case alphanumeric)
95 (keyboard characters)
23.5 28.2 32.9 37.6 42.3 47.0
25.9 31.0 36.2 41.4 46.5 51.7
29.8 35.7 41.7 47.6 53.6 59.5
32.9 39.4 46.0 52.6 59.1 65.7
Table 10.1: Bitsize of password space for various character combinations. The number of n- character passwords, given c choices per character, is cn. The table gives the base-2 logarithm of this number of possible passwords.
(lowercase)
36 (lowercase alphanumeric)
62 (mixed case alphanumeric)
95 (keyboard characters)
0.67 hr 17 hr 19 dy 1.3 yr 34 yr 890 yr
3.4 hr 120 hr 180 dy 18 yr 640 yr 23000 yr
51 hr 130 dy 22 yr 1400 yr 86000 yr 5.3×106 yr
430 hr 4.7 yr 440 yr 42000 yr 4.0×106 yr 3.8×108 yr
Table 10.2: Time required to search entire password space. The table gives the time T (in hours, days, or years) required to search or pre-compute over the entire specified spaces using a single processor (cf. Table 10.1). T = cn · t · y, where t is the number of times the password mapping is iterated, and y the time per iteration, for t = 25, y = 1/(125 000) sec. (This approximates the UNIX crypt command on a high-end PC performing DES at 1.0 Mbytes/s – see §10.2.3.)
(iii) Password-guessing and dictionary attacks
To improve upon the expected probability of success of an exhaustive search, rather than searching through the space of all possible passwords, an adversary may search the space in order of decreasing (expected) probability. While ideally arbitrary strings of n characters would be equiprobable as user-selected passwords, most (unrestricted) users select pass- words from a small subset of the full password space (e.g., short passwords; dictionary words; proper names; lowercase strings). Such weak passwords with low entropy are easily guessed; indeed, studies indicate that a large fraction of user-selected passwords are found in typical (intermediate) dictionaries of only 150 000 words, while even a large dictionary of 250 000 words represents only a tiny fraction of all possible n-character passwords (see Table 10.1).
Passwords found in any on-line or available list of words may be uncovered by an ad- versary who tries all words in this list, using a so-called dictionary attack. Aside from tradi- tional dictionaries as noted above, on-line dictionaries of words from foreign languages, or
§10.2 Passwords (weak authentication) 393
on specialized topics such as music, film, etc. are available. For efficiency in repeated use by an adversary, an “encrypted” (hashed) list of dictionary or high-probability passwords may be created and stored on disk or tape; password images from system password files may then be collected, ordered (using a sorting algorithm or conventional hashing), and then compared to entries in the encrypted dictionary. Dictionary-style attacks are not gen- erally successful at finding a particular user’s password, but find many passwords in most systems.
10.2.3 Case study – UNIX passwords
The UNIX2 operating system provides a widely known, historically important example of a fixed password system, implementing many of the ideas of §10.2.1. A UNIX password file contains a one-way function of user passwords computed as follows: each user password serves as the key to encrypt a known plaintext (64 zero-bits). This yields a one-way function of the key, since only the user (aside from the system, temporarily during password veri- fication) knows the password. For the encryption algorithm, a minor modification of DES (§7.4) is used, as described below; variations may appear in products outside of the USA. The technique described relies on the conjectured property that DES is resistant to known- plaintext attacks – given cleartext and the corresponding ciphertext, it remains difficult to find the key.
The specific technique makes repeated use of DES, iterating the encipherment t = 25 times (see Figure 10.2). In detail, a user password is truncated to its first 8 ASCII char- acters. Each of these provides 7 bits for a 56-bit DES key (padded with 0-bits if less than 8 characters). The key is used to DES-encrypt the 64-bit constant 0, with the output fed back as input t times iteratively. The 64-bit result is repacked into 11 printable characters (a 64-bit output and 12 salt bits yields 76 bits; 11 ASCII characters allow 77). In addition, a non-standard method of password salting is used, intended to simultaneously complicate dictionary attacks and preclude use of off-the-shelf DES hardware for attacks:
1. password salting. UNIX password salting associates a 12-bit “random” salt (12 bits taken from the system clock at time of password creation) with each user-selected password. The 12 bits are used to alter the standard expansion function E of the DES mapping (see §7.4), providing one of 4096 variations. (The expansion E creates a 48-bit block; immediately thereafter, the salt bits collectively determine one of 4096 permutations. Each bit is associated with a pre-determined pair from the 48-bit block, e.g., bit 1 with block bits 1 and 25, bit 2 with block bits 2 and 26, etc. If the salt bit is 1, the block bits are swapped, and otherwise they are not.) Both the hashed password and salt are recorded in the system password file. Security of any particular user’s password is unchanged by salting, but a dictionary attack now requires 212 = 4096 variations of each trial password.
2. preventing use of off-the-shelf DES chips. Because the DES expansion permutation E is dependent on the salt, standard DES chips can no longer be use
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