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83-443: The bcrypt function is the default password hash algorithm for OpenBSD , and was the default for some Linux distributions such as SUSE Linux . There are implementations of bcrypt in C , C++ , C# , Embarcadero Delphi , Elixir , Go , Java , JavaScript , Perl , PHP , Ruby , Python , Rust , Zig and other languages. Blowfish is notable among block ciphers for its expensive key setup phase. It starts off with subkeys in

166-575: A 16-byte (128-bit) salt value. The salt is typically a random value. The bcrypt function uses these inputs to compute a 24-byte (192-bit) hash. The final output of the bcrypt function is a string of the form: For example, with input password abc123xyz , cost 12 , and a random salt, the output of bcrypt is the string Where: The base-64 encoding in bcrypt uses the table ./ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789 , which differs from RFC   4648 Base64 encoding. $ 2$ (1999) The original bcrypt specification defined

249-454: A 64-bit block size. The GnuPG project recommends that Blowfish not be used to encrypt files larger than 4 GB due to its small block size. A reduced-round variant of Blowfish is known to be susceptible to known-plaintext attacks on reflectively weak keys. Blowfish implementations use 16 rounds of encryption, and are not susceptible to this attack. Bruce Schneier has recommended migrating to his Blowfish successor, Twofish . Blowfish2

332-419: A bug was discovered in crypt_blowfish , a PHP implementation of bcrypt. It was mis-handling characters with the 8th bit set. They suggested that system administrators update their existing password database, replacing $ 2a$ with $ 2x$ , to indicate that those hashes are bad (and need to use the old broken algorithm). They also suggested the idea of having crypt_blowfish emit $ 2y$ for hashes generated by

415-412: A certain length, or cannot accept a seed (i.e. allow double hashing) is less useful than one that does. A hash function is applicable in a variety of situations. Particularly within cryptography, notable applications include: A hash procedure must be deterministic —for a given input value, it must always generate the same hash value. In other words, it must be a function of the data to be hashed, in

498-407: A constant can be inverted to become a multiplication by the word-size multiplicative-inverse of that constant. This can be done by the programmer, or by the compiler. Division can also be reduced directly into a series of shift-subtracts and shift-adds, though minimizing the number of such operations required is a daunting problem; the number of machine-language instructions resulting may be more than

581-440: A different number of rounds, as even though it increases security against an exhaustive attack, it weakens the security guaranteed by the algorithm. And given the slow initialization of the cipher with each change of key, it is granted a natural protection against brute-force attacks, which doesn't really justify key sizes longer than 448 bits. Blowfish is a fast block cipher , except when changing keys. Each new key requires

664-450: A divisor M which is a prime number close to the table size, so h ( K ) ≡ K (mod M ) . The table size is usually a power of 2. This gives a distribution from {0, M − 1} . This gives good results over a large number of key sets. A significant drawback of division hashing is that division requires multiple cycles on most modern architectures (including x86 ) and can be 10 times slower than multiplication. A second drawback

747-453: A dozen and swamp the pipeline. If the microarchitecture has hardware multiply functional units , then the multiply-by-inverse is likely a better approach. We can allow the table size n to not be a power of 2 and still not have to perform any remainder or division operation, as these computations are sometimes costly. For example, let n be significantly less than 2 . Consider a pseudorandom number generator function P (key) that

830-425: A feasible amount of storage space searchable in a bounded amount of time regardless of the number of keys. In most applications, the hash function should be computable with minimum latency and secondarily in a minimum number of instructions. Computational complexity varies with the number of instructions required and latency of individual instructions, with the simplest being the bitwise methods (folding), followed by

913-409: A fixed-size table called a hash table . Use of a hash function to index a hash table is called hashing or scatter-storage addressing . Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for

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996-433: A good encryption rate in software, and no effective cryptanalysis of it has been found to date for smaller files. It is recommended Blowfish should not be used to encrypt files larger than 4GB in size, Twofish should be used instead. Blowfish has a 64-bit block size and therefore it could be vulnerable to Sweet32 birthday attacks. Schneier designed Blowfish as a general-purpose algorithm, intended as an alternative to

1079-404: A hash function which takes two parameters—the input data z , and the number n of allowed hash values. A common solution is to compute a fixed hash function with a very large range (say, 0 to 2  − 1 ), divide the result by n , and use the division's remainder . If n is itself a power of 2 , this can be done by bit masking and bit shifting . When this approach is used,

1162-634: A hash function, the uniformity of the distribution of hash values can be evaluated by the chi-squared test . This test is a goodness-of-fit measure: it is the actual distribution of items in buckets versus the expected (or uniform) distribution of items. The formula is ∑ j = 0 m − 1 ( b j ) ( b j + 1 ) / 2 ( n / 2 m ) ( n + 2 m − 1 ) , {\displaystyle {\frac {\sum _{j=0}^{m-1}(b_{j})(b_{j}+1)/2}{(n/2m)(n+2m-1)}},} where n

1245-896: A hash table, a hash function takes a key as an input, which is associated with a datum or record and used to identify it to the data storage and retrieval application. The keys may be fixed-length, like an integer, or variable-length, like a name. In some cases, the key is the datum itself. The output is a hash code used to index a hash table holding the data or records, or pointers to them. A hash function may be considered to perform three functions: A good hash function satisfies two basic properties: it should be very fast to compute, and it should minimize duplication of output values ( collisions ). Hash functions rely on generating favorable probability distributions for their effectiveness, reducing access time to nearly constant. High table loading factors, pathological key sets, and poorly designed hash functions can result in access times approaching linear in

1328-400: A list of shapes, similar images in an image database , and so on. Hash tables are also used to implement associative arrays and dynamic sets . A good hash function should map the expected inputs as evenly as possible over its output range. That is, every hash value in the output range should be generated with roughly the same probability . The reason for this last requirement is that

1411-407: A new key setup algorithm for Blowfish, dubbing the resulting cipher "Eksblowfish" ("expensive key schedule Blowfish"). The key setup begins with a modified form of the standard Blowfish key setup, in which both the salt and password are used to set all subkeys. There are then a number of rounds in which the standard Blowfish keying algorithm is applied, using alternatively the salt and the password as

1494-440: A polynomial modulo 2 instead of an integer to map n bits to m bits. In this approach, M = 2 , and we postulate an m th-degree polynomial Z ( x ) = x + ζ m −1 x + ⋯ + ζ 0 . A key K = ( k n −1 … k 1 k 0 ) 2 can be regarded as the polynomial K ( x ) = k n −1 x + ⋯ + k 1 x + k 0 . The remainder using polynomial arithmetic modulo 2

1577-549: A prefix of $ 2$ . This follows the Modular Crypt Format format used when storing passwords in the OpenBSD password file: $ 2a$ The original specification did not define how to handle non-ASCII character, nor how to handle a null terminator. The specification was revised to specify that when hashing strings: With this change, the version was changed to $ 2a$ $ 2x$ , $ 2y$ (June 2011) In June 2011,

1660-435: A probability of 50% because, if some bits are reluctant to change, then the keys become clustered around those values. If the bits want to change too readily, then the mapping is approaching a fixed XOR function of a single bit. Standard tests for this property have been described in the literature. The relevance of the criterion to a multiplicative hash function is assessed here. In data storage and retrieval applications,

1743-411: A single input bit is complemented, each of the output bits changes with a 50% probability. The reason for this property is that selected subsets of the keyspace may have low variability. For the output to be uniformly distributed, a low amount of variability, even one bit, should translate into a high amount of variability (i.e. distribution over the tablespace) in the output. Each bit should change with

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1826-546: A standard state, then uses this state to perform a block encryption using part of the key, and uses the result of that encryption (which is more accurate at hashing) to replace some of the subkeys. Then it uses this modified state to encrypt another part of the key, and uses the result to replace more of the subkeys. It proceeds in this fashion, using a progressively modified state to hash the key and replace bits of state, until all subkeys have been set. Provos and Mazières took advantage of this, and took it further. They developed

1909-522: Is ./ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789 . This means the encoding is not compatible with the more common RFC 4648 . Hash algorithm A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called hash values , hash codes , hash digests , digests , or simply hashes . The values are usually used to index

1992-491: Is K ( x ) mod Z ( x ) = h m −1 x + ⋯ h 1 x + h 0 . Then h ( K ) = ( h m −1 … h 1 h 0 ) 2 . If Z ( x ) is constructed to have t or fewer non-zero coefficients, then keys which share fewer than t bits are guaranteed to not collide. Blowfish (cipher) Blowfish is a symmetric-key block cipher , designed in 1993 by Bruce Schneier and included in many cipher suites and encryption products. Blowfish provides

2075-443: Is (barring computational efficiency concerns) generally a good choice as a hash function, but the converse need not be true. Hash tables often contain only a small subset of the valid inputs. For instance, a club membership list may contain only a hundred or so member names, out of the very large set of all possible names. In these cases, the uniformity criterion should hold for almost all typical subsets of entries that may be found in

2158-430: Is added to the table there. If the hash code indexes a full slot, then some kind of collision resolution is required: the new item may be omitted (not added to the table), or replace the old item, or be added to the table in some other location by a specified procedure. That procedure depends on the structure of the hash table. In chained hashing , each slot is the head of a linked list or chain, and items that collide at

2241-485: Is also the name of a cross-platform file encryption utility developed in 2002 that implements Blowfish. Blowfish's use of a 64-bit block size (as opposed to e.g. AES's 128-bit block size) makes it vulnerable to birthday attacks , particularly in contexts like HTTPS . In 2016, the SWEET32 attack demonstrated how to leverage birthday attacks to perform plaintext recovery (i.e. decrypting ciphertext) against ciphers with

2324-464: Is especially useful in distributed hash tables . In some applications, the input data may contain features that are irrelevant for comparison purposes. For example, when looking up a personal name, it may be desirable to ignore the distinction between upper and lower case letters. For such data, one must use a hash function that is compatible with the data equivalence criterion being used: that is, any two inputs that are considered equivalent must yield

2407-676: Is intolerably bad but rare, and average-case behavior can be nearly optimal (minimal collision ). Hash functions are related to (and often confused with) checksums , check digits , fingerprints , lossy compression , randomization functions , error-correcting codes , and ciphers . Although the concepts overlap to some extent, each one has its own uses and requirements and is designed and optimized differently. The hash function differs from these concepts mainly in terms of data integrity . Hash tables may use non-cryptographic hash functions , while cryptographic hash functions are used in cybersecurity to secure sensitive data such as passwords. In

2490-413: Is much larger than m —see the birthday problem . In special cases when the keys are known in advance and the key set is static, a hash function can be found that achieves absolute (or collisionless) uniformity. Such a hash function is said to be perfect . There is no algorithmic way of constructing such a function—searching for one is a factorial function of the number of keys to be mapped versus

2573-426: Is often an array with two or more indices (called a grid file , grid index , bucket grid , and similar names), and the hash function returns an index tuple . This principle is widely used in computer graphics , computational geometry , and many other disciplines, to solve many proximity problems in the plane or in three-dimensional space , such as finding closest pairs in a set of points, similar shapes in

bcrypt - Misplaced Pages Continue

2656-555: Is processed. Because the P-array is 576 bits long, and the key bytes are XORed through all these 576 bits during the initialization, many implementations support key sizes up to 576 bits. The reason for that is a discrepancy between the original Blowfish description, which uses 448-bit keys, and its reference implementation, which uses 576-bit keys. The test vectors for verifying third-party implementations were also produced with 576-bit keys. When asked which Blowfish version

2739-406: Is replaced with an expensive key setup (EksBlowfishSetup) function: The bcrypt algorithm depends heavily on its "Eksblowfish" key setup algorithm, which runs as follows: InitialState works as in the original Blowfish algorithm, populating the P-array and S-box entries with the fractional part of π {\displaystyle \pi } in hexadecimal. The ExpandKey function does

2822-421: Is stored in 8 bits (as in extended ASCII or ISO Latin 1 ), the table has only 2 = 256 entries; in the case of Unicode characters, the table would have 17 × 2 = 1 114 112 entries. The same technique can be used to map two-letter country codes like "us" or "za" to country names (26 = 676 table entries), 5-digit ZIP codes like 13083 to city names ( 100 000 entries), etc. Invalid data values (such as

2905-476: Is stronger than pbkdf2, scrypt, and argon2. bcrypt has a maximum password length of 72 bytes. This maximum comes from the first operation of the ExpandKey function that uses XOR on the 18 4-byte subkeys (P) with the password: The password (which is UTF-8 encoded), is repeated until it is 72-bytes long. For example, a password of: Is repeated until it matches the 72-bytes of the 18 P per-round subkeys: In

2988-405: Is that it will not break up clustered keys. For example, the keys 123000, 456000, 789000, etc. modulo 1000 all map to the same address. This technique works well in practice because many key sets are sufficiently random already, and the probability that a key set will be cyclical by a large prime number is small. Algebraic coding is a variant of the division method of hashing which uses division by

3071-400: Is the correct one, Bruce Schneier answered: "The test vectors should be used to determine the one true Blowfish". Another opinion is that the 448 bits limit is present to ensure that every bit of every subkey depends on every bit of the key, as the last four values of the P-array don't affect every bit of the ciphertext. This point should be taken in consideration for implementations with

3154-441: Is the number of keys, m is the number of buckets, and b j is the number of items in bucket j . A ratio within one confidence interval (such as 0.95 to 1.05) is indicative that the hash function evaluated has an expected uniform distribution. Hash functions can have some technical properties that make it more likely that they will have a uniform distribution when applied. One is the strict avalanche criterion : whenever

3237-531: Is then encrypted with the algorithm as it stands. The resultant ciphertext replaces P 1 and P 2 . The same ciphertext is then encrypted again with the new subkeys, and the new ciphertext replaces P 3 and P 4 . This continues, replacing the entire P-array and all the S-box entries. In all, the Blowfish encryption algorithm will run 521 times to generate all the subkeys – about 4 KB of data

3320-450: Is uniform on the interval [0, 2  − 1] . A hash function uniform on the interval [0, n − 1] is n P (key) / 2 . We can replace the division by a (possibly faster) right bit shift : n P (key) >> b . If keys are being hashed repeatedly, and the hash function is costly, then computing time can be saved by precomputing the hash codes and storing them with the keys. Matching hash codes almost certainly means that

3403-456: The Bloom filter , a space-efficient probabilistic data structure that is used to test whether an element is a member of a set . A special case of hashing is known as geometric hashing or the grid method . In these applications, the set of all inputs is some sort of metric space , and the hashing function can be interpreted as a partition of that space into a grid of cells . The table

bcrypt - Misplaced Pages Continue

3486-400: The 24-byte text: This generates 24 bytes of ciphertext, e.g.: The canonical OpenBSD implementation truncates this to 23 bytes: It is unclear why the canonical implementation deletes 8-bits from the resulting password hash. These 23 bytes become 31 characters when radix-64 encoded: The encoding used by the canonical OpenBSD implementation uses the same Base64 alphabet as crypt , which

3569-429: The aging DES and free of the problems and constraints associated with other algorithms. At the time Blowfish was released, many other designs were proprietary, encumbered by patents , or were commercial or government secrets. Schneier has stated that "Blowfish is unpatented, and will remain so in all countries. The algorithm is hereby placed in the public domain , and can be freely used by anyone." Notable features of

3652-522: The algorithm itself makes use of a 72 byte initial value. Although Provos and Mazières do not state the reason for the shorter restriction, they may have been motivated by the following statement from Bruce Schneier 's original specification of Blowfish, "The 448 [bit] limit on the key size ensures that the [ sic ] every bit of every subkey depends on every bit of the key." Implementations have varied in their approach of converting passwords into initial numeric values, including sometimes reducing

3735-462: The algorithm. One brief comment in the text mentions, but does not mandate, the possibility of simply using the ASCII encoded value of a character string: "Finally, the key argument is a secret encryption key, which can be a user-chosen password of up to 56 bytes (including a terminating zero byte when the key is an ASCII string)." Note that the quote above mentions passwords "up to 56 bytes" even though

3818-457: The ciphertext block, then using the P-entries in reverse order). Blowfish's key schedule starts by initializing the P-array and S-boxes with values derived from the hexadecimal digits of pi , which contain no obvious pattern (see nothing up my sleeve number ). The secret key is then, byte by byte, cycling the key if necessary, XORed with all the P-entries in order. A 64-bit all-zero block

3901-448: The cost of hashing-based methods goes up sharply as the number of collisions —pairs of inputs that are mapped to the same hash value—increases. If some hash values are more likely to occur than others, then a larger fraction of the lookup operations will have to search through a larger set of colliding table entries. This criterion only requires the value to be uniformly distributed , not random in any sense. A good randomizing function

3984-452: The country code "xx" or the ZIP code 00000) may be left undefined in the table or mapped to some appropriate "null" value. If the keys are uniformly or sufficiently uniformly distributed over the key space, so that the key values are essentially random, then they may be considered to be already "hashed". In this case, any number of any bits in the key may be extracted and collated as an index into

4067-427: The data or records themselves. Hashing is a computationally- and storage-space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often-exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of hash functions relies on statistical properties of key and function interaction: worst-case behavior

4150-475: The design include key-dependent S-boxes and a highly complex key schedule . Blowfish has a 64-bit block size and a variable key length from 32 bits up to 448 bits. It is a 16-round Feistel cipher and uses large key-dependent S-boxes . In structure it resembles CAST-128 , which uses fixed S-boxes. The adjacent diagram shows Blowfish's encryption routine. Each line represents 32 bits. There are five subkey-arrays: one 18-entry P-array (denoted as K in

4233-517: The diagram, to avoid confusion with the Plaintext) and four 256-entry S-boxes (S0, S1, S2 and S3). Every round r consists of 4 actions: The F-function splits the 32-bit input into four 8-bit quarters and uses the quarters as input to the S-boxes. The S-boxes accept 8-bit input and produce 32-bit output. The outputs are added modulo 2 and XORed to produce the final 32-bit output (see image in

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4316-431: The fixed algorithm. Nobody else, including Canonical and OpenBSD, adopted the idea of 2x/2y. This version marker change was limited to crypt_blowfish . $ 2b$ (February 2014) A bug was discovered in the OpenBSD implementation of bcrypt. It was using an unsigned 8-bit value to hold the length of the password. For passwords longer than 255 bytes, instead of being truncated at 72 bytes the password would be truncated at

4399-630: The following: Hence, ExpandKey( state , 0, key ) is the same as regular Blowfish key schedule since all XORs with the all-zero salt value are ineffectual. ExpandKey( state , 0, salt ) is similar, but uses the salt as a 128-bit key. Many implementations of bcrypt truncate the password to the first 72 bytes, following the OpenBSD implementation. The mathematical algorithm itself requires initialization with 18 32-bit subkeys (equivalent to 72 octets/bytes). The original specification of bcrypt does not mandate any one particular method for mapping text-based passwords from userland into numeric values for

4482-408: The hash code is taken as the middle 4 digits of the 17-digit number (ignoring the high digit) 8750. The mid-squares method produces a reasonable hash code if there is not a lot of leading or trailing zeros in the key. This is a variant of multiplicative hashing, but not as good because an arbitrary key is not a good multiplier. A standard technique is to use a modulo function on the key, by selecting

4565-406: The hash function must be chosen so that the result has fairly uniform distribution between 0 and n  − 1 , for any value of n that may occur in the application. Depending on the function, the remainder may be uniform only for certain values of n , e.g. odd or prime numbers . When the hash function is used to store values in a hash table that outlives the run of the program, and

4648-568: The hash table needs to be expanded or shrunk, the hash table is referred to as a dynamic hash table. A hash function that will relocate the minimum number of records when the table is resized is desirable. What is needed is a hash function H ( z , n ) (where z is the key being hashed and n is the number of allowed hash values) such that H ( z , n  + 1) = H ( z , n ) with probability close to n /( n  + 1) . Linear hashing and spiral hashing are examples of dynamic hash functions that execute in constant time but relax

4731-429: The hash table. For example, a simple hash function might mask off the m least significant bits and use the result as an index into a hash table of size 2 . A mid-squares hash code is produced by squaring the input and extracting an appropriate number of middle digits or bits. For example, if the input is 123 456 789 and the hash table size 10 000 , then squaring the key produces 15 241 578 750 190 521 , so

4814-475: The hashed value. The cost of computing this identity hash function is effectively zero. This hash function is perfect , as it maps each input to a distinct hash value. The meaning of "small enough" depends on the size of the type that is used as the hashed value. For example, in Java , the hash code is a 32-bit integer. Thus the 32-bit integer Integer and 32-bit floating-point Float objects can simply use

4897-439: The input data into chunks of specific size. Hash functions used for data searches use some arithmetic expression that iteratively processes chunks of the input (such as the characters in a string) to produce the hash value. In many applications, the range of hash values may be different for each run of the program or may change along the same run (for instance, when a hash table needs to be expanded). In those situations, one needs

4980-445: The item follows the same procedure until the item is located, an open slot is found, or the entire table has been searched (item not in table). Hash functions are also used to build caches for large data sets stored in slow media. A cache is generally simpler than a hashed search table, since any collision can be resolved by discarding or writing back the older of the two colliding items. Hash functions are an essential ingredient of

5063-538: The item is possible. The determinism is in the context of the reuse of the function. For example, Python adds the feature that hash functions make use of a randomized seed that is generated once when the Python process starts in addition to the input to be hashed. The Python hash ( SipHash ) is still a valid hash function when used within a single run, but if the values are persisted (for example, written to disk), they can no longer be treated as valid hash values, since in

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5146-409: The key, each round starting with the subkey state from the previous round. In theory, this is no stronger than the standard Blowfish key schedule, but the number of rekeying rounds is configurable; this process can therefore be made arbitrarily slow, which helps deter brute-force attacks upon the hash or salt. The input to the bcrypt function is the password string (up to 72 bytes), a numeric cost, and

5229-458: The keys are identical. This technique is used for the transposition table in game-playing programs, which stores a 64-bit hashed representation of the board position. A universal hashing scheme is a randomized algorithm that selects a hash function h among a family of such functions, in such a way that the probability of a collision of any two distinct keys is 1/ m , where m is the number of distinct hash values desired—independently of

5312-409: The lesser of 72 or the length modulo 256. For example, a 260 byte password would be truncated at 4 bytes rather than truncated at 72 bytes. bcrypt was created for OpenBSD. When they had a bug in their library, they decided to bump the version number. The bcrypt function below encrypts the text "OrpheanBeholderScryDoubt" 64 times using Blowfish . In bcrypt the usual Blowfish key setup function

5395-429: The mathematical sense of the term. This requirement excludes hash functions that depend on external variable parameters, such as pseudo-random number generators or the time of day. It also excludes functions that depend on the memory address of the object being hashed, because the address may change during execution (as may happen on systems that use certain methods of garbage collection ), although sometimes rehashing of

5478-487: The multiplicative methods, and the most complex (slowest) are the division-based methods. Because collisions should be infrequent, and cause a marginal delay but are otherwise harmless, it is usually preferable to choose a faster hash function over one that needs more computation but saves a few collisions. Division-based implementations can be of particular concern because a division requires multiple cycles on nearly all processor microarchitectures . Division ( modulo ) by

5561-410: The next run the random value might differ. It is often desirable that the output of a hash function have fixed size (but see below). If, for example, the output is constrained to 32-bit integer values, then the hash values can be used to index into an array. Such hashing is commonly used to accelerate data searches. Producing fixed-length output from variable-length input can be accomplished by breaking

5644-493: The number of items in the table. Hash functions can be designed to give the best worst-case performance, good performance under high table loading factors, and in special cases, perfect (collisionless) mapping of keys into hash codes. Implementation is based on parity-preserving bit operations (XOR and ADD), multiply, or divide. A necessary adjunct to the hash function is a collision-resolution method that employs an auxiliary data structure like linked lists , or systematic probing of

5727-440: The number of table slots that they are mapped into. Finding a perfect hash function over more than a very small set of keys is usually computationally infeasible; the resulting function is likely to be more computationally complex than a standard hash function and provides only a marginal advantage over a function with good statistical properties that yields a minimum number of collisions. See universal hash function . When testing

5810-580: The pre-processing equivalent of encrypting about 4 kilobytes of text, which is very slow compared to other block ciphers. This prevents its use in certain applications, but is not a problem in others. Blowfish must be initialized with a key. It is good practice to have this key hashed with a hash function before use. In one application Blowfish's slow key changing is actually a benefit: the password -hashing method (crypt $ 2, i.e. bcrypt) used in OpenBSD uses an algorithm derived from Blowfish that makes use of

5893-458: The property of uniformity to achieve the minimal movement property. Extendible hashing uses a dynamic hash function that requires space proportional to n to compute the hash function, and it becomes a function of the previous keys that have been inserted. Several algorithms that preserve the uniformity property but require time proportional to n to compute the value of H ( z , n ) have been invented. A hash function with minimal movement

5976-439: The same hash value. This can be accomplished by normalizing the input before hashing it, as by upper-casing all letters. There are several common algorithms for hashing integers. The method giving the best distribution is data-dependent. One of the simplest and most common methods in practice is the modulo division method. If the data to be hashed is small enough, then one can use the data itself (reinterpreted as an integer) as

6059-431: The slot are added to the chain. Chains may be kept in random order and searched linearly, or in serial order, or as a self-ordering list by frequency to speed up access. In open address hashing , the table is probed starting from the occupied slot in a specified manner, usually by linear probing , quadratic probing , or double hashing until an open slot is located or the entire table is probed (overflow). Searching for

6142-402: The slow key schedule; the idea is that the extra computational effort required gives protection against dictionary attacks . See key stretching . Blowfish has a memory footprint of just over 4 kilobytes of RAM . This constraint is not a problem even for older desktop and laptop computers , though it does prevent use in the smallest embedded systems such as early smartcards . Blowfish

6225-515: The strength of passwords containing non-ASCII characters. It is important to note that bcrypt is not a key derivation function (KDF) . For example, bcrypt cannot be used to derive a 512-bit key from a password. At the same time, algorithms like pbkdf2 , scrypt , and argon2 are password-based key derivation functions - where the output is then used for the purpose of password hashing rather than just key derivation. Password hashing generally needs to complete < 1000 ms. In this scenario, bcrypt

6308-400: The table to find an empty slot. Hash functions are used in conjunction with hash tables to store and retrieve data items or data records. The hash function translates the key associated with each datum or record into a hash code, which is used to index the hash table. When an item is to be added to the table, the hash code may index an empty slot (also called a bucket), in which case the item

6391-417: The table, not just for the global set of all possible entries. In other words, if a typical set of m records is hashed to n table slots, then the probability of a bucket receiving many more than m / n records should be vanishingly small. In particular, if m < n , then very few buckets should have more than one or two records. A small number of collisions is virtually inevitable, even if n

6474-407: The two keys. Universal hashing ensures (in a probabilistic sense) that the hash function application will behave as well as if it were using a random function, for any distribution of the input data. It will, however, have more collisions than perfect hashing and may require more operations than a special-purpose hash function. A hash function that allows only certain table sizes or strings only up to

6557-417: The upper right corner). After the 16th round, undo the last swap, and XOR L with K18 and R with K17 (output whitening). Decryption is exactly the same as encryption, except that P1, P2, ..., P18 are used in the reverse order. This is not so obvious because xor is commutative and associative. A common misconception is to use inverse order of encryption as decryption algorithm (i.e. first XORing P17 and P18 to

6640-420: The use of a hash function is a trade-off between search time and data storage space. If search time were unbounded, then a very compact unordered linear list would be the best medium; if storage space were unbounded, then a randomly accessible structure indexable by the key-value would be very large and very sparse, but very fast. A hash function takes a finite amount of time to map a potentially large keyspace to

6723-432: The value directly, whereas the 64-bit integer Long and 64-bit floating-point Double cannot. Other types of data can also use this hashing scheme. For example, when mapping character strings between upper and lower case , one can use the binary encoding of each character, interpreted as an integer, to index a table that gives the alternative form of that character ("A" for "a", "8" for "8", etc.). If each character

6806-427: The worst case a password is limited to 18 characters, when every character requires 4 bytes of UTF-8 encoding. For example: In 2024 a single-sign-on service by Okta, Inc. announced a vulnerability due to the password being concatenated after the username and the pair hashed with bcrypt, resulting in the password being ignored for logins with a long-enough username. The bcrypt algorithm involves repeatedly encrypting

6889-475: Was one of the first secure block ciphers not subject to any patents and therefore freely available for anyone to use. This benefit has contributed to its popularity in cryptographic software. bcrypt is a password hashing function which, combined with a variable number of iterations (work "cost"), exploits the expensive key setup phase of Blowfish to increase the workload and duration of hash calculations, further reducing threats from brute force attacks. bcrypt

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