1. Background

2. Description

3. Versioning history

4. Algorithm
     Expensive key setup    Expand key  

5. User input

6. See also

7. References

bcrypt is a password hashing function designed by Niels Provos and David Mazières, based on the Blowfish cipher, and presented at USENIX in 1999.^[1] Besides incorporating a salt to protect against rainbow table attacks, bcrypt is an adaptive function: over time, the iteration count can be increased to make it slower, so it remains resistant to brute-force search attacks even with increasing computation power.

The bcrypt function is the default password hash algorithm for OpenBSD^[2] and other systems including some Linux distributions such as SUSE Linux.^[3]

There are implementations of bcrypt for C, C++, C#, Go,^[4] Java,^[5][6] JavaScript,^[7] Elixir,^[8] Perl, PHP, Python,^[9] Ruby and other languages.

Background

Blowfish is notable among block ciphers for its expensive key setup phase. It starts off with subkeys in 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 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 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.

Description

The prefix "$2a$" or "$2b$" (or "$2y$") in a hash string in a shadow password file indicates that hash string is a bcrypt hash in modular crypt format.^[10]

The rest of the hash string includes the cost parameter, a 128-bit salt (Radix-64 encoded as 22 characters), and 184 bits of the resulting hash value (Radix-64 encoded as 31 characters)^[11]. The Radix-64 encoding uses the unix/crypt alphabet, and is not 'standard' Base-64^[12][13]. The cost parameter specifies a key expansion iteration count as a power of two, which is an input to the crypt algorithm.

For example, the shadow password record $2a$10$N9qo8uLOickgx2ZMRZoMyeIjZAgcfl7p92ldGxad68LJZdL17lhWy specifies a cost parameter of 10, indicating 2¹⁰ key expansion rounds. The salt is N9qo8uLOickgx2ZMRZoMye and the resulting hash is IjZAgcfl7p92ldGxad68LJZdL17lhWy. Per standard practice, the user's password itself is not stored.

Versioning history

The original Bcrypt specification defined a prefix of $2$. This follows the Modular Crypt Format^[14] format used when storing passwords in the OpenBSD password file:

• $1$: MD5-based crypt ('md5crypt')
• $2$: Blowfish-based crypt ('bcrypt')
• $sha1$: SHA-1-based crypt ('sha1crypt')
• $5$: SHA-256-based crypt ('sha256crypt')
• $6$: SHA-512-based crypt ('sha512crypt')

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:

• the string must be UTF-8 encoded
• the null terminator must be included

With this change, the version was changed to $2a$^[15]

In June 2011, a bug was discovered in crypt_blowfish, a PHP implementation of BCrypt. It was mis-handling characters with the 8th bit set.^[16] 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 the fixed algorithm.

Nobody else, including canonical OpenBSD, adopted the idea of 2x/2y. This version marker change was limited to crypt_blowfish.

A bug was discovered in the OpenBSD implementation of bcrypt. They were storing the length of their strings in an unsigned char (i.e. 8-bit Byte).^[15] If a password was longer than 255 characters, it would overflow and wrap at 255.^[17]

BCrypt was created for OpenBSD. When they had a bug in their library, they decided to bump the version number.

Algorithm

The bcrypt algorithm is the result of encrypting the text "OrpheanBeholderScryDoubt" 64 times using Blowfish. In bcrypt the usual Blowfish key setup function is replaced with an expensive key setup (EksBlowfishSetup) function:

Function bcrypt

       cost:     Number (4..31)                      log2(Iterations). e.g. 12 ==> 212 = 4,096 iterations       salt:     array of Bytes (16 bytes)           random salt       password: array of Bytes (1..72 bytes)        UTF-8 encoded password

       hash:     array of Bytes (24 bytes) 

    ''state''  EksBlowfishSetup(''cost'', ''salt'', ''password'')    

repeat (64)

       ''ctext''  EncryptECB(''state'', ''ctext'') //encrypt using standard Blowfish in ECB mode 

return Concatenate(cost, salt, ctext)

Expensive key setup

The bcrypt algorithm depends heavily on its "Eksblowfish" key setup algorithm, which runs as follows:

Function EksBlowfishSetup

       cost:     Number (4..31)                      log2(Iterations). e.g. 12 ==> 212 = 4,096 iterations       salt:     array of Bytes (16 bytes)           random salt       password: array of Bytes (1..72 bytes)        UTF-8 encoded password

       state:    opaque BlowFish state structure      ''state''  InitialState()    ''state''  ExpandKey(''state'', ''salt'', ''password'')

repeat (2^cost)

       ''state''  ExpandKey(state, 0, password)       ''state''  ExpandKey(state, 0, salt) 

InitialState works as in the original Blowfish algorithm, populating the P-array and S-box entries with the fractional part of in hexadecimal.

Expand key

The ExpandKey function does the following:

Function ExpandKey(state, salt, password)

       state:    Opaque BlowFish state structure     Internally contains P-array and S-box entries       salt:     array of Bytes (16 bytes)           random salt       password: array of Bytes (1..72 bytes)        UTF-8 encoded password

       state:    opaque BlowFish state structure  

       Pn  Pn xor ''password''[32(n-1)..32n-1] //treat the password as cyclic 

    ''block''  Encrypt(''state'', ''salt''[0..63])    P1  ''block''[0..31]  //lower 32-bits    P2  ''block''[32..63] //upper 32-bits 

       ''block''  Encrypt(''state'', ''block'' '''xor''' ''salt''[64(n-1)..64n-1]) //encrypt using the current key schedule and treat the salt as cyclic       P2n-1  ''block''[0..31] //lower 32-bits       P2n  ''block''[32..63]  //upper 32-bits 

          ''block''  Encrypt(''state'', ''block'' '''xor''' ''salt''[64(n-1)..64n-1]) //as above          Si[2n]    ''block''[0..31]  //lower 32-bits          Si[2n+1]  ''block''[32..63]  //upper 32-bits

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.

User input

Many implementations of bcrypt truncate the password to the first 72 bytes.

The mathematical algorithm itself requires initialization with 18 32-bit subkeys (equivalent to 72 octets/bytes). The original specification^[1] of bcrypt does not mandate any one particular method for mapping text-based passwords from userland into numeric values for 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 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,^[18] "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 the strength of passwords containing non-ASCII characters.^[19]

See also

• bcrypt is also the name of a cross-platform file encryption utility implementing Blowfish developed in 2002.^{[20][21][22][23]}
• Argon2 (The algorithm selected by the Password Hashing Competition in 2015)
• Crypt (C)#Blowfish-based scheme crypt{{snd}} password storage and verification scheme{{snd}} Blowfish
• Key stretching
• PBKDF2 (Password-Based Key Derivation Function 2)
• scrypt

References

• Bloop-ish
• Bloop-ish (Black-ish)
• B Loop (Portland Streetcar)
• Bloor CI
• Bloor-Danforth streetcar
• Bloor-Danforth Subway Line
• Bloor, David
• Bloor, James
• Bloor-Lansdowne GO Station
• Bloor Theatre
• Bloor West streetcar route
• Bloor-Yonge station
• Bloor-Yonge (TTC)
• Bloor–Lansdowne GO Station
• Bloor–Yonge (TTC)
• Blops3
• Blops 4
• Bloque Andaluz de Izquierdas
• Bloque de busqueda (telenovela)
• Bloque de búsqueda
• Bloque de Búsqueda
• Bloque de búsqueda (telenovela)
• Bloque de búsqueda (TV series)
• Bloque por Asturies
• Blorenge butres