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Blowfish
The round function (Feistel function) of Blowfish
General
Designer(s):	Bruce Schneier
First published:	1993
Successor(s):	Twofish
Cipher detail
Key size(s):	32-448 bits in steps of 8 bits; default 128 bits
Block size(s):	64 bits
Structure:	Feistel network
Rounds:	16
Best public cryptanalysis
Four rounds of Blowfish are susceptible to a second-order differential attack (Rijmen, 1997); for a class of weak keys, 14 rounds of Blowfish can be distinguished from a pseudorandom permutation (Vaudenay, 1996).

In cryptography, Blowfish is a keyed, symmetric block cipher, designed in 1993 by Bruce Schneier and included in a large number of cipher suites and encryption products. Blowfish provides a good encryption rate in software and no effective cryptanalysis of it has been found to date. However, the Advanced Encryption Standard now receives more attention.

Schneier designed Blowfish as a general-purpose algorithm, intended as a replacement for the aging DES and free of the problems associated with other algorithms. At the time, many other designs were proprietary, encumbered by patents or kept as 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 the design include key-dependent S-boxes and a highly complex key schedule.

Contents 1 The algorithm 2 Cryptanalysis of Blowfish 3 Blowfish in practice 4 See also 5 Notes and references 6 External links

Blowfish has a 64-bit block size and a variable key length from 0 up to 448 bits [1]. It is a 16-round Feistel cipher and uses large key-dependent S-boxes. It is similar in structure to CAST-128, which uses fixed S-boxes.

The diagram to the left shows the action of Blowfish. Each line represents 32 bits. The algorithm keeps two subkey arrays: the 18-entry P-array and four 256-entry S-boxes. The S-boxes accept 8-bit input and produce 32-bit output. One entry of the P-array is used every round, and after the final round, each half of the data block is XORed with one of the two remaining unused P-entries.

The diagram to the right shows Blowfish's F-function. The function splits the 32-bit input into four eight-bit quarters, and uses the quarters as input to the S-boxes. The outputs are added modulo 2³² and XORed to produce the final 32-bit output.

Since Blowfish is a Feistel network, it can be inverted simply by XORing P₁₇ and P₁₈ to 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 XORed with the P-entries in order (cycling the key if necessary). A 64-bit all-zero block is then encrypted with the algorithm as it stands. The resultant ciphertext replaces P₁ and P₂. The ciphertext is then encrypted again with the new subkeys, and P₃ and P₄ are replaced by the new ciphertext. 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 4KB of data is processed.

There is no effective cryptanalysis on the full-round version of Blowfish known publicly as of 2006, although the 64-bit block size is now considered too short, because encrypting more than 2³² data blocks (32 GiB) with it can begin to leak information about the plaintext in most modes of operation due to the birthday attack. While the short block size does not pose any serious concerns for routine consumer applications like e-mail, in applications where large amounts of data are encrypted, encryption keys must be rotated before the amount of encrypted data approaches the birthday bound.^{[citation needed]}

In 1996, Serge Vaudenay found a known-plaintext attack requiring 2^{8r + 1} known plaintexts to break, where r is the number of rounds. Moreover, he also found a class of weak keys that can be detected and broken by the same attack with only 2^{4r + 1} known plaintexts. This attack cannot be used against the regular Blowfish; it assumes knowledge of the key-dependent S-boxes. Vincent Rijmen, in his Ph.D. thesis, introduced a second-order differential attack that can break four rounds and no more. There remains no known way to break the full 16 rounds, apart from a brute-force search. ^[1]

Blowfish is one of the fastest block ciphers in widespread use, except when changing keys. Each new key requires pre-processing equivalent to 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. In one application, it is actually a benefit: the password-hashing method used in OpenBSD uses an algorithm derived from Blowfish that makes use of the slow key schedule; the idea is that the extra computational effort required gives protection against dictionary attacks.

In some implementations, Blowfish has a relatively large memory footprint of just over 4 kilobytes of RAM. This is not a problem even for older smaller desktop and laptop computers, but it does prevent use in the smallest embedded systems such as early smartcards.

Blowfish is not subject to any patents and is therefore freely available for anyone to use. This benefit has contributed to its popularity in cryptographic software.

• Twofish
• MacGuffin
• Advanced Encryption Standard

1. ^ Serge Vaudenay (1996). "On the Weak Keys of Blowfish" (PostScript). Retrieved on 2006-08-23.

• Vincent Rijmen, "Cryptanalysis and design of iterated block ciphers", doctoral dissertation, October 1997.
• Bruce Schneier, Description of a New Variable-Length Key, 64-bit Block Cipher (Blowfish). Fast Software Encryption 1993: 191-204 [2].
• Bruce Schneier, The Blowfish Encryption Algorithm -- One Year Later, Dr. Dobb's Journal, 20(9), p. 137, September 1995 [3].
• Serge Vaudenay, "On the weak keys of Blowfish," Fast Software Encryption (FSE'96), LNCS 1039, D. Gollmann, Ed., Springer-Verlag, 1996, pp. 27--32.

• Official Blowfish website
• List of products using Blowfish
• SCAN's entry for Blowfish
• Blowfish JavaScript implementation and Page Encryption
• Blowfish PHP implementation
• Blowfish Java implementation (LGPL)

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