# Blowfish Algorithm Is A Feistel Network Computer Science Essay

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The data transformation process for PocketBrief uses the Blowfish Algorithm for Encryption and Decryption, respectively. The details and working of the algorithm are

given below.

Blowfish is a symmetric block cipher that can be effectively used for encryption and

safeguarding of data. It takes a variable-length key, from 32 bits to 448 bits, making it

ideal for securing data. Blowfish was designed in 1993 by Bruce Schneier as a fast, free

alternative to existing encryption algorithms. Blowfish is unpatented and license-free,

and is available free for all uses.

Blowfish Algorithm is a Feistel Network, iterating a simple encryption function 16

times. The block size is 64 bits, and the key can be any length up to 448 bits. Although

there is a complex initialization phase required before any encryption can take place, the

actual encryption of data is very efficient on large microprocessors.

Blowfish is a variable-length key block cipher. It is suitable for applications where the

key does not change often, like a communications link or an automatic file encryptor. It is

significantly faster than most encryption algorithms when implemented on 32-bit

microprocessors with large data caches.

## Feistel Networks

A Feistel network is a general method of transforming any function (usually called an Ffunction)

into a permutation. It was invented by Horst Feistel and has been used in many

block cipher designs. The working of a Feistal Network is given below:

_ Split each block into halves

_ Right half becomes new left half

_ New right half is the final result when the left half is XORâ€™d with the result of

applying f to the right half and the key.

_ Note that previous rounds can be derived even if the function f is not invertible.

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The Blowfish Algorithm:

_ Manipulates data in large blocks

_ Has a 64-bit block size.

_ Has a scalable key, from 32 bits to at least 256 bits.

_ Uses simple operations that are efficient on microprocessors.

e.g., exclusive-or, addition, table lookup, modular- multiplication. It does not

use variable-length shifts or bit-wise permutations, or conditional jumps.

_ Employs precomputable subkeys.

On large-memory systems, these subkeys can be precomputed for faster

operation. Not precomputing the subkeys will result in slower operation, but it

should still be possible to encrypt data without any precomputations.

_ Consists of a variable number of iterations.

For applications with a small key size, the trade-off between the complexity of

a brute-force attack and a differential attack make a large number of iterations

superfluous. Hence, it should be possible to reduce the number of iterations

with no loss of security (beyond that of the reduced key size).

_ Uses subkeys that are a one-way hash of the key.

This allows the use of long passphrases for the key without compromising

security.

_ Has no linear structures that reduce the complexity of exhaustive search.

_ Uses a design that is simple to understand. This facilitates analysis and increase

the confidence in the algorithm. In practice, this means that the algorithm will be

a Feistel iterated block cipher.

## DESCRIPTION OF THE ALGORITHM

Blowfish is a variable-length key, 64-bit block cipher. The algorithm consists of two

parts: a key-expansion part and a data- encryption part. Key expansion converts a key of

at most 448 bits into several subkey arrays totaling 4168 bytes.

Data encryption occurs via a 16-round Feistel network. Each round consists of a keydependent

permutation, and a key- and data-dependent substitution. All operations are

XORs and additions on 32-bit words. The only additional operations are four indexed

array data lookups per round.

## Subkeys

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Blowfish uses a large number of subkeys. These keys must be precomputed before any

data encryption or decryption.

_ The P-array consists of 18 32-bit subkeys:

P1, P2,..., P18.

_ There are four 32-bit S-boxes with 256 entries each:

S1,0, S1,1,..., S1,255;

S2,0, S2,1,..,, S2,255;

S3,0, S3,1,..., S3,255;

S4,0, S4,1,..,, S4,255.

## Encryption

Blowfish has 16 rounds.

The input is a 64-bit data element, x.

Divide x into two 32-bit halves: xL, xR.

Then, for i = 1 to 16:

xL = xL XOR Pi

xR = F(xL) XOR xR

Swap xL and xR

After the sixteenth round, swap xL and xR again to undo the last swap.

Then, xR = xR XOR P17 and xL = xL XOR P18.

Finally, recombine xL and xR to get the ciphertext.

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Decryption is exactly the same as encryption, except that P1, P2,..., P18 are used in the

reverse order.

Implementations of Blowfish that require the fastest speeds should unroll the loop and

ensure that all subkeys are stored in cache.

## Generating the Subkeys

The subkeys are calculated using the Blowfish algorithm:

1. Initialize first the P-array and then the four S-boxes, in order, with a fixed string.

This string consists of the hexadecimal digits of pi (less the initial 3): P1 =

0x243f6a88, P2 = 0x85a308d3, P3 = 0x13198a2e, P4 = 0x03707344, etc.

2. XOR P1 with the first 32 bits of the key, XOR P2 with the second 32-bits of the

key, and so on for all bits of the key (possibly up to P14). Repeatedly cycle

through the key bits until the entire P-array has been XORed with key bits. (For

every short key, there is at least one equivalent longer key; for example, if A is a

64-bit key, then AA, AAA, etc., are equivalent keys.)

3. Encrypt the all-zero string with the Blowfish algorithm, using the subkeys

described in steps (1) and (2).

4. Replace P1 and P2 with the output of step (3).

5. Encrypt the output of step (3) using the Blowfish algorithm with the modified

subkeys.

6. Replace P3 and P4 with the output of step (5).

7. Continue the process, replacing all entries of the P array, and then all four S-boxes

in order, with the output of the continuously changing Blowfish algorithm.

In total, 521 iterations are required to generate all required subkeys. Applications can

store the subkeys rather than execute this derivation process multiple times.

## DESIGN DECISIONS

A 64-bit block size yields a 32-bit word size, and maintains block-size compatibility with

existing algorithms. Blowfish is easy to scale up to a 128-bit block, and down to smaller

block sizes.

The fundamental operations were chosen with speed in mind. XOR, ADD, and MOV

from a cache are efficient on both Intel and Motorola architectures. All subkeys fit in the

cache of a 80486, 68040, Pentium, and PowerPC.

The Feistel Network that makes up the body of Blowfish is designed to be as simple as

possible, while still retaining the desirable cryptographic properties of the structure.

In algorithm design, there are two basic ways to ensure that the key is long enough to

ensure a particular security level. One is to carefully design the algorithm so that the

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entire entropy of the key is preserved, so there is no better way to cryptanalyze the

algorithm other than brute force. The other is to design the algorithm with so many key

bits that attacks that reduce the effective key length by several bits are irrelevant. Since

Blowfish is designed for large microprocessors with large amounts of memory, the latter

has been chosen. But it works equally well on Handheld systems with a decent

microprocessor.

The subkey generation process is designed to preserve the entire entropy of the key and

to distribute that entropy uniformly throughout the subkeys. It is also designed to

distribute the set of allowed subkeys randomly throughout the domain of possible

subkeys. The digits of pi were chosen as the initial subkey table for two reasons: because

it is a random sequence not related to the algorithm, and because it could either be stored

as part of the algorithm or derived when needed. But if the initial string is non-random in

any way (for example, ASCII text with the high bit of every byte a 0), this nonrandomness

will propagate throughout the algorithm.

In the subkey generation process, the subkeys change slightly with every pair of subkeys

generated. This is primarily to protect against any attacked of the subkey generation

process that exploit the fixed and known subkeys. It also reduces storage requirements.

The 448 limit on the key size ensures that the every bit of every subkey depends on every

bit of the key.

The key bits are repeatedly XORed with the digits of pi in the initial P-array to prevent

the following potential attack: Assume that the key bits are not repeated, but instead

padded with zeros to extend it to the length of the P-array. An attacker might find two

keys that differ only in the 64-bit value XORed with P1 and P2 that, using the initial

known subkeys, produce the same encrypted value. If so, he can find two keys that

produce all the same subkeys. This is a highly tempting attack for a malicious key

generator. To prevent this same type of attack, the initial plaintext value in the subkeygeneration

process is fixed.

The subkey-generation algorithm does not assume that the key bits are random. Even

highly correlated key bits, such as an alphanumeric ASCII string with the bit of every

byte set to 0, will produce random subkeys. However, to produce subkeys with the same

entropy, a longer alphanumeric key is required.

The time-consuming subkey-generation process adds considerable complexity for a

brute-force attack. The subkeys are too long to be stored on a massive tape, so they would

have to be generated by a brute-force cracking machine as required. A total of 522

iterations of the encryption algorithm are required to test a single key, effectively adding

29 steps to any brute-force attack.

The most efficient way to break Blowfish is through exhaustive search of the keyspace.

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