**Blowfish Cipher Tutorials - Herong's Tutorial Examples** - Version 2.00, by Dr. Herong Yang

Key Schedule (Sub-Keys and S-Boxes) Algorithm

The Blowfish Key Schedule (Sub-Keys Generation) algorithm is provided to generate 18 Sub-keys and 4 S-boxes, using user provided secret key and hexadecimal digits of the fractional portion of constant Pi, (3.1415927... - 3) = 0.1415927... as input.

In the previous tutorial, we left two parts undefined in the Blowfish encryption algorithm:

- 18 Sub-keys: P{1), P(2), ..., P(18) - Each Sub-key is 32 bits long.
- 4 S-boxes: S1[], S2[], S3[], S4[] - Each S-box has 256 elements. Each element is 32 bits long.

Here is the suggested Blowfish key schedule algorithm, which should be used to construct 18 Sub-keys and 4 S-boxes:

Input: K: The key - 32 bits or more PI: The binary representation of the fractional portion of "pi" = 3.1415927... - 3.0 = 2/16 + 4*/16**2 + 3/16**3 + 15/16**4 + ... = 0x243f6a8885a308d313198a2e03707344... Output: P1, P2, ..., P18: 18 32-bit sub-keys S1[], S2[], S3[], S4[]: 4 S-boxes, 32-bit 256-element arrays Algorithm - Blowfish Key Schedule Generation: (P1, P2, ..., P18, S1[], S2[], S3[], S4[]) = PI K' = (K, K, K, ...), Repeat the key to 18*32 bits long (P1, P2, ..., P18) = (P1, P2, ..., P18) XOR K' T = (0x000000, 0x000000), Setting initial clear text T = Blowfish(T), Applying Blowfish process (P1, P2) = T, Updating first two sub-keys T = Blowfish(T), Applying Blowfish process (P3, P4) = T ...... T = Blowfish(T) (P17, P18) = T T = Blowfish(T) (S1[0], S1[1]) = T T = Blowfish(T) (S1[2], S1[3]) = T ...... T = Blowfish(T) (S1[254], S1[255]) = T T = Blowfish(T) (S2[0], S2[1]) = T ...... T = Blowfish(T) (S4[254], S4[255]) = T

Note that:

- To initialize 18 sub-keys and 4 S tables, we need 18*32 + 4*256*32 = 576 + 32768 = 33344 binary digits of PI, or 33344/4 = 8336 hex digits of PI.
- To finalize 18 sub-keys and 4 S tables, we need to apply Blowfish algorithm (18+4*256)/2 = 1042/2 = 521 times.
- The secret key, K, has an variable length from 32 bits to 18*32=576 bits (72 bytes) long.
- The Blowfish process is used as part of the key schedule algorithm.

Now we have completed the entire Blowfish encryption algorithm, which takes a give secret key, constructs Sub-keys and S-boxes, then apply the Blowfish process on the given 64-bit block.

Last update: 2015.

Table of Contents

Blowfish Cipher Encryption Algorithm

►Key Schedule (Sub-Keys and S-Boxes) Algorithm

Efficient Form of the Blowfish Algorithm

Blowfish Cipher Decryption Algorithm

Proof of Blowfish Cipher Algorithm

First 8336 Fractional Hex Digits of PI

piqpr8.c - Generating Hex Digits of PI

OpenSSL "enc -bf-ecb" for Blowfish/ECB Encryption

OpenSSL "enc -bf-cbc" for Blowfish/CBC Encryption

OpenSSL "enc -bf-cfb" for Blowfish/CFB Encryption

OpenSSL "enc -bf-ofb" for Blowfish/OFB Encryption