OFB (Output FeedBack) as a Stream Cipher

This section describes how DES OFB (Output FeedBack) operation mode can be modified as a 1-bit stream cipher or a 1-byte stream cipher.

OFB (Output FeedBack) operation mode can be described with notations defined earlier as the following formula and diagram:

```C[i] = P[i] XOR O[i]
O[i] = E(O[i-1])
O[1] = E(IV)

IV
|        -----|        -----|
E()     /     E()     /     E()
|--O[1]       |--O[2]       |--O[3]
|             |             |
P[1]--XOR     P[2]--XOR     P[3]--XOR
|             |             |
C[1]          C[2]          C[3]
```

As you can see from the formula and the diagram, in OFB mode, each block of plaintext is XORed with the current output block to generate the current ciphertext block. The current output block is obtained by applying the encryption process on the previous output block. Note that for the first block, the Initial Vector (IV) is used as the previous output block.

In order to run the OFB operation mode as a stream cipher, FIPS 81 defines OFB variations where plaintext blocks can have any size less than 64 bits. To describe OFB variations, we need the following additional notations:

k - Representing the size plaintext blocks. k can have a value between 1 and 64.

Fk() - Representing a filter function that take the first k bits of a 64-bit block.

I = I[1], I[2], I[3], ..., I[i], ... - Representing the input block, I, used as input to the DES encryption process.

Sk() - Representing a shifting function that shifts k bits out of the input block from the left side. The missing k bits are taken from the output block.

With the above notations, a k-bit OFB operation mode variation can be described as:

```C[i] = P[i] XOR Fk(O[i])
O[i] = E(I[i])
I[i] = Sk(I[i-1], O[i-1])
I[1] = IV

IV
|
I[1]------Sk()--I[2]------Sk()--I[3]
|       /       |       /       |
E()     /       E()     /       E()
|--O[1]         |--O[2]         |--O[3]
Fk()            Fk()            Fk()
|               |               |
P[1]--XOR       P[2]--XOR       P[3]--XOR
|               |               |
C[1]            C[2]            C[3]
```

Note that there are some special cases of OFB variations:

• The 64-bit OFB variation is the original OFB operation mode.
• The 8-bit OFB variation is a stream cipher that takes 1 byte (8 bits) from the plaintext message at a time.
• The 1-bit OFB variation is a stream cipher that takes 1 bit from the plaintext message at a time.