How RC6 encryption algorithm works

RC6 is a symmetric key algorithm for block encryption designed by Ron Rivest in 1998, four years after the proposal of its predecessor, the RC5 encryption algorithm.

Although the high-level processing remains very similar to RC5, there are a few differences between the two algorithms, as outlined below:

Parameterization

Similar to RC5, RC6 is parameterized, word-oriented algorithm. Since it uses four registers, there is a four-word input (plaintext) and a four-word output (ciphertext), each of size $w$ bits. The parameters are as follows:

Word size: $w$

This is the word size in bits. As RC6 uses four-word inputs and outputs, the blocks are $4w$ bits long each. For instance, if $w$ is $32$ bits, then the input block will be $128$ bit long.

Number of rounds: $r$

This is the non-negative number of rounds. This parameter influences the size $t$ of the expanded key table $S$ that is derived from the user-supplied secret key. The formula for $t$ is as follows:

Length of secret key: $b$

This is the number of bytes in the secret key, $K$, provided by the user. Supported key sizes include $16, 24,$ and $32$ bytes up to $255$ bytes ($2040$ bits).

Given these parameters, the notation for the algorithm is as follows:

The proposed version of the algorithm was $RC6-32/20/x$, which implies there are four $32$ bit word blocks and $20$ rounds. $x$ denotes key sizes of $16, 32,$and $64$ bytes.

Primitive operations

RC6 uses four primitive operations and their inverses. These are:

• Addition: This refers to the two's complement addition of words and is denoted by $+$. The inverse of this is subtraction, denoted by $-$.

• Bitwise XOR: This is the bitwise exclusive-OR of words and is denoted by $\oplus$.

• Left rotation: This is the cyclic left rotation of words, denoted by $x <<< y$, where $x$ is the word, and $y$ is the number of bits to be shifted. The inverse is cyclic right rotation, represented by $x>>>y$.

• Integer multiplication: This refers to multiplication modulo $2^w$ and is denoted by $\times$.

The algorithm

The RC6 algorithm consists of three main components, as mentioned:

• Key expansion

• Encryption

• Decryption

Let us take a look at each of these in detail.

Key expansion algorithm

The key expansion algorithm is almost identical to RC5, except that it derives more words (four instead of two) from the secret key. This process is carried out over four steps, as detailed below:

Step one: Initializing P and Q

RC6 uses two word-sized constants, $P$ and $Q$. They are defined as follows:

Where $e$ is the base of natural logarithms and $\phi$ is the golden ratio.

Step two: Converting the secret key $K$ from bytes to words

The secret key array, $K[0...b-1]$, is used to initialize a new array, $L[0...c-1]$, where $c=\lceil b/u \rceil$ and $u=w/8$ bytes per word. $L$ is first initialized with $0$, and the pseudocode for loading $K$ to it is as follows:

Step three: Initializing the array $S$

Recall that $S$ is the expanded key table of size $t=2(r+2)$. Using the magic constants, $P$ and $Q$, we use the following pseudocode to initialize the expanded key table:

Step four: Key mixing

The last step of the key expansion algorithm involves mixing the provided secret key thrice over the arrays $S$ and $L$. In the given pseudocode, $A$ and $B$ are registers that hold the input words.

Encryption

Now that we have the expanded key in the array $S[0...t-1]$, we can perform the encryption algorithm as specified below. The registers are $A, B, C,$ and $D$ which hold both the input (plaintext) and output (ciphertext). Moreover, the first byte of the plaintext (or ciphertext) is placed in the least-significant byte of $A$ while the last byte of the plaintext is placed in the most-significant byte of $D$.

The final pseudocode is as follows:

At the end of $r$ rounds, registers $A, B, C,$ and $D$ hold the ciphertext.

The diagram below illustrates the encryption process:

Decryption

The pseudocode for the decryption algorithm is the exact reverse of the encryption algorithm, as shown: