How can I address the SHA3 state vector in programming terms?

Question

I've been working on an implementation of SHA3, and I'm getting a bit muddled on this particular aspect of the algorithm. The addressing scheme of the state vector is given by the following diagram:

My issue with the above is: How does one go about addressing this in terms of actual code? I am using a 3 dimensional array to express the state vector, but this leads to obvious issues since the conventional mapping of an array (0 index is first) differs from the above convention used in SHA3.

For example, if I wanted to address the (0,0,0) bit in the SHA3 state array, the following expression would achieve this:

state_vector[2][2][0]

I find this highly cumbersome however because when implementing the actual round algorithms, the intended x and y values do not directly map to the array indices. Addressing state_vector[0][0][0] would return the very first index in the array instead of the (0,0,0) bit in the SHA3 state array.

Is there a way I can get around this in code?

Sorry, I know this is probably a stupid question.

Answer 1

The way this is customarily implemented is as a 5×5 array of 64-bit words, an array of 25 64-bit words or, if you believe your architecture (say, AArch64) will have a lot of registers, as 25 individual 64-bit words. (I prefer the second option because it's simpler to work with.) Typically they are indeed ordered in the typical order for arrays, and one simply rewrites things accordingly.

Usually this isn't a problem, because the operations are specified in terms of words in relation to each other, such as in the theta and chi steps. It's common to simply code rho and pi together such that it involves reading a word, rotating it, and storing it in the destination word, and in such a case you can simply just reorder the rotation constants as you need to.

If you want to get very fancy, you can write this as an SIMD implementation, but I think it's easier to see how it works in a practical implementation if you write it as a one- or two-dimensional array of words first.