Implementation of Speck cipher

Question

I am trying to implement the speck cipher as specified here: Speck Cipher. On page 18 of the document you can find some speck pseudo-code I want to implement.

It seems that I got a problem on understanding the pseudo-code. As you can find there, x and y are plaintext words with length n. l[m-2],...l[0], k[0] are key words (as for words, they have length n right?). When you do the key expansion, we iterate for i from 0 to T-2, where T are the round numbers (for example 34). However I get an IndexOutofBoundsException, because the array with the l's has only m-2 positions and not T-2.

Can someone clarify what the key expansions does and how?

Answer 1

Ah, I get where the confusion lies:

l[m-2],...l[0], k[0]

these are the input key words, in other words, they represent the key. These are not declarations of the size of the arrays, as you might expect if you're a developer.

Then the subkey's in array k should be derived, using array l for intermediate values.

According to the formulas, taking the largest i, i.e. i_max = T - 2 you get a highest index for array l of i_max + m - 1 = T - 2 + m - 1 = T + m - 3 and therefore a size of the array of one more: T + m - 2. The size of a zero-based array is always the index of the last element - plus one, after all.

Similarly, for subkey array k you get a highest index of i_max + 1, which is T - 2 + 1 or T - 1. Again, the size of the array is one more, so there are T elements in k. This makes a lot of sense if you require T round keys :)

Note that it seems possible to simply redo the subkey derivation for each round if you require a minimum of RAM. The entire l array doesn't seem necessary either. For software implementations that doesn't matter a single iota of course.