I'm trying to implement a merkle tree consistency proof, but I'm stuck at understanding the algorithm

Question

I'm trying to implement a merkle tree consistency algorithm with this paper:

https://books.google.de/books?id=CokSDQAAQBAJ&lpg=PA147&dq=merkle%20consistency%20proof&hl=de&pg=PA148#v=onepage&q&f=false

However, I am kinda stuck on the consistency check, because I always land in an infinite loop when I execute the ConsProofSub part.

Example:

New tree has 8 , old tree has 7 leaves.

Going through the previous function, I am obtaining m = 7 , the leaves of my new tree as vector E and true as b .

The function goes through the recursive code flow, until we reach this situation:

E now has 2 elements, so n = 2 .

m = 1 , due to previous subtractions in the recursive call for m < k , as well as b = false .

We don't fall in the m = n && b = false if, as m and n are not equal.

k is now being calculated as, again, 2 , because the ceiling is correcting the resulting 1/2 from log2(n)/2 to 1 .

We fall into the m <= k case, and once again, we are recursively calling the function with the exact same parameters. Now we are in an infinite loop.

However, I can't seem to figure out what i am doing wrong. I feel like the ceiling in the k calculation is the problem. It basically makes it impossible to get out of the loop, because k will seemingly always be higher than m after some iterations.

Any advice / hint on my mistake here?

EDIT: What's interesting is the fact that the algorithm seems to work perfectly when n is an odd number. It only seems to fail for even numbers. I just tried it with a new tree of 7 leafs, and it works like a charm, delivering the correct nodes needed to prove consistency.

However, I'm still unable to figure out what changes would have to be made to make it work with even numbers.

Answer 1

There seems to be a mistake in the book. The case when m = n and b = true needs to be handled separately. A bit more detailed description of the algorithm can be found in RFC 6962 .

Here is how you can fix it: