Storing data in a Merkle tree

Apollo 11

12/30/22, 1:59 PM

I had the idea of storing large amounts of data in a small space using a Merkle tree. But from what I understand about Merkle trees is you cannot extract the data from the Merkle root (since hashes are not reversible). Though I wonder, is there a way to use an encryption algorithm that gives a fixed output length like how we use hashes in Merkle trees? I know my question is hard to understand but looking at this diagram may give you a better idea of what I am trying to do here:

1 + 0

hash

hash-tree

Score:2

Crypto

poncho

12/30/22, 2:58 PM

If I understand you right, you are asking if there was a way to take the $n$-bit Merkle tree root, and use it to extract the multiple files that are the leaves.

Obviously, if the information within the files is more than $n$ bits, you can't - if there are $2^n$ possible roots, then no procedure can extract more than $2^n$ different values from it, and it doesn't matter what function you use as the "hash"

0 + 3

Apollo 11

12/30/22, 3:03 PM

Thank you for your answer. I am a newbie to cryptography. So can you explain what you mean by “n-bit”?

poncho

12/30/22, 3:08 PM

@Apollo11: the root of the Merkle tree will be some value, and we usually represent that value as a serial of bits (or bytes, where each byte consists of 8 bits - in crypto, we more often count bits rather than bytes). By $n$-bit tree root, we mean that $n$ bits are used.

Apollo 11

12/30/22, 3:14 PM

Thank you for your explanation. I understand now.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: Storing data in a Merkle tree

TH: การจัดเก็บข้อมูลในต้นไม้ Merkle

RO: Stocarea datelor într-un arbore Merkle

RU: Хранение данных в дереве Меркла

VI: Lưu trữ dữ liệu trong cây Merkle

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