Crypto-Current (064)

§5.8612 — Decentralization of the ledger requires massive multiplication, and thus an effective method of compression. Only in this way does it become tractable to distributed, modestly-sized nodes. The crucial computer science innovation in this regard is the Merkle Tree. The capabilities drawn upon date back over a decade before linked timestamping, with Ralph Merkle’s original hash tree patent was granted in 1979.[1]

§5.86121 — Hashes are economizations.[2] They reduce the cost of checking, by securely summarizing units of data, and therefore cheapen the process of verification. Any radically decentralized (open fully-peer-to-peer) network is necessarily trustless, since it connects strangers in the absence of validating authorities. Consisting of both massively redundant distributed databases and numerous untrusted nodes, checking is at once especially inconvenienced, and especially necessary.

§5.86122 — As their name suggests, Merkle Trees map an order of proliferation, typically – though not necessarily – modeled by successive bifurcation. Their function, however, is the precise inverse of tree-like exponential growth. A Merkle Tree works towards its roots, in increments of convergence. As users proceed down the tree, hashes of network content are bundled, recursively, into ever more comprehensive groups. The ‘root’ or (confusingly) ‘top hash’ over-hashes the entire tree. It thus serves as a concise compendium for the entire network, against which the hash of any file (or block) can be conveniently checked. Recursive hashing – hashes of hashes of (ever more) hashes – is the principle of the ‘tree’.

§5.86122 — Cryptographic hashing has a peculiarly intimate[3] relationship with cryptocurrency, and thus with money as such in its emergent characteristics. This is in part, and primarily, because the hash is the privileged semiotic of singularity – to the extent that ‘hash collision’ is calamitous for it. Hashing therefore tends to affinity with the allocative or economic sign.

[1] Ralph Merkle’s hash-tree patent (US4309569A) is titled a “Method of providing digital signatures”. Its abstract (in full) runs: “The invention comprises a method of providing a digital signature for purposes of authentication of a message, which utilizes an authentication tree function of a one-way function of a secret number.” The description that follows expands upon its potential applications. “The present invention has been described with respect to authentication of signatures. However, its use is not limited to signatures. It may be used to authenticate a piece of information in a list of information, or one item in a list of items.”

The patent can be accessed online at:

[2] See §2.31

[3] See §3.422-4

1 thought on “Crypto-Current (064)

  1. “It may be used to authenticate a piece of information in a list of information, or one item in a list of items.”

    Or one outcome of a script/contract in a logical tree of outcomes…
    “What is a Bitcoin Merkelized Abstract Syntax Tree?”
    “Taproot: Privacy preserving switchable scripting”

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