The Nakamoto Signature might be a thing. In 2014, the Sidechains whitepaper by Back et al introduced the term Dynamic Membership Multiple-party Signature or DMMS -- because we love complicated terms and long impassable acronyms.
Or maybe we don't. I can never recall DMMS nor even get it right without thinking through the words; in response to my cognitive poverty, Adam Back suggested we call it a Nakamoto signature.
That's actually about right in cryptology terms. When a new form of cryptography turns up and it lacks an easy name, it's very often called after its inventor. Famous companions to this tradition include RSA for Rivest, Shamir, Adleman; Schnorr for the name of the signature that Bitcoin wants to move to. Rijndael is our most popular secret key algorithm, from the inventors names, although you might know it these days as AES. In the old days of blinded formulas to do untraceable cash, the frontrunners were signatures named after Chaum, Brands and Wagner.
On to the Nakamoto signature. Why is it useful to label it so?
Because, with this literary device, it is now much easier to talk about the blockchain. Watch this:
The blockchain is a shared ledger where each new block of transactions - the 10 minutes thing - is signed with a Nakamoto signature.
Each can be covered as a separate topic. For example:
the shared ledger can be seen as a series of blocks, each of which is a single document presented for signature. Each block consists of a set of transactions built on the previous set. Each succeeding block changes the state of the accounts by moving money around; so given any particular state we can create the next block by filling it with transactions that do those money moves, and signing it with a Nakamoto signature.
Having described the the shared ledger, we can now attack the Nakamoto signature:
A Nakamoto signature is a device to allow a group to agree on a shared document. To eliminate the potential for inconsistencies aka disagreement, the group engages in a lottery to pick one person's version as the one true document. That lottery is effected by all members of the group racing to create the longest hash over their copy of the document. The longest hash wins the prize and also becomes a verifiable 'token' of the one true document for members of the group: the Nakamoto signature.
That's it, in a nutshell. That's good enough for most people. Others however will want to open that nutshell up and go deeper into the hows, whys and whethers of it all. You'll note I left plenty of room for argument above; Economists will look at the incentive structure in the lottery, and ask if a prize in exchange for proof-of-work is enough to encourage an efficient agreement, even in the presence of attackers? Computer scientists will ask 'what happens if...' and search for ways to make it not so. Entrepreneurs might be more interested in what other documents can be signed this way. Cryptographers will pounce on that longest hash thing.
But for most of us we can now move on to the real work. We haven't got time for minutia. The real joy of the Nakamoto signature is that it breaks what was one monolithic incomprehensible problem into two more understandable ones. Divide and conquer!
The Nakamoto signature needs to be a thing. Let it be so!