Satoshi Nakamoto drew from the history of cryptocurrencies since David Chaum’s seminal blinding formula in the 1980s.  He postulated that the flaw with existing approaches to cryptocurrencies was that a single powerful attacker could undermine and destroy the system.  In order to to defeat the powerful attacker, Satoshi decentralised the control of the cryptocurrency over an open set of participants, designed a consensus algorithm to align the interests of the majority to find agreement, and thus overcome byzantine actions by minority parties.

This invention works in two parts.  Constructing a shared ledger amongst all participants was the first step.  By sharing the entire ledger of transactions, all participants could convince themselves that their own transactions were validly entered, that all value derived from an authentic source, and that the entire ledger balanced.

The second part was to agree on the ledger.  Using induction, and agreeing on all prior ledger states, Satoshi reduced the problem to agreeing what each new appending block is.  The first batch, or genesis block, was created by Satoshi.  The next block, and each successive block, included a consensus signature over this block and the previous block, creating a chain of blocks, or the blockchain.

In order to secure consensus over each new block, Satoshi employed a novel technique based on proof of work to create a form of signature.  The Nakamoto Signature is a lottery in which everyone calculates a difficult puzzle, being a SHA2 message digest with many leading zeros over their own view of a valid block.  The first person to reach a threshold value in the puzzle wins the prize:  the honour of selecting that block, and the right to create or mine an agreed amount of bitcoins in the first transaction.

By creating a financial prize to find the winning hash, Satoshi incentivised the participants to fight for the winning valid block, and thus ensured many participants working through the validity of the new transactions.  Because proof of work is a cryptographically fair operation, the fairness decentralised the fight for the winning hash, and the resulting incentives were aligned to ensure the integrity, security and value of the system.  In effect, energy was traded for money, and prize-Bitcoin awarded to miners could be sold off to others for use as money.  Thus was created a virtuous feedback loop to incentivise all to verify the correctness of the block and agree to it.

By ensuring that no person could obtain an advantage over others, and by ensuring that anyone could join without exclusion, Satoshi created the Nash equilibrium to permit normally byzantine parties to enter and share safely in the definition of a shared network of contested assets.