As with counterfeit money, such double-spending leads to inflation by creating a new amount of copied currency that did not previously exist.
Fundamental cryptographic techniques to prevent double-spending, while preserving anonymity in a transaction, are the introduction of an authority (and hence centralization) for blind signatures and, particularly in offline systems, secret splitting.
Its cryptographic protocol used a proof-of-work consensus mechanism where transactions are batched into blocks and chained together using a linked list of hash pointers (blockchain).
Any server can produce a block by solving a computationally difficult puzzle (specifically finding a partial hash collision) called mining.
Due to the nature of a decentralized blockchain, and in lack of a central authority to do so, the correct succession of transactions is defined only by the dominating consensus.
This leads to the possibility of one actor gaining majority control over the entities deciding said consensus, to force their own version of events, including alternative and double transactions.
For the attack to be economically viable, the market cap of the currency must be sufficiently large to justify the cost to rent hashing power.