digital signature

A digital signature is a way to prove that a specific message came from a specific person and has not been altered since — using math instead of ink. Unlike a handwritten signature, which looks the same on every document and can be traced, a digital signature is a unique number computed from both the message and the signer's secret private key, so it is impossible to forge without that key and impossible to reuse on a different message.

It works hand in hand with public-key cryptography. To sign, you combine the message with your private key to produce the signature. To verify, anyone takes the message, the signature, and your public key, and runs a check that passes only if the signature was genuinely made by your private key for exactly that message. The private key never leaves your hands, yet the whole world can confirm your authorship. Change even one character of the message afterward and the signature stops matching.

This gives three guarantees at once: authenticity (it really came from the keyholder), integrity (the contents were not tampered with), and non-repudiation (the signer cannot later deny it). On a blockchain, every transaction must carry a valid digital signature from the owner of the funds being moved; without it, the network simply rejects the transaction. That single check is what stops anyone from spending coins that are not theirs.