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Advanced Cryptography

Digital signature

A cryptographic proof that a message was created by the holder of a private key and has not been altered.

Digital signature at a glance
A digital signature is created with a private key and checked with the public key Message "pay 1 BTC" Private key kept secret by the signer Signature 3045…f2ab Attach to transaction Signing proves: "I approved this exact message" verification by anyone Verify (no secrets needed) message signature public key verify() Valid ✓ Message unchanged Verification succeeds: only the holder of the private key could have produced this signature. Message tampered with Verification fails instantly — even a single changed byte invalidates the signature.

In simple terms

You sign a hash of the message with your private key. Anyone with your public key can verify it.

Analogy

A handwritten signature that is mathematically impossible to copy onto a different document.

Going deeper

Signatures give authenticity, integrity and non-repudiation in one primitive. Ed25519 (used by SSH and modern protocols) signs with a single pass of Curve25519; verification is cheap enough to run on every certificate and firmware image you load.

Common mistake

A signature is not encryption — the message stays readable. Also: never reuse a nonce in ECDSA; bad nonce selection has leaked private keys in the wild.

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