![](https://cdn.steemitimages.com/DQmUXGNRGByzh21WyQ6uVUV8CxiGpjfrkBKxUjNsKQKozud/image.png)

<p>So far, we have not delved into any detail about “digital signatures.” In this
article we look at how digital signatures work and how they can present
proof of ownership of a private key without revealing that private key</p>
<p>The digital signature algorithm used in bitcoin is the Elliptic Curve Digital
Signature Algorithm, or ECDSA. ECDSA is the algorithm used for digital
signatures based on elliptic curve private/public key pairs, as described in
“Elliptic Curve Cryptography Explained”. ECDSA is used by the script
functions OP_CHECKSIG, OP_CHECKSIGVERIFY, OP_CHECKMULTISIG, and
OP_CHECKMULTISIGVERIFY. Any time you see those in a locking script, the
unlocking script must contain an ECDSA signature.</p>
<p>A digital signature serves three purposes in bitcoin (see the following
sidebar). First, the signature proves that the owner of the private key, who is
by implication the owner of the funds, has authorized the spending of those
funds. Secondly, the proof of authorization is undeniable (nonrepudiation).
Thirdly, the signature proves that the transaction (or specific parts of the
transaction) have not and cannot be modified by anyone after it has been
signed.</p>
<p>Note that each transaction input is signed independently. This is critical, as
neither the signatures nor the inputs have to belong to or be applied by the
same “owners.” In fact, a specific transaction scheme called “CoinJoin” uses
this fact to create multi-party transactions for privacy</p>
<center><h1>NOTE</h1></center>
<center>Each transaction input and any signature it may contain is completely independent of any
other input or signature. Multiple parties can collaborate to construct transactions and sign
only one input each.</center>