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Signatures

In the Transactions Section, you learned how transactions are composed. In this section you will learn how to authorize them.

Before a transaction is sent to the network, it must first be authorized by the sender. Authorization occurs through the addition of a signature to the transaction object. Specifically, a transaction object, when signed, is wrapped in a SignedTxn object that includes the transaction and a type of signature.

There are three types of signatures:

Single Signatures

A single signature corresponds to a signature from the private key of an Algorand public/private key pair.

This is an example of a transaction signed by an Algorand private key displayed with goal clerk inspect command:

{
  "sig": "ynA5Hmq+qtMhRVx63pTO2RpDrYiY1wzF/9Rnnlms6NvEQ1ezJI/Ir9nPAT6+u+K8BQ32pplVrj5NTEMZQqy9Dw==",
  "txn": {
    "amt": 10000000,
    "fee": 1000,
    "fv": 4694301,
    "gen": "testnet-v1.0",
    "gh": "SGO1GKSzyE7IEPItTxCByw9x8FmnrCDexi9/cOUJOiI=",
    "lv": 4695301,
    "rcv": "QC7XT7QU7X6IHNRJZBR67RBMKCAPH67PCSX4LYH4QKVSQ7DQZ32PG5HSVQ",
    "snd": "EW64GC6F24M7NDSC5R3ES4YUVE3ZXXNMARJHDCCCLIHZU6TBEOC7XRSBG4",
    "type": "pay"
  }
}
This transaction sends 10 Algo from "EW64GC..." to "QC7XT7..." on TestNet. The transaction was signed with the private key that corresponds to the "snd" address of "EW64GC...". The base64 encoded signature is shown as the value of the "sig" field.

Multisignatures

When the sender of a transaction is the address of a multisignature account then authorization requires a subset of signatures, equal to or greater than the threshold value, from the associated private keys of the addresses that multisignature account is composed of. See Multisignature Accounts for details on how to configure a multisignature account.

Important

Upon signing, either the signing agent or the transaction needs to know the composition of the multisignature account, i.e. the ordered addresses, threshold, and version.

Here is what the same transaction above would look like if sent from a ⅔ multisig account.

{
  "msig": {
    "subsig": [
      {
        "pk": "SYGHTA2DR5DYFWJE6D4T34P4AWGCG7JTNMY4VI6EDUVRMX7NG4KTA2WMDA"
      },
      {
        "pk": "VBDMPQACQCH5M6SBXKQXRWQIL7QSR4FH2UI6EYI4RCJSB2T2ZYF2JDHZ2Q"
      },
      {
        "pk": "W3KONPXCGFNUGXGDCOCQYVD64KZOLUMHZ7BNM2ZBK5FSSARRDEXINLYHPI"
      }
    ],
    "thr": 2,
    "v": 1
  },
  "txn": {
    "amt": 10000000,
    "fee": 1000,
    "fv": 4694301,
    "gen": "testnet-v1.0",
    "gh": "SGO1GKSzyE7IEPItTxCByw9x8FmnrCDexi9/cOUJOiI=",
    "lv": 4695301,
    "rcv": "QC7XT7QU7X6IHNRJZBR67RBMKCAPH67PCSX4LYH4QKVSQ7DQZ32PG5HSVQ",
    "snd": "GQ3QPLJL4VKVGQCHPXT5UZTNZIJAGVJPXUHCJLRWQMFRVL4REVW7LJ3FGY",
    "type": "pay"
  }
}
The difference between this transaction and the one above is the form of its signature component. For multisignature accounts, an "msig" struct is added which contains the 3 public addresses ("pk"), the threshold value ("thr") and the multisig version "v". This transaction is still unsigned but the addition of the correct "msig" struct is confirmation that the transaction is "aware" of the fact that the sender is multisig and will have no trouble accepting sub-signatures from single keys even if the signing agent does not contain information about its multisignature properties.

Tip

Adding the "msig" template to make the transaction "aware" of its multisig sender is highly recommended, particularly in cases where the transaction is signed by multiple parties or offline. Without it, the signing agent would need to have its own knowledge of the multisignature account. For example, goal can sign a multisig transaction that does not contain an "msig" template if the multisig address was created within its wallet. On signing, it will add the "msig" template.

Sub-signatures can be added to the transaction one at a time, cumulatively, or merged together from multiple transactions. Here is the same transaction above, fully authorized:

{
  "msig": {
    "subsig": [
      {
        "pk": "SYGHTA2DR5DYFWJE6D4T34P4AWGCG7JTNMY4VI6EDUVRMX7NG4KTA2WMDA",
        "s": "xoQkPyyqCPEhodngmOTP2930Y2GgdmhU/YRQaxQXOwh775gyVSlb1NWn70KFRZvZU96cMtq6TXW+r4sK/lXBCQ=="
      },
      {
        "pk": "VBDMPQACQCH5M6SBXKQXRWQIL7QSR4FH2UI6EYI4RCJSB2T2ZYF2JDHZ2Q"
      },
      {
        "pk": "W3KONPXCGFNUGXGDCOCQYVD64KZOLUMHZ7BNM2ZBK5FSSARRDEXINLYHPI",
        "s": "p1ynP9+LZSOZCBcrFwt5JZB2F+zqw3qpLMY5vJBN83A+55cXDYp5uz/0b+vC0VKEKw+j+bL2TzKSL6aTESlDDw=="
      }
    ],
    "thr": 2,
    "v": 1
  },
  "txn": {
    "amt": 10000000,
    "fee": 1000,
    "fv": 4694301,
    "gen": "testnet-v1.0",
    "gh": "SGO1GKSzyE7IEPItTxCByw9x8FmnrCDexi9/cOUJOiI=",
    "lv": 4695301,
    "rcv": "QC7XT7QU7X6IHNRJZBR67RBMKCAPH67PCSX4LYH4QKVSQ7DQZ32PG5HSVQ",
    "snd": "GQ3QPLJL4VKVGQCHPXT5UZTNZIJAGVJPXUHCJLRWQMFRVL4REVW7LJ3FGY",
    "type": "pay"
  }
}

The two signatures are added underneath their respective addresses. Since 2 meets the threshold, this transaction is now fully authorized and can be sent to the network.

Info

Adding more sub-signatures than the threshold requires is unnecessary but perfectly valid.

How-To

Extend the example from the Multisignature Account section by creating, signing, and sending a transaction from a multisig account on TestNet.

const algosdk = require('algosdk');


const token = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa";
const server = "http://localhost";
const port = 4001;
const keypress = async () => {
    process.stdin.setRawMode(true)
    return new Promise(resolve => process.stdin.once('data', () => {
        process.stdin.setRawMode(false)
        resolve()
    }))
}

(async () => {
    // recover accounts
    // paste in mnemonic phrases here for each account
    let account1_mnemonic = "PASTE phrase for account 1";
    let account2_mnemonic = "PASTE phrase for account 2";
    let account3_mnemonic = "PASTE phrase for account 3"
    // never use mnemonics in production code, replace for demo purposes only

    let account1 = algosdk.mnemonicToSecretKey(account1_mnemonic);
    let account2 = algosdk.mnemonicToSecretKey(account2_mnemonic);
    let account3 = algosdk.mnemonicToSecretKey(account3_mnemonic);
    console.log(account1.addr);
    console.log(account2.addr);
    console.log(account3.addr);

    // Setup the parameters for the multisig account
    const mparams = {
        version: 1,
        threshold: 2,
        addrs: [
            account1.addr,
            account2.addr,
            account3.addr,
        ],
    };

    let multsigaddr = algosdk.multisigAddress(mparams);
    console.log("Multisig Address: " + multsigaddr);
    //Pause execution to allow using the dispenser on testnet to put tokens in account
    console.log("Add funds to multisig account using the TestNet Dispenser: ");
    console.log("https://dispenser.testnet.aws.algodev.network?account=" + multsigaddr);
    console.log("Once funded, press any key to continue");
    await keypress();
    try {
        let algodclient = new algosdk.Algodv2(token, server, port);

        // Get the relevant params from the algod
        let params = await algodclient.getTransactionParams().do();
        // comment out the next two lines to use suggested fee
        // params.fee = 1000;
        // params.flatFee = true;

        const receiver = account3.addr;
        let names = '{"firstName":"John", "lastName":"Doe"}';
        const enc = new TextEncoder();
        const note = enc.encode(names);


        let txn = algosdk.makePaymentTxnWithSuggestedParams(multsigaddr, receiver, 100000, undefined, note, params);
        let txId = txn.txID().toString();
        // Sign with first signature

        let rawSignedTxn = algosdk.signMultisigTransaction(txn, mparams, account1.sk).blob;
        //sign with second account
        let twosigs = algosdk.appendSignMultisigTransaction(rawSignedTxn, mparams, account2.sk).blob;
        //submit the transaction
        await algodclient.sendRawTransaction(twosigs).do();

        // Wait for confirmation
        const confirmedTxn = await algosdk.waitForConfirmation(algodclient, txId, 4);
        //Get the completed Transaction
        console.log("Transaction " + txId + " confirmed in round " + confirmedTxn["confirmed-round"]);
        let mytxinfo = JSON.stringify(confirmedTxn.txn.txn, undefined, 2);
        console.log("Transaction information: %o", mytxinfo);
        let string = new TextDecoder().decode(confirmedTxn.txn.txn.note);
        console.log("Note field: ", string);
        const obj = JSON.parse(string);
        console.log("Note first name: %s", obj.firstName);


    } catch (err) {
        console.log(err.message);
    }
})().then(process.exit)
import json
from algosdk.v2client import algod
from algosdk import account, encoding, mnemonic
from algosdk.future.transaction import Multisig, PaymentTxn, MultisigTransaction
import base64
from algosdk.future.transaction import *

# Change these values with mnemonics
mnemonic1 = "PASTE phrase for account 1"
mnemonic2 = "PASTE phrase for account 2"
mnemonic3 = "PASTE phrase for account 3"
# never use mnemonics in production code, replace for demo purposes only

# For ease of reference, add account public and private keys to
# an accounts dict.

private_key_1 = mnemonic.to_private_key(mnemonic1)
account_1 = mnemonic.to_public_key(mnemonic1)

private_key_2 = mnemonic.to_private_key(mnemonic2)
account_2 = mnemonic.to_public_key(mnemonic2)

private_key_3 = mnemonic.to_private_key(mnemonic3)
account_3 = mnemonic.to_public_key(mnemonic3)



# create a multisig account
version = 1  # multisig version
threshold = 2  # how many signatures are necessary
msig = Multisig(version, threshold, [account_1, account_2])

print("Multisig Address: ", msig.address())
print('Go to the below link to fund the created account using testnet faucet: \n https://dispenser.testnet.aws.algodev.network/?account={}'.format(msig.address())) 

input("Press Enter to continue...")

# Specify your node address and token. This must be updated.
# algod_address = ""  # ADD ADDRESS
# algod_token = ""  # ADD TOKEN

# sandbox
algod_address = "http://localhost:4001"
algod_token = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

# Initialize an algod client
algod_client = algod.AlgodClient(algod_token, algod_address)

# get suggested parameters
params = algod_client.suggested_params()
# comment out the next two (2) lines to use suggested fees
# params.flat_fee = True
# params.fee = 1000

# create a transaction
sender = msig.address()
recipient = account_3
amount = 10000
note = "Hello Multisig".encode()
txn = PaymentTxn(sender, params, recipient, amount, None, note, None)

# create a SignedTransaction object
mtx = MultisigTransaction(txn, msig)

# sign the transaction
mtx.sign(private_key_1)
mtx.sign(private_key_2)

# print encoded transaction
# print(encoding.msgpack_encode(mtx))


    # wait for confirmation 
try:
# send the transaction
    txid = algod_client.send_raw_transaction(
    encoding.msgpack_encode(mtx))    
    print("TXID: ", txid)   
    confirmed_txn = wait_for_confirmation(algod_client, txid, 6)  
    print("Result confirmed in round: {}".format(confirmed_txn['confirmed-round']))
    print("Transaction information: {}".format(
        json.dumps(confirmed_txn, indent=4)))
    print("Decoded note: {}".format(base64.b64decode(
        confirmed_txn["txn"]["txn"]["note"]).decode()))
except Exception as err:
    print(err)
package com.algorand.javatest.multisig;


import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;

import com.algorand.algosdk.account.Account;
import com.algorand.algosdk.v2.client.common.AlgodClient;
import com.algorand.algosdk.v2.client.common.Response;
import com.algorand.algosdk.v2.client.model.PendingTransactionResponse;
import com.algorand.algosdk.v2.client.model.TransactionParametersResponse;
import com.algorand.algosdk.algod.client.ApiException;
import com.algorand.algosdk.crypto.Address;
import com.algorand.algosdk.crypto.Ed25519PublicKey;
import com.algorand.algosdk.crypto.MultisigAddress;
import com.algorand.algosdk.transaction.SignedTransaction;
import com.algorand.algosdk.transaction.Transaction;
import com.algorand.algosdk.util.Encoder;
import java.util.Scanner;
import org.json.JSONObject;
import com.algorand.algosdk.v2.client.model.PostTransactionsResponse;
import com.algorand.algosdk.v2.client.Utils;

/**
* Test Multisignature
*
*/
public class Multisig {

    public AlgodClient client = null;

    // utility function to connect to a node
    private AlgodClient connectToNetwork() {

        // Initialize an algod client
        // final String ALGOD_API_ADDR = "algod-address<PLACEHOLDER>";
        // final String ALGOD_API_TOKEN = "algod-token<PLACEHOLDER>";


        // sandbox
        // Initialize an algod client
        final String ALGOD_API_ADDR = "localhost";
        final Integer ALGOD_PORT = 4001;
        final String ALGOD_API_TOKEN = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa";

        AlgodClient client = new AlgodClient(ALGOD_API_ADDR, ALGOD_PORT, ALGOD_API_TOKEN);
        return client;

    }



    static Scanner scan = new Scanner(System.in);
    public void multisigExample() throws Exception {

        if (client == null)
            this.client = connectToNetwork();
        //  never use mnemonics in production code, replace for demo purposes only


        final String account1_mnemonic = "<var>your-25-word-mnemonic</var>"
        final String account2_mnemonic = "<var>your-25-word-mnemonic</var>"
        final String account3_mnemonic = "<var>your-25-word-mnemonic</var>"

        Account act1 = new Account(account1_mnemonic);
        Account act2 = new Account(account2_mnemonic);
        Account act3 = new Account(account3_mnemonic);
        System.out.println("Account1: " + act1.getAddress());
        System.out.println("Account2: " + act2.getAddress());
        System.out.println("Account3: " + act3.getAddress());
        final String DEST_ADDR = act3.getAddress().toString();
        // List for Pks for multisig account
        List<Ed25519PublicKey> publicKeys = new ArrayList<>();
        publicKeys.add(act1.getEd25519PublicKey());
        publicKeys.add(act2.getEd25519PublicKey());
        publicKeys.add(act3.getEd25519PublicKey());
        // Instantiate the Multisig Account
        MultisigAddress msa = new MultisigAddress(1, 2, publicKeys);
    ;
        System.out.println("Multisignature Address: " + msa.toString());
        System.out.println("Navigate to this link and dispense:  https://dispenser.testnet.aws.algodev.network?account=" + msa.toString());            
        System.out.println("PRESS ENTER KEY TO CONTINUE...");     
        scan.nextLine();
        // setup transaction   
        try {
            Response < TransactionParametersResponse > resp = client.TransactionParams().execute();
            if (!resp.isSuccessful()) {
                throw new Exception(resp.message());
            }
            TransactionParametersResponse params = resp.body();
            if (params == null) {
                throw new Exception("Params retrieval error");
            }                      
            BigInteger amount = BigInteger.valueOf(100000); // 100000 microAlgos = .1 Algo
            // add some notes to the transaction
            byte[] notes = "These are some notes encoded in some way!".getBytes();
            // Setup Transaction
            Address sender = new Address(msa.toString());

            Transaction tx = Transaction.PaymentTransactionBuilder()
                    .sender(sender)
                    .amount(amount)
                    .receiver(DEST_ADDR)
                    .note(notes)
                    .suggestedParams(params).build();
            // Sign the Transaction for two accounts
            SignedTransaction signedTx = act1.signMultisigTransaction(msa, tx);
            SignedTransaction completeTx = act2.appendMultisigTransaction(msa, signedTx);
            // Msgpack encode the signed transaction
            byte[] encodedTxBytes = Encoder.encodeToMsgPack(completeTx);

            // Submit the transaction to the network
            Response < PostTransactionsResponse > rawtxresponse = client.RawTransaction().rawtxn(encodedTxBytes).execute();
            if (!rawtxresponse.isSuccessful()) {
                throw new Exception(rawtxresponse.message());
            }
            String id = rawtxresponse.body().txId;
            // Wait for transaction confirmation
            PendingTransactionResponse pTrx = Utils.waitForConfirmation(client, id, 4);

            System.out.println("Transaction " + id + " confirmed in round " + pTrx.confirmedRound);
            // Read the transaction
            JSONObject jsonObj = new JSONObject(pTrx.toString());
            System.out.println("Transaction information (with notes): " + jsonObj.toString(2));
            System.out.println("Decoded note: " + new String(pTrx.txn.tx.note));
        } catch (ApiException e) {
            // This is generally expected, but should give us an informative error message.
            System.err.println("Exception when calling algod#rawTransaction: " + e.getResponseBody());
        }
    }  
    public static void main(String args[]) throws Exception {
        Multisig t = new Multisig();
        t.multisigExample();
    }
}
package main

import (
    "context"
    "crypto/ed25519"
    "fmt"
    json "encoding/json"
    "github.com/algorand/go-algorand-sdk/future"
    "github.com/algorand/go-algorand-sdk/client/v2/algod"   
    "github.com/algorand/go-algorand-sdk/crypto"
    "github.com/algorand/go-algorand-sdk/mnemonic"
    "github.com/algorand/go-algorand-sdk/transaction"
    "github.com/algorand/go-algorand-sdk/types"
)

// UPDATE THESE VALUES
// const algodAddress = "Your ADDRESS"
// const algodToken = "Your TOKEN"

// sandbox
const algodAddress = "http://localhost:4001"
const algodToken = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"

// Accounts to be used through examples
func loadAccounts() (map[int][]byte, map[int]string) {
    // Shown for demonstration purposes. NEVER reveal secret mnemonics in practice.
    // Change these values to use the accounts created previously.

    // Paste in mnemonic phrases for all three accounts
    mnemonic1 := "PASTE phrase for account 1"
    mnemonic2 := "PASTE phrase for account 2"
    mnemonic3 := "PASTE phrase for account 3"
    // never use mnemonics in production code, replace for demo purposes only


    mnemonics := []string{mnemonic1, mnemonic2, mnemonic3}
    pks := map[int]string{1: "", 2: "", 3: ""}
    var sks = make(map[int][]byte)

    for i, m := range mnemonics {
        var err error
        sk, err := mnemonic.ToPrivateKey(m)
        sks[i+1] = sk
        if err != nil {
            fmt.Printf("Issue with account %d private key conversion.", i+1)
        }
        // derive public address from Secret Key.
        pk := sk.Public()
        var a types.Address
        cpk := pk.(ed25519.PublicKey)
        copy(a[:], cpk[:])
        pks[i+1] = a.String()
        fmt.Printf("Loaded Key %d: %s\n", i+1, pks[i+1])
    }
    return sks, pks
}


// PrettyPrint prints Go structs
func PrettyPrint(data interface{}) {
    var p []byte
    //    var err := error
    p, err := json.MarshalIndent(data, "", "\t")
    if err != nil {
        fmt.Println(err)
        return
    }
    fmt.Printf("%s \n", p)
}

func main() {

    // Initialize an algodClient
    algodClient, err := algod.MakeClient(algodAddress, algodToken)
    if err != nil {
        return
    }
    // Get network-related transaction parameters and assign
    txParams, err := algodClient.SuggestedParams().Do(context.Background())
    if err != nil {
        fmt.Printf("error getting suggested tx params: %s\n", err)
        return
    }
    // comment out the next two (2) lines to use suggested fees
    // txParams.FlatFee = true
    // txParams.Fee = 1000
    // Get pre-defined set of keys for example
    sks, pks := loadAccounts()


    addr1, _ := types.DecodeAddress(pks[1])
    addr2, _ := types.DecodeAddress(pks[2])
    addr3, _ := types.DecodeAddress(pks[3])     

    ma, err := crypto.MultisigAccountWithParams(1, 2, []types.Address{
        addr1,
        addr2,
        addr3,
    })

    if err != nil {
        panic("invalid multisig parameters")
    }

    fromAddr, _ := ma.Address()
    // Fund account
    fmt.Println("Fund multisig account using testnet faucet:\n--> https://dispenser.testnet.aws.algodev.network?account=" + fromAddr.String())
    fmt.Println("--> Once funded, press ENTER key to continue...")


    //  fmt.Scanln() // wait for Enter Key

    toAddr := addr3.String()
    var amount uint64 = 10000
    note := []byte("Hello World")
    genID := txParams.GenesisID
    genHash := txParams.GenesisHash
    firstValidRound := uint64(txParams.FirstRoundValid)
    lastValidRound := uint64(txParams.LastRoundValid)
    var minFee uint64 = 1000
    txn, err := transaction.MakePaymentTxn(
        fromAddr.String(),
        toAddr,
        minFee,     // fee per byte
        amount,  // amount
        firstValidRound, // first valid round
        lastValidRound, // last valid round
        note,    // note
        "",     // closeRemainderTo
        genID,     // genesisHash
        genHash,     // genesisHash
    )

    txid, txBytes, err := crypto.SignMultisigTransaction(sks[1], ma, txn)
    if err != nil {
        println(err.Error)
        panic("could not sign multisig transaction")
    }
    fmt.Printf("Made partially-signed multisig transaction with TxID %s: %x\n", txid, txBytes)

    txid, twoOfThreeTxBytes, err := crypto.AppendMultisigTransaction(sks[2], ma, txBytes)

    if err != nil {
        panic("could not append signature to multisig transaction")
    }
    fmt.Printf("Appended bytes %x\n", twoOfThreeTxBytes)

    fmt.Printf("Made 2-out-of-3 multisig transaction with TxID %s: %x\n", txid, twoOfThreeTxBytes)


    // We can also merge raw, partially-signed multisig transactions:
    // otherTxBytes := ... // generate another raw multisig transaction 
    // txid, mergedTxBytes, err := crypto.MergeMultisigTransactions(twoOfThreeTxBytes, otherTxBytes)

    // Broadcast the transaction to the network
    txid, err = algodClient.SendRawTransaction(twoOfThreeTxBytes).Do(context.Background())


    // Wait for confirmation
    confirmedTxn, err := future.WaitForConfirmation(algodClient,txid,  4, context.Background())
    if err != nil {
        fmt.Printf("Error waiting for confirmation on txID: %s\n", txid)
        return
    }
    fmt.Printf("Confirmed Transaction: %s in Round %d\n", txid ,confirmedTxn.ConfirmedRound)

    txnJSON, err := json.MarshalIndent(confirmedTxn.Transaction.Txn, "", "\t")
    if err != nil {
        fmt.Printf("Can not marshall txn data: %s\n", err)
    }
    fmt.Printf("Transaction information: %s\n", txnJSON)

    fmt.Printf("Decoded note: %s\n", string(confirmedTxn.Transaction.Txn.Note))

}
# Sign cumulatively
$ goal clerk multisig sign -t multisig.txn -a $ADDRESS1
$ goal clerk multisig sign -t multisig.txn -a $ADDRESS2

# Or sign two separate files and merge
$ goal clerk multisig sign -t multisig1.txn -a $ADDRESS1
$ goal clerk multisig sign -t multisig2.txn -a $ADDRESS2
$ goal clerk multisig merge multisig1.txn multisig2.txn --out=merged.stxn
# algokey takes account-level mnemonics at the time of signing
# requires the transaction to include the msig struct before signing
$ algokey multisig --txfile=multisig1.txn --outfile=multisig1.stxn -m <25-word-mnemonic>
$ algokey multisig --txfile=multisig2.txn --outfile=multisig2.stxn -m <25-word-mnemonic>

# Use goal to merge the the *.stxn files.

Logic Signatures

Logic signatures authorize transactions associated with an Algorand Smart Contract. Logic signatures are added to transactions to authorize spends from a Contract Account or from a Delegated Account.

A full explanation of Logic Signatures can be found in the Algorand Smart Contract Usage Modes Guide.

Related How-To

Info

Full running code examples for each SDK are available within the GitHub repo for V1 and V2 at /examples/multisig and for download (.zip).