how many public address we can found into memonics 12 word ?

[BtcMaxi2090]

 12-word mnemonic phrase can represent a vast number of unique addresses. How much is this number big ? Can anyone explain me also how it work please?

[1714548897]

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[1714548897]

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[1714548897]

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[1714548897]

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[BtcMaxi2090]

 From the seed derived from the mnemonic, a virtually unlimited number of private keys can be generated. How much are those private keys? Also each private key represent its own public address that is derived from the private key

[hosseinimr93]

Let's say we have a bitcoin wallet generated using the standard derivation path of m/44'/0'/0' and addresses are generated at m/44'/0'/0'/x/y. (x is the change index and y is the address index).

If we only change the address index, we can generate 2^32 addresses. The address index can be in the range of 0 to  2^32 -1 (or 0xFFFFFFFF in hexadecimal system).
If we change the change index as well, we can have 2^33 addresses. The change index can be either 0 or 1.


We can also generate addresses using non-standard derivation paths with changing the account index. We can generate addresses using the derivation path of m/44'/0'/1', m/44'/0'/2' and so on.
Like the address index, the account index can be also in the range of 0 to 2^32 - 1.

With changing the account index, the change index and the address index, we can generate 2^65 addresses.


We can also generate more addresses with using BIP49 and BIP84 standards.
If we consider the three BIP44, BIP49 and BIP84 standards, we can generate 3 * 2^65 addresses.


We can still generate more addresses with using more complicated non-standard derivation paths.

[Zaguru12]

In simpler terms as explained above by hosseinimr93 it is around 4 billion possible child addresses from each parent extended key which is gotten from 2^32 base on Hierarchy Deterministic wallet limitation which is one of the most common wallets currently been used.
You can look it up here from From antonopoulos mastering bitcoin: https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch05.asciidoc#navigating-the-hd-wallet-tree-structure

[pooya87]

Technically speaking BIP32 is like a key derivation function so you should be able to derive as many child keys as you want from it without limiting yourself to the standard derivation paths. Meaning from m/0 to m/0xffffffff then from m/0/0 to m/0xffffffff/0xffffffff and so on.
The only limit I can think of is the depth that needs to be encoded into the Base58 encoded extended keys, since it is only one byte so you can only continue the above paths 256 times!

[o_e_l_e_o]

Here's a previous answer I gave to this question:

Well, as per BIP32, extended keys have 1 byte for the level they are at. 0x00 for the master key, 0x01 for the first level, 0x02 for the second level, and so on, up to 0xFF. This means you can have a total of 255 levels after the m. It also allows 4 bytes for the index. This means a total of 2³² possible indices for each of those 255 levels. So a single seed phrase can generate (2³²)²⁵⁵ + (2³²)²⁵⁴ + (2³²)²⁵³ + (2³²)²⁵² + .... private keys. This number works out at 2.5*10²⁴⁵⁶, which is many orders of magnitude higher than the set of all possible private keys (a little less than 2²⁵⁶). This means that not only can any seed phrase (almost certainly) generate any private key at the right derivation path, but any seed phrase can generate any private key billions and billions of times over at many different derivation paths.

The answer is a single seed phrase can generate 2.5*10²⁴⁵⁶ possible child keys when following the BIP32 protocol.

[BtcMaxi2090]

thank you everyone for your answer. i have another question now

if someone have his mnemonics and lost the private key of the pub address where he store his money. How could he restore it ?

[hosseinimr93]

if someone have his mnemonics and lost the private key of the pub address where he store his money. How could he restore it ?

If you have a seed phrase (which is a series of words and it's also called mnemonic phrase), you don't need to keep individual private keys and that's one of advantages of having a HD wallet with seed phrase.
Note that your seed phrase can generate all your private keys and that's all you need.

[Knight Hider]

Read my signature: Each 24 word seed covers all possible Bitcoin addresses. Think about what this means for a while, it's truly amazing.

[BtcMaxi2090]

if someone have his mnemonics and lost the private key of the pub address where he store his money. How could he restore it ?

If you have a seed phrase (which is a series of words and it's also called mnemonic phrase), you don't need to keep individual private keys and that's one of advantages of having a HD wallet with seed phrase.
Note that your seed phrase can generate all your private keys and that's all you need.

But how would you find the specified adderss with balance >0 ? What's way to find it ?

[ecdsa123]

Let's analyze:


seeds: 12 words

in dictionary we have 2048 words:

so according combination of words from dictionary and taking 12 : we got:

2048**12 = 5,444,517,870,735,245,796,800,000 possibilities addreses of one kind type like pwsh, segwit,pwpkh...

in example we have 12 words and combination beetween them we have

12**12 = 8 916 100 448 256 possibilities:)

[hosseinimr93]

But how would you find the specified adderss with balance >0 ? What's way to find it ?

Most wallets use standard derivation paths.


m/44'/0'/0' is usually used for generating legacy addresses and the first receiving legacy address is generated at m/44'/0'/0'/0/0
m/49'/0'/0' is usually used for generating nested segwit addresses and the first receiving nested segwit address is generated at m/49'/0'/0'/0/0   
m/84'/0'/0' is usually used for generating native segwit addresses and the first receiving native segwit address is generated at m/84'/0'/0'/0/0   


For example, if you import a BIP39 seed phrase in electrum (without changing the derivation path) to generate a native segwit wallet, by default it gives you 20 receiving addresses and 10 change addresses.
The 20 receiving addresses would be generated at m/84'/0'/0'/0/0 - m/84'/0'/0'/0/19 and the 10 change addresses would be generated at m/84'/0'/0'/1/0 - m/84'/0'/0'/1/19


In the case you have generated your addresses using a non-standard derivation path for any reason, you need to know the derivation path as well and you still don't need to save individual private keys.

[o_e_l_e_o]

But how would you find the specified adderss with balance >0 ? What's way to find it ?

Know the derivation path. If you don't know it, you have to brute force it. Provided you've followed one of the various BIP protocols this will be easy enough to do. If you have used something non-standard, this might be easy or impossible.

For example, let's say I generated an address at something like this, and did not back up this path:

Code:

m/3960204'/946011'/3720125'/749317'/3739'/82051'/104969'/960302295`/29502019/17472/81332/6785

This is exponentially more difficult to brute force than a seed phrase itself, and so my coins on that path would be unrecoverable.

[BtcMaxi2090]

thank you all about your feed back i really appreciate that

can someone give me link about good docs that explain very well the concept of derivation path ? i want really deep undertsand about it

this is amazing, math are so beautiful with bitcoin

[Samlucky O]

thank you everyone for your answer. i have another question now

if someone have his mnemonics and lost the private key of the pub address where he store his money. How could he restore it ?

I think it will not be possible to restore without your 12 seed phrase. It is always a slogan here in this forum that "not your key not your coin" Whatever that makes you to lost your key your coin is gone forever. That is why it's often advisable to keep your information in a safe place so that when you are locked out of your privacy then you can use your key to prove the wrightful owner. And Mean while there is no mistakes on you key phrase spelling.  Make sure when writing it down check each spelling correctly because if you spell right in replacement of wright I think you might still be not able to sign in OR login to your wallet.

When dealing with a non custodial wallet or DEX there is need to keep your key imidiately after you open your wallet. Because we makes this mistakes due to procrastination. Always saying I will do it later... Until you lost your phone or you mistakenly delete the wallet on your phone without saving the seed phrase. Imidiately that is done, all your asset in that wallet is gone.

[ranochigo]

thank you all about your feed back i really appreciate that

can someone give me link about good docs that explain very well the concept of derivation path ? i want really deep undertsand about it

this is amazing, math are so beautiful with bitcoin

BIP32 is the standard for deriving the addresses from the seeds, and BIP44(https://github.com/bitcoin/bips/blob/master/bip-0044.mediawiki) is one of the path that was introduced as a BIP previously. Some of the wallets use this derivation path while there are some wallet that uses the other forms of derivation path.

You should be able to find the meanings of the path level in BIP44.

[o_e_l_e_o]

can someone give me link about good docs that explain very well the concept of derivation path ? i want really deep undertsand about it

https://learnmeabitcoin.com/technical/derivation-paths
https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch05.asciidoc