I imagine the next to be true:
- Sequences of keys generated from seeds are indistinguishable from random sequences (besides at extraordinarily giant scales).
- Seeds with the tiniest distinction produce utterly totally different sequences.
- The sequences are infinite in size.
- The weather of the sequences are members of a finite set.
The implications needs to be clear.
An extended, meandering and unsatisfyingly-unquantified reply is perhaps:
Should you add (or omit) a passphrase, does it generate the identical non-public key someday?
The most well-liked definition for 24-word seed phrases, that are additionally referred to as restoration phrases typically, is BIP-39
This permits for an non-compulsory further passphrase for use along with the seed phrase when calculating the non-public keys. The passphrase provides an additional layer of safety and totally different passphrases will trigger totally different non-public keys to be generated.
This technique is invariably used with BIP-32 Hierarchical Deterministic (HD) wallets. These wallets generate, not only one, however a complete sequence of personal keys from the seed information.
The consequence is, when you lose your pockets and neglect your passphrase, you’ll be able to’t get well management over your cash solely utilizing the seed phrase.
Observe that some wallets additionally use a password or passphrase to encrypt some or all of their pockets information. This can be a totally different passphrase from the one used with the seed phrase when creating a brand new pockets or recovering a misplaced pockets. It’s simple to get confused by this. Do not get them blended up.
Addendum
Let’s imagine you create pockets A and pockets B as follows
| Pockets | seed phrase | move phrase |
|---|---|---|
| A | boss rural month arm exit elegant eight grain palace biology pistol management exterior album slab prime boil take in tree imply road giggle head frozen | Alex |
| B | boss rural month arm exit elegant eight grain palace biology pistol management exterior album slab prime boil take in tree imply road giggle head frozen | Axle |
As a result of Alex is just not Axle, Wallets A and B will every generate a special sequence of personal keys. Lets name these sequences baskets A and B.
Let’s imagine you’re a very busy particular person, maybe you purchase Amazon, eBay and Alibaba and make each transaction worldwide, pay to a brand new non-public key in one among your wallets, alternating them.
Within the very brief time period (the primary million years say), Maybe baskets A and B shall be disjoint units.
Nevertheless
Each secret is in each basket, given sufficient time.
Each secret is in each basket an infinite variety of instances, given infinite time.
See Bitcoin collider
After all, the Earth shall be be swallowed by the Solar within the forseeable future, so there will not be sufficient time. You’d need to ask a statistician and base an estimate on a prediction of future computing energy and the way which may be bounded by the quantity of matter within the accessible universe and numerous different bodily constraints.
