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 completely different sequences.
- The sequences are infinite in size.
- The weather of the sequences are members of a finite set.
The implications ought to be clear.
An extended, meandering and unsatisfyingly-unquantified reply is perhaps:
When you add (or omit) a passphrase, does it generate the identical non-public key someday?
The preferred definition for 24-word seed phrases, that are additionally known as restoration phrases generally, is BIP-39
This enables for an non-obligatory further passphrase for use along with the seed phrase when calculating the non-public keys. The passphrase provides an additional layer of safety and completely different passphrases will trigger completely different non-public keys to be generated.
This method is invariably used with BIP-32 Hierarchical Deterministic (HD) wallets. These wallets generate, not only one, however an entire sequence of personal keys from the seed information.
The consequence is, for those who lose your pockets and overlook your passphrase, you possibly can’t recuperate 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 completely different passphrase from the one used with the seed phrase when creating a brand new pockets or recovering a misplaced pockets. It’s straightforward to get confused by this. Do not get them blended up.
Addendum
Shall we say 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 high boil take up tree imply avenue giggle head frozen | Alex |
| B | boss rural month arm exit elegant eight grain palace biology pistol management exterior album slab high boil take up tree imply avenue giggle head frozen | Axle |
As a result of Alex isn’t Axle, Wallets A and B will every generate a distinct sequence of personal keys. Lets name these sequences baskets A and B.
Shall we say you’re a very busy individual, maybe you purchase Amazon, eBay and Alibaba and make each transaction worldwide, pay to a brand new non-public key in one in every of your wallets, alternating them.
Within the very quick time period (the primary million years say), Maybe baskets A and B can be disjoint units.
Nonetheless
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
In fact, the Earth can be be swallowed by the Solar within the forseeable future, so there is probably not sufficient time. You’d must 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 varied different bodily constraints.
