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 needs to be clear.
An extended, meandering and unsatisfyingly-unquantified reply could be:
In the event you add (or omit) a passphrase, does it generate the identical personal 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 enables for an elective extra passphrase for use along with the seed phrase when calculating the personal keys. The passphrase provides an additional layer of safety and completely different passphrases will trigger completely different personal 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 collection of personal keys from the seed information.
The consequence is, for those who lose your pockets and overlook your passphrase, you may’t recuperate management over your cash solely utilizing the seed phrase.
Notice 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 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 outdoors album slab prime boil take up tree imply road giggle head frozen | Alex |
| B | boss rural month arm exit elegant eight grain palace biology pistol management outdoors album slab prime boil take up tree imply road giggle head frozen | Axle |
As a result of Alex shouldn’t be Axle, Wallets A and B will every generate a distinct 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 personal 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 shall be disjoint units.
Nevertheless
Each secret is in each basket, given sufficient time.
Each secret is in each basket an infinite variety of occasions, given infinite time.
See Bitcoin collider
In fact, the Earth shall be be swallowed by the Solar within the forseeable future, so there will not be sufficient time. You’d should ask a statistician and base an estimate on a prediction of future computing energy and the way that could be bounded by the quantity of matter within the accessible universe and varied different bodily constraints.
