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I imagine the next to be true:
- Sequences of keys generated from seeds are indistinguishable from random sequences (besides at extraordinarily massive 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 ought to be clear.
An extended, meandering and unsatisfyingly-unquantified reply is likely to be:
If you happen to 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 non-compulsory extra passphrase for use along with the seed phrase when calculating the personal keys. The passphrase provides an additional layer of safety and totally different passphrases will trigger totally 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 knowledge.
The consequence is, in case you lose your pockets and overlook your passphrase, you’ll be able to’t get better management over your cash solely utilizing the seed phrase.
Word that some wallets additionally use a password or passphrase to encrypt some or all of their pockets knowledge. 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 combined 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 high boil soak up tree imply road giggle head frozen | Alex |
| B | boss rural month arm exit elegant eight grain palace biology pistol management outdoors album slab high boil soak up tree imply road giggle head frozen | Axle |
As a result of Alex is just not Axle, Wallets A and B will every generate a unique sequence of personal keys. Lets name these sequences baskets A and B.
Let’s imagine you’re a very busy individual, 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 will probably be disjoint units.
Nonetheless
Each key’s in each basket, given sufficient time.
Each key’s in each basket an infinite variety of instances, given infinite time.
See Bitcoin collider
In fact, the Earth will probably be be swallowed by the Solar within the forseeable future, so there might 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 numerous different bodily constraints.
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