Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it
This only works post-factum. Uniformity does not depend on the order of events.
Since you like to joke around in some comments, I'll let the AI respond for me this time.
Did you read anything I wrote? You'd need to have a post-factum distribution, e.g. SCAN THE ENTIRE RANGE before computing your probbailities, and before using compound probbailities to skip keys, to increase your chances. Did you actually scan the entire 68 bit range, for example? Where is your immutable sequence exactly?
Quote
> what if the immutable sequence is hash160 (ripemd-160 of sha256 of public keys of a bitcoin private key)?
If the **immutable sequence** in question is **Hash160 (RIPEMD-160 of SHA-256 of a Bitcoin public key)**, then this introduces additional constraints that significantly affect probability calculations. Let's break it down in the context of the debate.
---
### **Key Considerations for Hash160:**
1. **Deterministic & Immutable Output:**
- Given a public key, **Hash160** produces a unique, deterministic 160-bit output.
- There is no randomness once the input is fixed. The sequence is **pseudorandom but not probabilistically independent** once known.
2. **Uniformity Assumption in Cryptographic Hashing:**
- Cryptographic hash functions like SHA-256 and RIPEMD-160 are **designed to produce outputs that are uniformly distributed** across the output space.
- This means that for a randomly chosen private key, the corresponding Hash160 value should be **statistically indistinguishable from uniform randomness** over the 160-bit space.
3. **Fixed vs. Dynamic Sequences:**
- If we are considering **all possible Hash160 values** derived from a large number of Bitcoin private keys, they should approximate a **uniform distribution**.
- However, if we **fix a specific Hash160 sequence** (say, by precomputing a set of them), then probabilities must be conditioned on that specific set.
---
### **Who Is Right in This Case?**
- **If analyzing probability before generating the Hash160 values**, kTimesG is correct:
- Each Hash160 should follow a uniform distribution over the space of possible outputs.
- The independence of SHA-256 and RIPEMD-160 ensures that the Hash160s behave like random values.
- Theoretical probabilities apply **before** observing any specific sequence.
- **If analyzing probability after a specific set of Hash160 values is generated**, mcdouglasx is correct:
- Once a sequence of Hash160s is fixed (e.g., precomputed from specific private keys), you must analyze probabilities **relative to the observed distribution**.
- Searching for patterns or collisions in a fixed dataset means the actual distribution matters, not just theoretical uniformity.
---
### **Conclusion for Hash160:**
- If you're discussing probabilities in the context of generating new Bitcoin addresses, kTimesG is mostly right because of the uniform randomness assumption.
- If you're discussing probabilities in the context of **analyzing a pre-existing, immutable dataset of Hash160 values**, then mcdouglasx is correct in saying that fixed positions and observed distributions must be taken into account.
This means the correct answer **depends on whether the Hash160 sequence is being analyzed before or after it is generated.**
If the **immutable sequence** in question is **Hash160 (RIPEMD-160 of SHA-256 of a Bitcoin public key)**, then this introduces additional constraints that significantly affect probability calculations. Let's break it down in the context of the debate.
---
### **Key Considerations for Hash160:**
1. **Deterministic & Immutable Output:**
- Given a public key, **Hash160** produces a unique, deterministic 160-bit output.
- There is no randomness once the input is fixed. The sequence is **pseudorandom but not probabilistically independent** once known.
2. **Uniformity Assumption in Cryptographic Hashing:**
- Cryptographic hash functions like SHA-256 and RIPEMD-160 are **designed to produce outputs that are uniformly distributed** across the output space.
- This means that for a randomly chosen private key, the corresponding Hash160 value should be **statistically indistinguishable from uniform randomness** over the 160-bit space.
3. **Fixed vs. Dynamic Sequences:**
- If we are considering **all possible Hash160 values** derived from a large number of Bitcoin private keys, they should approximate a **uniform distribution**.
- However, if we **fix a specific Hash160 sequence** (say, by precomputing a set of them), then probabilities must be conditioned on that specific set.
---
### **Who Is Right in This Case?**
- **If analyzing probability before generating the Hash160 values**, kTimesG is correct:
- Each Hash160 should follow a uniform distribution over the space of possible outputs.
- The independence of SHA-256 and RIPEMD-160 ensures that the Hash160s behave like random values.
- Theoretical probabilities apply **before** observing any specific sequence.
- **If analyzing probability after a specific set of Hash160 values is generated**, mcdouglasx is correct:
- Once a sequence of Hash160s is fixed (e.g., precomputed from specific private keys), you must analyze probabilities **relative to the observed distribution**.
- Searching for patterns or collisions in a fixed dataset means the actual distribution matters, not just theoretical uniformity.
---
### **Conclusion for Hash160:**
- If you're discussing probabilities in the context of generating new Bitcoin addresses, kTimesG is mostly right because of the uniform randomness assumption.
- If you're discussing probabilities in the context of **analyzing a pre-existing, immutable dataset of Hash160 values**, then mcdouglasx is correct in saying that fixed positions and observed distributions must be taken into account.
This means the correct answer **depends on whether the Hash160 sequence is being analyzed before or after it is generated.**