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Can two private keys generate the same public Bitcoin address?
In the world of cryptocurrency, private keys are unique and randomly generated by wallets for storing and managing digital assets. However, the question arises: can two private keys generate the same public Bitcoin address?
To understand this concept, let's delve into some technical details.
Public Key Generation
A public key is a pair of values (private_key, public_key) where the private key is used to obtain the corresponding public key. This process involves encrypting the private key using a cryptographic hash function, and then using the base64-encoded hash value as the public key.
For example, in Ethereum, each user has his own unique address, which is derived from his private key. The public key is generated using the Ethereum public key generation algorithm (EVPGenPubKey). This algorithm takes two parameters: a private key and a salt value, and generates a random public key that can be used to generate addresses.
Two private keys and the same address
Now let's consider a scenario in which two users have private keys ka
and kb
. If both wallets generate their public addresses using the same private keys, it is theoretically possible that they will receive the same public address.
Here's why:
- Similarity of hash functions: if the implementation of the EVPGenPubKey algorithm in Ethereum uses similar hash functions for both private keys, there is a possibility that the two generated public addresses may be similar.
- Randomness and salt generation: even if the hash function is different, the randomness and salt values used to generate the public key can still result in similar or identical public addresses.
However, it is important to note that this scenario assumes:
- Private keys
ka
andkb
were randomly generated and have no prior relationship.
- The Ethereum implementation uses a consistent hash function for both private keys.
- No collisions (ie, several different private keys generate the same public address).
Conclusion
Although it is theoretically possible for two users with identical private keys to generate identical public Bitcoin addresses, there are several factors that reduce this probability:
- Hash Function Randomness and Consistency
: The hash functions used by Ethereum must be consistent for all users.
- User-Specific Salt Values: Each user's salt value is randomly generated for each transaction, which helps mitigate collisions.
- Global Random Number Generator (GRNG)
: Ethereum uses GRNG to generate random numbers for the private key and other parameters.
In conclusion, it should be noted that although two users with the same private keys can generate the same public address, the probability that this will happen is extremely small due to the peculiarities of the implementation and the randomness present in the process of generating the private key of Ethereum.