Ethereum: Can two private keys generate the same (public) Bitcoin address?

Can two private keys generate the same public address as Bitcoin?

In the cryptocurrency world, private keys are unique and randomly generated by wallets to store and manage digital assets. However, the question arises: Can two private keys generate the same public address as Bitcoin?

To understand this concept, let’s dive 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 derive the corresponding public key. This process involves encrypting the private key with a cryptographic hash function and then assuming the coded hash value with base64 as a public key.

In Ethereum, for example, each user has its own unique address derived from its private key. The public key is generated using the Ethereum (Evpgenpubkey) public key generation algorithm. This algorithm takes two parameters: the private key and a salt value and generates a random public key that can be used to create addresses.

Two private keys and the same address

Now, let’s consider the scenario where two users have private keys ka and kb ‘. If the two wallets generate their public addresses using these same private keys, it is theoretically possible that they end up with the same public address.

Here’s why:

• Similarity in the functions of hash : If the implementation of the evpgenpubkey algorithm ethhereum uses similar hash functions for both private keys, there is a chance that the two generated public addresses may be similar.

• Randomidan and salt generation : Even if the functions of hash are different, randomness and salt values ​​used to generate the public key can still result in similar or identical public addresses.

However, it is essential to note that this scenario assumes:

• Private keys ka and kb ‘were randomly generated and do not have a previous relationship.

• Ethereum implementation uses a consistent hash function for both private keys.

• There are no collisions (ie several different private keys generate the same public address).

Conclusion

Although it is theoretically possible for two users with similar private keys to generate the same public addresses as Bitcoin, there are several factors that reduce this probability:

• Randomidan and consistency of the function of hash : Hash functions used by Ethereum should be consistent in all users.

2.

• Global random numbers (GRNG)

  : Ethereum uses a grng to generate random numbers to the private key and other parameters.

In conclusion, although it is possible for two users with similar private keys to generate the same public address, the probability of this occurrence is extremely low due to the details of the implementation and randomness involved in the Ethereum private key generation process.

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