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

Can Two Private Keys Generate the Same Public Bitcoin Address?

In the world of cryptocurrency, 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 Bitcoin address?

To understand this concept, let’s dive into some technical details.

Generating a Public Key

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 taking the base64-encoded hash value as the public key.

In Ethereum, for example, each user has their own unique address, which is derived from their private key. The public key is generated using Ethereum’s public key generation algorithm (EVPGenPubKey). This algorithm takes two parameters: the private key and the 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 both wallets generate their public addresses using the same private keys, it is theoretically possible for them to end up with the same public address.

Here’s why:

• Similarity in hash functions: If Ethereum’s implementation of the EVPGenPubKey algorithm uses similar hash functions for both private keys, there is a chance that the two generated public addresses will be similar.

• Generation of randomness and salt: Even if the hash functions are 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:

• The private keys ka and kb are randomly generated and have no prior connection.

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

• There are no collisions (i.e. multiple different private keys generate the same public address).

Conclusion

While it is theoretically possible for two users with similar private keys to generate the same 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 across 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, while it is possible for two users with similar private keys to generate the same public address, the probability of this happening is extremely low due to the implementation details and randomness involved in Ethereum’s private key generation process.