Bitcoin: BIP39’s checksum generation

BIP39 Checksum Generation: A Deep Dive into Its Mechanics

As any Bitcoin enthusiast or developer familiar with Bitcoin Improvement Proposal 39 (BIP39) knows, checksum generation is a crucial aspect of the wallet format used to store and manage private keys. In this article, we’ll dive into how BIP39 checksum generation works and what factors contribute to incorrect results.

What is BIP39?

BIP39 is an algorithm designed to generate and store private keys for Bitcoin addresses in a secure and decentralized manner. It uses a combination of mathematical techniques to ensure that the generated key is unique, unguessable, and resistant to brute-force attacks.

The Checksum Generation Process

The checksum generation process involves generating a SHA-256 hash of a specific portion of the private key, which is then used as input to BIP39’s checksum algorithm. The resulting hash is compared to a pre-computed table (PCT) of hashes, and if they match within a certain tolerance, the generated private key is considered valid.

The Basic Idea Behind Checksum

When it comes to generating the checksum, we are basically looking for a SHA-256 hash that is close enough to the input hash. This can be achieved by taking (Bitlen/32) bits of the input hash and using them as input to the SHA-256 algorithm.

The Problem: Incorrect Results

While the basic idea behind checksum generation seems good, we have all experienced cases where the generated private key is incorrect due to various factors. A common problem is that the input hash may not be long enough or have too many leading zeros, causing the checksum algorithm to produce an incorrect result.

Key Factors Contributing to Incorrect Results

There are several key factors that can contribute to incorrect results when generating the checksum:

• Leading Zeros: If the input hash has leading zeros, they can cause problems when generating the checksum.

• Long Input Hashes: Input hashes that are short or too long may not be hashed properly by the SHA-256 algorithm.

• Hash Overflows: In rare cases, the input hash can overflow and produce incorrect results due to the limitations of the SHA-256 algorithm.

• Tolerance Issues

  : The tolerance value used in BIP39’s checksum algorithm can introduce errors if not set correctly.

Improving_checksum() Function

In 2019, a popular Bitcoin developer, Zorin, implemented an improved version of the checksum function called improvecum. This new implementation addresses some of the key issues mentioned above and provides more accurate results.

The improvecum function uses a different approach to generating the checksum, which takes into account the length of the input hash. It also uses a more robust tolerance value that helps mitigate errors caused by leading zeros or long input hashes.

Conclusion

While BIP39’s checksum generation is theoretically sound, incorrect results can occur due to various factors such as leading zeros, long input hashes, hash overflows, and tolerance issues. The improvecum function provides a more reliable solution for generating private keys using BIP39.

By understanding how the checksum generation process works and what contributes to incorrect results, developers and enthusiasts can take steps to improve their private key generation and ensure secure use of Bitcoin.