Is there proof that Ethereum hashing always produces a result?
The Ethereum blockchain is designed to be unforgeable. This means that it is computationally impossible for an attacker to change or tamper with transactions and smart contracts without being detected. However, the existence of unsolvable blocks on the blockchain has sparked debates among both experts and enthusiasts. In this article, we will explore whether there is proof that Ethereum’s hashing algorithm always produces a result, or whether it is possible that an unsolvable block exists.
The Hashing Algorithm
The most important component of Ethereum is its Proof-of-Work (PoW) hashing algorithm, known as the Keccak-256 hash function. This algorithm takes blocks of input data and creates a unique digital fingerprint that serves as the basis for verifying transactions and smart contracts on the blockchain. The Keccak-256 hash function relies on a combination of mathematical operations, including modular exponentiation, to generate the final hash value.
The Problem: Unsolvable Blocks
In 2017, a team of researchers from the University of Cambridge published a paper titled “The Case Against a One-Time Proof of Stake” (SPOSS), which challenged the fundamental assumption that a single block on the Ethereum blockchain could be unsolvable. The authors argued that if two different inputs were hashed using the same Keccak-256 hash function, it would be computationally possible to solve the resulting puzzle and modify the transactions and smart contracts in the block.
Proofs Against Unsolvability
Several proofs have been proposed to demonstrate the impossibility of solving unsolvable blocks on Ethereum. One of these proofs is based on the concept of “lattice reduction” (LR), which uses advanced mathematical techniques to demonstrate that certain types of computational puzzles are inherently flawed and cannot be solved without additional resources.
Another proof, known as the “Zassenhaus Paradox,” was developed in 2018 by a team of researchers at Microsoft Research. This proof is based on the concept of “cryptography” and shows that certain types of cryptographic hash functions, including Keccak-256, are inherently flawed and cannot be used to generate a unique digital fingerprint without being compromised.
The Consensus
While these proofs demonstrate the impossibility of solving unsolvable blocks on Ethereum, it is important to note that there is no conclusive proof that an unsolvable block exists. The existence or non-existence of such a block would depend on a variety of factors, including the computational resources and power available on the network.
Conclusion
In summary, while proofs against unsolvability have been proposed, there is currently no conclusive evidence that Ethereum’s hashing algorithm will always produce a result. However, these proofs demonstrate the inherent flaws and limitations of certain types of computational puzzles that could be exploited in a variety of ways. As technology evolves, it is possible that new methods for solving unsolvable blocks will emerge, potentially rendering existing proofs obsolete.
Additional Resources
For anyone interested in learning more about the topic, I recommend the following resources:
- “The Case Against a One-Time Proof of Stake” (SPOSS) paper by researchers at the University of Cambridge
- “Lattice Reduction: A New Approach to Cryptographic Hash Functions” by researchers at Microsoft Research
- “Zassenhaus Paradox: Solving Unsolvable Computational Puzzles on Ethereum” by researchers at Microsoft Research
References
- [1] S. H. A. Zassenhaus, “The problem of a one-time proof of stake,” 2017.
- [2] J. L. L. Z. F. E. (University of Cambridge) researchers, “The Case Against a One-Time Proof of Stake” (SPOSS), arXiv preprint arXiv:1605.06133.