Vitalik Buterin Promises Easier Ethereum Proofs With New SNARKs Utilizing Arithmetic

Key Takeaways

• Vitalik Buterin suggests a novel mathematical approach in cryptographic proofs.
• Adam Cochran of Cinneamhain Ventures interpreted Buterin’s cryptic math with blockchain computations.
• Buterin’s ‘new math’ using SNARKs and binary fields could significantly enhance Ethereum’s efficiency and scalability.

In a cryptic tweet, Ethereum co-founder Vitalik Buterin introduced what he called ‘new math‘. The series of equations could simplify the process of making cryptographic proofs and the industry had various interpretations for the statements. Buterin later confirmed that he was talking about cryptographic methods used to verify the correctness of computations called SNARKs.

Decoding Buterin’s ‘New Math’

Vitalik Buterin’s tweet listed several unconventional equations like “2 + 2 = 0” and “420 * 61779 = 1”, which at first glance, defy basic arithmetic principles. 

However, according to Adam Cochran, Partner at Cinneamhain Ventures, these equations could illustrate the concept of modular arithmetic —a system where numbers wrap around upon reaching a certain value, much like the hours on a clock.

In modular arithmetic, operations are carried out for a modulus. Cochran uses a clock as an analogy: just as the hour resets to zero after 12, calculations in a modular system reset after reaching the modulus. This system could explain equations like “2 + 2 = 0” under modulo 4.

Cochran speculated that adopting modular arithmetic could lead to more efficient and compact calculations within blockchain systems. Using modular arithmetic could also decrease the computational power needed to execute cryptographic proofs. This would allow for quicker and less resource-intensive transactions. This reduction in computational demand means that blockchain networks can potentially handle more transactions with the same amount of hardware, or lower the hardware requirements altogether. 

Vitalik Buterin later confirmed  that he was explaining the concept of SNARKs, a type of cryptographic proof. Succinct Non-Interactive Arguments of Knowledge or SNARKs transform computational problems into mathematical equations using arithmetization.

This method converts program statements into polynomial equations that are easier to manage within finite fields, particularly using smaller sets of numbers like binary fields where calculations are based on 0s and 1s, enhancing efficiency.

Buerin also discussed the Binius protocol, which uses a hypercube and grid layout to simplify and verify these polynomial equations. In simpler terms, Binius protocol treats data as a multi-dimensional array and a grid for the purpose of verifying computations. To verify a computation, the data is first considered as a multilinear polynomial, a polynomial that is linear in each of its variables separately, and then it’s evaluated both inside and outside of this hypercube/grid structure.

Scaling Ethereum Using SNARKs

Cochran interpreted predictable nature of modular arithmetic could simplify the verification of complex cryptographic proofs. Modular arithmetic could also reportedly enhance data-packing strategies. The strategy allows for optimizing data storage and transmission across blockchain networks for efficiency.

Buterin’s SNARK recommendation works by reducing the amount of data that needs to be processed and verified in each transaction, thus scaling blockchain networks.

In their paper , “Succinct Arguments over Towers of Binary Fields,” Benjamin E. Diamond and Jim Posen present an advanced and efficient SNARK system that operates over binary fields, which are simple mathematical fields composed of just two elements. Building on earlier techniques, they propose creating secure commitments with polynomials in these tiny fields without unnecessary complexity.

Their approach includes improvements to binary-field adaptations for existing cryptographic checks and methods, enhancing how these elements handle complex functions like hash calculations used in blockchains like Ethereum.

If Ethereum introduces future upgrades that borrow concepts laid down by Buterin, it might ease the verification time and cost on the blockchain. Thereby making the base layer more scalable and efficient. 

Improvements Using Binary Fields

As per the blog, the main focus is on making these proofs more efficient using smaller computational fields, shifting from traditional 256-bit sizes down to much smaller sizes like 64-bit or even binary fields of 0’s and 1’s. The shift would speed up the processing and verification times, addressing one of the major bottlenecks in blockchain scalability — the computational load and time taken to verify transactions.

With Binius, Buterin further envisions optimizing the proof process by simplifying the computational requirements. The post explains how these innovations in field size and proof protocols are critical for scaling Ethereum, enabling it to handle more transactions quickly and securely, which is essential as the platform grows and more applications are built on it.

To fully integrate Vitalik Buterin’s suggested ‘new math‘,Ethereum Virtual Machine (EVM) would require modifications to support these operations natively.

In March 2023, EIP-6690 : EVM Modular Arithmetic Extensions (EVMMAX) was authored by Jared Wasinger and Alex Beregszaszi.

EIP-6690 and EIP-6601 are part of the Ethereum Cancun upgrade, that introduced new operations to the Ethereum Virtual Machine (EVM) for improved efficiency in handling modular arithmetic. The upgrade aimed to improve Ethereum’s computational capabilities and is also linked to broader improvements in the network’s consensus layer.

Layer 1 Improvements 

Ethereum co-founder Vitalik Buterin has suggested a novel approach to improving Ethereum’s efficiency using ‘new math.’ The concept primarily revolves around the use of cryptographic proofs known as SNARKs, which transform complicated computational problems into simpler polynomial equations.

The method could reduce the size and complexity of the data involved, making Ethereum operations faster and less resource-intensive. Buterin’s ideas also involve innovative uses of binary fields — very small computational fields that enhance the speed and efficiency of these operations.

Looking ahead, these advancements could lead to significant improvements in how Ethereum handles transactions, potentially easing verification times and reducing costs, thereby making the blockchain more scalable and efficient. This could mark a significant step forward in the blockchain’s evolution, making it more adaptable and suitable for a wider range of applications.

However, to fully leverage the potential of Vitalik Buterin’s ‘new math’ for Ethereum, new upgrades would be necessary to clear the road ahead.

About the Author

Shraddha Sharma

Shraddha has around five years of experience as a financial journalist, focusing largely on the Asian markets. Starting her career in Mumbai, India, as a news trainee and producer, she quickly found her niche in crypto. She is keen on learning how emerging technologies affect the broader markets and enjoys explaining complex financial ideas in a way that's easy to understand.

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