Ethereum: What’s the exact definition of the alt_bn128 curve used by the Ethereum’s precompile?
I can provide you with an explanation of the Ethereum curve alt_bn128.
The Ethereum curve alt_bn128 is a type of elliptic curve designed for use in the precompile mechanism of the Ethereum network. Precompilation is a feature that allows developers to compile and deploy functions or contracts directly in the Ethereum Virtual Machine (EVM) without worrying about implementation details.
The alt_bn128 curve is one of several curves that can be used for this purpose, but it stands out for its specific characteristics. Here’s a breakdown of what makes it unique:
- 256-bit curve: The Ethereum alt_bn128 curve uses the popular NTRU (Narrow Field Digital Signature) cryptosystem, which is widely used in many cryptographic systems.
- Field B-n-128
: The
alt_bn128curve works in a specific field designated as B-n-128, where n is usually equal to 16 or 32. This field allows efficient multiplication and exponentiation of the numbers in the curve.
- Options specific to Alt_bn128
: The alt_bn128 curve has some unique parameters that are designed to optimize performance when working with certain data types, such as binary vectors (Bn).
In the Ethereum precompilation mechanism, functions or contracts compiled using the alt_bn128 curve can be deployed directly to the EVM without going through a normal contract call. This allows developers to write more efficient and scalable code.
However, there seems to be some confusion regarding the field values used in Ethereum. The prime field (p) is usually 2^256 – 1, while the base field (q) is usually 2^8 + 1 = 257 or 2^32 – 1 = 2147483647.
The alt_bn128 curve can use a different prime field value than what is shown in neuromancer. This discrepancy can be caused by various reasons, such as:
- Differences in the implementation of the alt_bn128 curve by Ethereum developers.
- Different usage scenarios that may require certain field values for optimal performance or security.
- The possibility that neuromancer uses a different value of the simple field than what is usually used in Ethereum.
To provide more accurate information, it is best to refer to the official Ethereum documentation or contact an Ethereum developer who can clarify the use of the alt_bn128 curve in the Ethereum ecosystem.