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mitschabaude committed Dec 6, 2023
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# Foreign Field Arithmetic

A foreign field is a [finite field](https://en.wikipedia.org/wiki/Modular_arithmetic) different from the native field of the proof system. o1js exposes operations like modular addition and multiplication that work in any finite field of size less than 2^256.
A foreign field is a [finite field](https://en.wikipedia.org/wiki/Modular_arithmetic) different from the native field of the proof system. o1js exposes operations like modular addition and multiplication that work in any finite field of size less than 2^259.

Foreign fields are useful for implementing cryptographic algorithms in provable code. For example, you use them for verification of Ethereum-compatible ECDSA signatures ([coming](https://github.com/o1-labs/o1js/pull/1240) [soon](https://github.com/o1-labs/o1js/pull/1291)).

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