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# effcient-ffa
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# Efficient Foreign-Field Arithmetic in PLONK
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Formalization of soundness and correctness proofs of efficient foreign field arithmetic (FFA) developed at IOG/Midnight.
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## Requirements
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```
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EASYCRYPT_REVISION = a214a56
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JASMIN_VERSION = 2023.06.1
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ALT-ERGO >= v2.5.1
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CVC4 >= 1.8
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Z3 >= 4.8.7
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```
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## Contents
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* `FFA_soundness.ec` the proof that whenever the system of constraints is satisfied then we have correctly multipled foreign field elements.
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* `FFA_completeness.ec` the converse of the above.
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* `FFA.ec` some common definitions.
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