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# The halo2 Book
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[halo2](README.md)
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- [Concepts](concepts.md)
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- [Proof systems](concepts/proofs.md)
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- [UltraPLONK Arithmetization](concepts/arithmetization.md)
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- [Cores](concepts/cores.md)
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- [Chips](concepts/chips.md)
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- [Gadgets](concepts/gadgets.md)
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- [User Documentation](user.md)
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- [A simple example](user/simple-example.md)
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- [Lookup tables](user/lookup-tables.md)
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- [Gadgets](user/gadgets.md)
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- [Tips and tricks](user/tips-and-tricks.md)
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- [Design](design.md)
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- [Proving system](design/proving-system.md)
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- [Lookup argument](design/proving-system/lookup.md)
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- [Permutation argument](design/proving-system/permutation.md)
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- [Circuit commitments](design/proving-system/circuit-commitments.md)
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- [Vanishing argument](design/proving-system/vanishing.md)
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- [Multipoint opening argument](design/proving-system/multipoint-opening.md)
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- [Inner product argument](design/proving-system/inner-product.md)
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- [Comparison to other work](design/proving-system/comparison.md)
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- [Implementation](design/implementation.md)
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- [Fields](design/implementation/fields.md)
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- [Gadgets](design/gadgets.md)
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- [SHA-256](design/gadgets/sha256.md)
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- [16-bit table chip](design/gadgets/sha256/table16.md)
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- [Background Material](background.md)
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- [Fields](background/fields.md)
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- [Polynomials](background/polynomials.md)
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- [Cryptographic groups](background/groups.md)
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- [Elliptic curves](background/curves.md)
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- [UltraPLONK arithmetisation](background/upa.md)
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- [Polynomial commitment using inner product argument](background/pc-ipa.md)
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- [Recursion](background/recursion.md)
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