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2021-05-18 12:17:00 -07:00
< ol class = "chapter" > < li class = "chapter-item expanded affix " > < a href = "../../index.html" > halo2< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../concepts.html" > < strong aria-hidden = "true" > 1.< / strong > Concepts< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../concepts/proofs.html" > < strong aria-hidden = "true" > 1.1.< / strong > Proof systems< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../concepts/arithmetization.html" > < strong aria-hidden = "true" > 1.2.< / strong > UltraPLONK Arithmetization< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../concepts/cores.html" > < strong aria-hidden = "true" > 1.3.< / strong > Cores< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../concepts/chips.html" > < strong aria-hidden = "true" > 1.4.< / strong > Chips< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../concepts/gadgets.html" > < strong aria-hidden = "true" > 1.5.< / strong > Gadgets< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../../user.html" > < strong aria-hidden = "true" > 2.< / strong > User Documentation< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../user/dev-tools.html" > < strong aria-hidden = "true" > 2.1.< / strong > Developer tools< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../user/simple-example.html" > < strong aria-hidden = "true" > 2.2.< / strong > A simple example< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../user/lookup-tables.html" > < strong aria-hidden = "true" > 2.3.< / strong > Lookup tables< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../user/gadgets.html" > < strong aria-hidden = "true" > 2.4.< / strong > Gadgets< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../user/tips-and-tricks.html" > < strong aria-hidden = "true" > 2.5.< / strong > Tips and tricks< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../../design.html" > < strong aria-hidden = "true" > 3.< / strong > Design< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../design/proving-system.html" > < strong aria-hidden = "true" > 3.1.< / strong > Proving system< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/lookup.html" > < strong aria-hidden = "true" > 3.1.1.< / strong > Lookup argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/permutation.html" > < strong aria-hidden = "true" > 3.1.2.< / strong > Permutation argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/circuit-commitments.html" > < strong aria-hidden = "true" > 3.1.3.< / strong > Circuit commitments< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/vanishing.html" > < strong aria-hidden = "true" > 3.1.4.< / strong > Vanishing argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/multipoint-opening.html" > < strong aria-hidden = "true" > 3.1.5.< / strong > Multipoint opening argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/inner-product.html" class = "active" > < strong aria-hidden = "true" > 3.1.6.< / strong > Inner product argument< / a > < / li > < li class = "chapter-item expanded " > < a href = "../../design/proving-system/comparison.html" > < strong aria-hidden = "true" > 3.1.7.< / strong > Comparison to other work< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../../design/implementation.html" > < strong aria-hidden = "true" > 3.2.< / strong > Implementation< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../design/implementation/fields.html" > < strong aria-hidden = "true" > 3.2.1.< / strong > Fields< / a > < / li > < / ol > < / li > < li class = "chapter-item expanded " > < a href = "../../design/gadgets.html" > < strong aria-hidden = "true" > 3.3.< / strong > Gadgets< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../design/gadgets/sha256.html" > < strong aria-hidden = "true" > 3.3.1.< / strong > SHA-256< / a > < / li > < li > < ol class = "section" > < li class = "chapter-item expanded " > < a href = "../../design/gadgets/sha256/table16.html" > < strong aria-hidden = "true" > 3.3.1.1.< / strong > 16-bit table chip< / a > < / li > < / ol > < / li > < / ol > < / li > < / ol > < / li > < li
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< h1 > < a class = "header" href = "#inner-product-argument" id = "inner-product-argument" > Inner product argument< / a > < / h1 >
< p > Halo 2 uses a polynomial commitment scheme for which we can create polynomial commitment
opening proofs, based around the Inner Product Argument.< / p >
< blockquote >
< p > TODO: Explain Halo 2's variant of the IPA.< / p >
< p > It is very similar to < span class = "katex" > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.8777699999999999em;vertical-align:-0.19444em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > PC< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.32833099999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord text mtight" > < span class = "mord mtight" > DL< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mord" > .< / span > < span class = "mord text" > < span class = "mord" > Open< / span > < / span > < / span > < / span > < / span > from Appendix A.2 of < a href = "https://eprint.iacr.org/2020/499" > BCMS20< / a > .
See < a href = "comparison.html#bcms20-appendix-a2" > this comparison< / a > for details.< / p >
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