1"use strict";(globalThis.webpackChunkdocs=globalThis.webpackChunkdocs||[]).push([[1144],{25471(e,r,d){d.r(r),d.d(r,{assets:()=>c,contentTitle:()=>l,default:()=>p,frontMatter:()=>a,metadata:()=>i,toc:()=>o});const i=JSON.parse('{"id":"libraries/standard_library/cryptographic_primitives/embedded_curve_ops","title":"Scalar multiplication","description":"See how you can perform scalar multiplication in Noir","source":"@site/versioned_docs/version-v1.0.0-rc.0/libraries/standard_library/cryptographic_primitives/embedded_curve_ops.mdx","sourceDirName":"libraries/standard_library/cryptographic_primitives","slug":"/libraries/standard_library/cryptographic_primitives/embedded_curve_ops","permalink":"/docs/v1.0.0-rc.0/libraries/standard_library/cryptographic_primitives/embedded_curve_ops","draft":false,"unlisted":false,"editUrl":"https://github.com/noir-lang/noir/edit/master/docs/versioned_docs/version-v1.0.0-rc.0/libraries/standard_library/cryptographic_primitives/embedded_curve_ops.mdx","tags":[],"version":"v1.0.0-rc.0","frontMatter":{"title":"Scalar multiplication","description":"See how you can perform scalar multiplication in Noir","keywords":["cryptographic primitives","Noir project","scalar multiplication"]},"sidebar":"sidebar","previous":{"title":"Ciphers","permalink":"/docs/v1.0.0-rc.0/libraries/standard_library/cryptographic_primitives/ciphers"},"next":{"title":"Hash methods","permalink":"/docs/v1.0.0-rc.0/libraries/standard_library/cryptographic_primitives/hashes"}}');var n=d(74848),s=d(28453),t=d(8037);const a={title:"Scalar multiplication",description:"See how you can perform scalar multiplication in Noir",keywords:["cryptographic primitives","Noir project","scalar multiplication"]},l=void 0,c={},o=[{value:"embedded_curve_ops::multi_scalar_mul",id:"embedded_curve_opsmulti_scalar_mul",level:2},{value:"embedded_curve_ops::fixed_base_scalar_mul",id:"embedded_curve_opsfixed_base_scalar_mul",level:2},{value:"embedded_curve_ops::embedded_curve_add",id:"embedded_curve_opsembedded_curve_add",level:2},{value:"Parameters:",id:"parameters",level:3},{value:"Returns:",id:"returns",level:3}];function u(e){const r={admonition:"admonition",blockquote:"blockquote",code:"code",h2:"h2",h3:"h3",li:"li",p:"p",pre:"pre",ul:"ul",...(0,s.R)(),...e.components};return(0,n.jsxs)(n.Fragment,{children:[(0,n.jsx)(r.p,{children:"The following functions perform operations over the embedded curve whose coordinates are defined by the configured noir field.\nFor the BN254 scalar field, this is BabyJubJub or Grumpkin."}),"\n",(0,n.jsx)(r.admonition,{type:"note",children:(0,n.jsxs)(r.p,{children:["Suffixes ",(0,n.jsx)(r.code,{children:"_low"})," and ",(0,n.jsx)(r.code,{children:"_high"})," denote low and high limbs of a scalar."]})}),"\n",(0,n.jsx)(r.h2,{id:"embedded_curve_opsmulti_scalar_mul",children:"embedded_curve_ops::multi_scalar_mul"}),"\n",(0,n.jsx)(r.p,{children:"Performs multi scalar multiplication over the embedded curve.\nThe function accepts arbitrary amount of point-scalar pairs on the input, it multiplies the individual pairs over\nthe curve and returns a sum of the resulting points."}),"\n",(0,n.jsxs)(r.p,{children:["Points are represented as ",(0,n.jsx)(r.code,{children:"EmbeddedCurvePoint"})," structs with ",(0,n.jsx)(r.code,{children:"x"})," and ",(0,n.jsx)(r.code,{children:"y"})," coordinates, scalars as ",(0,n.jsx)(r.code,{children:"EmbeddedCurveScalar"})," structs with ",(0,n.jsx)(r.code,{children:"lo"})," and ",(0,n.jsx)(r.code,{children:"hi"})," limbs."]}),"\n",(0,n.jsx)(r.pre,{children:(0,n.jsx)(r.code,{className:"language-rust",metastring:'title="multi_scalar_mul" showLineNumbers ',children:"pub fn multi_scalar_mul<let N: u32>(\n points: [EmbeddedCurvePoint; N],\n scalars: [EmbeddedCurveScalar; N],\n) -> EmbeddedCurvePoint\n"})}),"\n",(0,n.jsxs)(r.blockquote,{children:["\n",(0,n.jsx)("sup",{children:(0,n.jsx)("sub",{children:(0,n.jsx)("a",{href:"https://github.com/noir-lang/noir/blob/master/noir_stdlib/src/embedded_curve_ops.nr#L131-L136",target:"_blank",rel:"noopener noreferrer",children:"Source code: noir_stdlib/src/embedded_curve_ops.nr#L131-L136"})})}),"\n"]}),"\n",(0,n.jsx)(r.p,{children:"example"}),"\n",(0,n.jsx)(r.pre,{children:(0,n.jsx)(r.code,{className:"language-rust",children:"use std::embedded_curve_ops::{EmbeddedCurvePoint, EmbeddedCurveScalar, multi_scalar_mul};\n\nfn main(point_x: Field, point_y: Field, scalar_low: Field, scalar_high: Field) {\
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