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Tentative fix for #345 - constant-time scalar mul with endomorphism acceleration wrong result #346
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181 changes: 181 additions & 0 deletions
181
tests/math_elliptic_curves/t_ec_shortw_prj_edge_case_345.nim
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| # https://github.com/mratsim/constantine/issues/345 | ||
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| import ../../constantine/math/arithmetic | ||
| import ../../constantine/math/io/io_fields | ||
| import ../../constantine/math/io/io_bigints | ||
| import ../../constantine/math/config/curves | ||
| import ../../constantine/math/extension_fields/towers | ||
| import ../../constantine/math/elliptic/ec_shortweierstrass_affine | ||
| import ../../constantine/math/elliptic/ec_shortweierstrass_projective | ||
| import ../../constantine/math/elliptic/ec_scalar_mul | ||
| import ../../constantine/math/elliptic/ec_scalar_mul_vartime | ||
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| #------------------------------------------------------------------------------- | ||
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| type B = BigInt[254] | ||
| type F = Fp[BN254Snarks] | ||
| type F2 = QuadraticExt[F] | ||
| type G = ECP_ShortW_Prj[F2, G2] | ||
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| #------------------------------------------------------------------------------- | ||
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| # size of the scalar field | ||
| let r : B = fromHex( B ,"0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001" ) | ||
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| let expo : B = fromHex( B, "0x7b17fcc286b01af79176aa7da3a8615020eacda89a90e4ff5d0a085483f0448" ) | ||
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| let expoA_fr = fromHex( Fr[BN254Snarks],"0x1234567890123456789001234567890" ) | ||
| var expoB_fr = fromHex( Fr[BN254Snarks],"0x7b17fcc286b01af79176aa7da3a8615020eacda89a90e4ff5d0a085483f0448" ) | ||
| expoB_fr -= expoA_fr | ||
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| let expoA = expoA_fr.toBig() | ||
| let expoB = expoB_fr.toBig() | ||
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| # debugEcho "expo:" , expo.toHex() | ||
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| let zeroF : F = fromHex( F, "0x00" ) | ||
| let oneF : F = fromHex( F, "0x01" ) | ||
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| #------------------------------------------------------------------------------- | ||
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| # standard generator of G2 | ||
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| let gen2_xi : F = fromHex( F, "0x1adcd0ed10df9cb87040f46655e3808f98aa68a570acf5b0bde23fab1f149701" ) | ||
| let gen2_xu : F = fromHex( F, "0x09e847e9f05a6082c3cd2a1d0a3a82e6fbfbe620f7f31269fa15d21c1c13b23b" ) | ||
| let gen2_yi : F = fromHex( F, "0x056c01168a5319461f7ca7aa19d4fcfd1c7cdf52dbfc4cbee6f915250b7f6fc8" ) | ||
| let gen2_yu : F = fromHex( F, "0x0efe500a2d02dd77f5f401329f30895df553b878fc3c0dadaaa86456a623235c" ) | ||
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| let gen2_x : F2 = F2( coords: [gen2_xi, gen2_xu] ) | ||
| let gen2_y : F2 = F2( coords: [gen2_yi, gen2_yu] ) | ||
| let gen2_z : F2 = F2( coords: [oneF , zeroF ] ) | ||
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| let gen2 : G = G( x: gen2_x, y: gen2_y, z: gen2_z ) | ||
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| #------------------------------------------------------------------------------- | ||
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| template echo(intercept: untyped) = | ||
| # This intercepts system.echo | ||
| # Delete this template to debug intermediate steps | ||
| discard | ||
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| proc printF( x: F ) = | ||
| echo(" = " & x.toDecimal) | ||
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| proc printF2( z: F2) = | ||
| echo(" 1 ~> " & z.coords[0].toDecimal ) | ||
| echo(" u ~> " & z.coords[1].toDecimal ) | ||
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| proc printG( pt: G ) = | ||
| var aff : ECP_ShortW_Aff[F2, G2]; | ||
| aff.affine(pt) | ||
| echo(" affine x coord: "); printF2( aff.x ) | ||
| echo(" affine y coord: "); printF2( aff.y ) | ||
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| #------------------------------------------------------------------------------- | ||
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| template test(scalarProc: untyped) = | ||
| proc `test _ scalarProc`() = | ||
| var p : G | ||
| var q : G | ||
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| echo("") | ||
| echo("sanity check: g2^r should be infinity") | ||
| p = gen2 | ||
| p.scalarProc(r) | ||
| printG(p) | ||
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| echo("") | ||
| echo("LHS = g2^expo") | ||
| p = gen2 | ||
| p.scalarProc(expo) | ||
| printG(p) | ||
| let lhs : G = p | ||
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| echo("") | ||
| echo("RHS = g2^expoA * g2^expoB, where expo = expoA + expoB") | ||
| p = gen2 | ||
| q = gen2 | ||
| p.scalarProc(expoA) | ||
| q.scalarProc(expoB) | ||
| p += q | ||
| printG(p) | ||
| let rhs : G = p | ||
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| echo("") | ||
| echo("reference from SageMath") | ||
| echo(" sage x coord:") | ||
| echo(" 1 -> 17216390949661727229956939928583223226083668728437958793715435751523027888005 ") | ||
| echo(" u -> 3082945034329785101034278215941854680789766318859358488904629243958221738137 ") | ||
| echo(" sage y coord:") | ||
| echo(" 1 -> 20108673238932196920264801702661201943173809015346082727725783869161803474440 ") | ||
| echo(" u -> 10405477402946058176045590740070709500904395284580129777629727895349459816649 ") | ||
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| echo("") | ||
| echo("LHS - RHS = ") | ||
| p = lhs | ||
| p -= rhs | ||
| printG(p) | ||
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| doAssert p.isInf().bool() | ||
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| `test _ scalarProc`() | ||
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| system.echo "issue #345 - scalarMul" | ||
| test(scalarMul) | ||
| system.echo "issue #345 - scalarMul_vartime" | ||
| test(scalarMul_vartime) | ||
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| system.echo "SUCCESS - issue #345" | ||
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| #------------------------------------------------------------------------------- | ||
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| #[ | ||
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| SageMath code | ||
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| # BN128 elliptic curve | ||
| p = 21888242871839275222246405745257275088696311157297823662689037894645226208583 | ||
| r = 21888242871839275222246405745257275088548364400416034343698204186575808495617 | ||
| h = 1 | ||
| Fp = GF(p) | ||
| Fr = GF(r) | ||
| A = Fp(0) | ||
| B = Fp(3) | ||
| E = EllipticCurve(Fp,[A,B]) | ||
| gx = Fp(1) | ||
| gy = Fp(2) | ||
| gen = E(gx,gy) # subgroup generator | ||
| print("scalar field check: ", gen.additive_order() == r ) | ||
| print("cofactor check: ", E.cardinality() == r*h ) | ||
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| # extension field | ||
| R.<x> = Fp[] | ||
| Fp2.<u> = Fp.extension(x^2+1) | ||
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| # twisted curve | ||
| B_twist = Fp2(19485874751759354771024239261021720505790618469301721065564631296452457478373 + 266929791119991161246907387137283842545076965332900288569378510910307636690*u ) | ||
| E2 = EllipticCurve(Fp2,[0,B_twist]) | ||
| size_E2 = E2.cardinality(); | ||
| cofactor_E2 = size_E2 / r; | ||
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| gen2_xi = Fp( 0x1adcd0ed10df9cb87040f46655e3808f98aa68a570acf5b0bde23fab1f149701 ) | ||
| gen2_xu = Fp( 0x09e847e9f05a6082c3cd2a1d0a3a82e6fbfbe620f7f31269fa15d21c1c13b23b ) | ||
| gen2_yi = Fp( 0x056c01168a5319461f7ca7aa19d4fcfd1c7cdf52dbfc4cbee6f915250b7f6fc8 ) | ||
| gen2_yu = Fp( 0x0efe500a2d02dd77f5f401329f30895df553b878fc3c0dadaaa86456a623235c ) | ||
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| gen2_x = gen2_xi + u * gen2_xu | ||
| gen2_y = gen2_yi + u * gen2_yu | ||
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| gen2 = E2(gen2_x, gen2_y) | ||
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| print("g2^r: ", gen2*r ) | ||
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| expo = 0x7b17fcc286b01af79176aa7da3a8615020eacda89a90e4ff5d0a085483f0448 | ||
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| print("g2^expo: ") | ||
| print(gen2*expo) | ||
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| ]# | ||
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| #------------------------------------------------------------------------------- |
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This is the main change. Papers that introduce the Babai's rounding unfortunately use shifts but do not go over the negative special case.