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Fused projective line eval (#96)
* Reorg line functions to allow for Jacobian eval * 2x faster Miller loop!!! with fused line eval double * Support Line Double Fusion for D-Twists * Implement fused line addition
This commit is contained in:
Mamy Ratsimbazafy
GitHub
parent
986245b5c1
commit
fc1c3472ce
@ -98,6 +98,8 @@ const testDesc: seq[tuple[path: string, useGMP: bool]] = @[
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# Edge cases highlighted by past bugs
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("tests/t_ec_shortw_prj_edge_cases.nim", false),
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# Pairing
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("tests/t_pairing_bls12_377_line_functions.nim", false),
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("tests/t_pairing_bls12_381_line_functions.nim", false),
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("tests/t_pairing_mul_fp12_by_lines.nim", false),
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("tests/t_pairing_cyclotomic_fp12.nim", false),
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("tests/t_pairing_bn254_nogami_optate.nim", false),
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58
constantine/pairing/lines_common.nim
Normal file
58
constantine/pairing/lines_common.nim
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@ -0,0 +1,58 @@
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# Constantine
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# Copyright (c) 2018-2019 Status Research & Development GmbH
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# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
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# Licensed and distributed under either of
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# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
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# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
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# at your option. This file may not be copied, modified, or distributed except according to those terms.
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import
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std/typetraits,
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../primitives,
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../config/[common, curves],
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../arithmetic,
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../towers,
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../elliptic/[
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ec_shortweierstrass_affine,
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ec_shortweierstrass_projective
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],
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../io/io_towers
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type
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Line*[F; twist: static SexticTwist] = object
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## Packed line representation over a E'(Fp^k/d)
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## with k the embedding degree and d the twist degree
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## i.e. for a curve with embedding degree 12 and sextic twist
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## F is Fp2
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##
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## Assuming a Sextic Twist
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##
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## Out of 6 Fp2 coordinates, 3 are 0 and
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## the non-zero coordinates depend on the twist kind.
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##
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## For a D-twist,
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## (x, y, z) corresponds to an sparse element of Fp12
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## with Fp2 coordinates: xy00z0
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## For a M-Twist
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## (x, y, z) corresponds to an sparse element of Fp12
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## with Fp2 coordinates: xyz000
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x*, y*, z*: F
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func toHex*(line: Line, order: static Endianness = bigEndian): string =
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result = static($line.typeof.genericHead() & '(')
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for fieldName, fieldValue in fieldPairs(line):
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when fieldName != "x":
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result.add ", "
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result.add fieldName & ": "
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result.appendHex(fieldValue, order)
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result.add ")"
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# Line evaluation
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# --------------------------------------------------
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func line_update*(line: var Line, P: ECP_ShortW_Aff) =
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## Update the line evaluation with P
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## after addition or doubling
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## P in G1
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line.x *= P.y
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line.z *= P.x
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@ -16,7 +16,10 @@ import
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ec_shortweierstrass_affine,
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ec_shortweierstrass_projective
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],
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../io/io_towers
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../io/io_towers,
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./lines_common
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export lines_common
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# ############################################################
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#
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@ -34,58 +37,16 @@ import
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# and Patrick Longa and Jefferson E. Ricardini, 2013
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# https://eprint.iacr.org/2013/722.pdf
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# http://sac2013.irmacs.sfu.ca/slides/s1.pdf
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#
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# TODO: Implement fused line doubling and addition
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# from Costello2009 or Aranha2010
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# We don't need the complete formulae in the Miller Loop
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# - Efficient Implementation of Bilinear Pairings on ARM Processors
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# Gurleen Grewal, Reza Azarderakhsh,
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# Patrick Longa, Shi Hu, and David Jao, 2012
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# https://eprint.iacr.org/2012/408.pdf
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type
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Line*[F; twist: static SexticTwist] = object
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## Packed line representation over a E'(Fp^k/d)
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## with k the embedding degree and d the twist degree
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## i.e. for a curve with embedding degree 12 and sextic twist
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## F is Fp2
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##
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## Assuming a Sextic Twist
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##
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## Out of 6 Fp2 coordinates, 3 are 0 and
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## the non-zero coordinates depend on the twist kind.
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##
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## For a D-twist,
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## (x, y, z) corresponds to an sparse element of Fp12
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## with Fp2 coordinates: xy00z0
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## For a M-Twist
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## (x, y, z) corresponds to an sparse element of Fp12
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## with Fp2 coordinates: xyz000
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x*, y*, z*: F
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# Line evaluation only
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# -----------------------------------------------------------------------------
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func toHex*(line: Line, order: static Endianness = bigEndian): string =
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result = static($line.typeof.genericHead() & '(')
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for fieldName, fieldValue in fieldPairs(line):
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when fieldName != "x":
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result.add ", "
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result.add fieldName & ": "
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result.appendHex(fieldValue, order)
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result.add ")"
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# Line evaluation
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# --------------------------------------------------
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func `*=`(a: var Fp2, b: Fp) =
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## Multiply an element of Fp2 by an element of Fp
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# TODO: make generic and move to tower_field_extensions
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a.c0 *= b
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a.c1 *= b
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func line_update(line: var Line, P: ECP_ShortW_Aff) =
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## Update the line evaluation with P
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## after addition or doubling
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## P in G1
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line.x *= P.y
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line.z *= P.x
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func line_eval_double*(line: var Line, T: ECP_ShortW_Proj) =
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func line_eval_double(line: var Line, T: ECP_ShortW_Proj) =
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## Evaluate the line function for doubling
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## i.e. the tangent at T
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##
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@ -158,7 +119,7 @@ func line_eval_double*(line: var Line, T: ECP_ShortW_Proj) =
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B -= v # B = 3bξ Z² - Y² (M-twist)
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# B = 3b Z² - ξ Y² (D-twist)
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func line_eval_add*(line: var Line, T: ECP_ShortW_Proj, Q: ECP_ShortW_Aff) =
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func line_eval_add(line: var Line, T: ECP_ShortW_Proj, Q: ECP_ShortW_Aff) =
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## Evaluate the line function for addition
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## i.e. the line between T and Q
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##
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@ -206,16 +167,138 @@ func line_eval_add*(line: var Line, T: ECP_ShortW_Proj, Q: ECP_ShortW_Aff) =
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C.neg() # C = -(Y₁-Z₁Y₂)
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func line_eval_fused_double(line: var Line, T: var ECP_ShortW_Proj) =
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## Fused line evaluation and elliptic point doubling
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# Grewal et al, 2012 adapted to Scott 2019 line notation
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var A {.noInit.}, B {.noInit.}, C {.noInit.}: Line.F
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var E {.noInit.}, F {.noInit.}, G {.noInit.}: Line.F
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template H: untyped = line.x
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const b3 = 3*Line.F.C.getCoefB()
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var snrY = T.y
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when Line.F.C.getSexticTwist() == D_Twist:
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snrY *= SexticNonResidue
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A.prod(T.x, snrY)
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A.div2() # A = XY/2
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B.square(T.y) # B = Y²
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C.square(T.z) # C = Z²
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var snrB = B
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when Line.F.C.getSexticTwist() == D_Twist:
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snrB *= SexticNonResidue
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E = C
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E *= b3
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when Line.F.C.getSexticTwist() == M_Twist:
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E *= SexticNonResidue # E = 3b'Z² = 3bξ Z²
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F = E
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F *= 3 # F = 3E = 9bZ²
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G.sum(snrB, F)
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G.div2() # G = (B+F)/2
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H.sum(T.y, T.z)
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H.square()
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H -= B
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H -= C # lx = H = (Y+Z)²-(B+C)= 2YZ
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line.z.square(T.x)
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line.z *= 3 # lz = 3X²
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when Line.F.C.getSexticTwist() == D_Twist:
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line.z *= SexticNonResidue
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line.y.diff(E, snrB) # ly = E-B = 3b'Z² - Y²
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# In-place modification: invalidates `T.` calls
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T.x.diff(snrB, F)
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T.x *= A # X₃ = A(B-F) = XY/2.(Y²-9b'Z²)
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# M-twist: XY/2.(Y²-9bξZ²)
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# D-Twist: ξXY/2.(Y²ξ-9bZ²)
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T.y.square(G)
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E.square()
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E *= 3
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T.y -= E # Y₃ = G² - 3E² = (Y²+9b'Z²)²/4 - 3*(3b'Z²)²
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# M-twist: (Y²+9bξZ²)²/4 - 3*(3bξZ²)²
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# D-Twist: (ξY²+9bZ²)²/4 - 3*(3bZ²)²
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when Line.F.C.getSexticTwist() == D_Twist:
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H *= SexticNonResidue
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T.z.prod(snrB, H) # Z₃ = BH = Y²((Y+Z)² - (Y²+Z²)) = 2Y³Z
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# M-twist: 2Y³Z
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# D-twist: 2ξ²Y³Z
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# Correction for Fp4 towering
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H.neg() # lx = -H
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when Line.F.C.getSexticTwist() == M_Twist:
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H *= SexticNonResidue
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# else: the SNR is already integrated in H
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func line_eval_fused_add(line: var Line, T: var ECP_ShortW_Proj, Q: ECP_ShortW_Aff) =
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## Fused line evaluation and elliptic point addition
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# Grewal et al, 2012 adapted to Scott 2019 line notation
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var
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A {.noInit.}: Line.F
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B {.noInit.}: Line.F
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C {.noInit.}: Line.F
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D {.noInit.}: Line.F
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E {.noInit.}: Line.F
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F {.noInit.}: Line.F
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G {.noInit.}: Line.F
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H {.noInit.}: Line.F
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I {.noInit.}: Line.F
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template lambda: untyped = line.x
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template theta: untyped = line.z
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template J: untyped = line.y
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A.prod(Q.y, T.z)
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B.prod(Q.x, T.z)
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theta.diff(T.y, A) # θ = Y₁ - Z₁X₂
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lambda.diff(T.x, B) # λ = X₁ - Z₁X₂
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C.square(theta)
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D.square(lambda)
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E.prod(D, lambda)
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F.prod(T.z, C)
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G.prod(T.x, D)
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H.double(G)
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H.diffAlias(F, H)
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H += E
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I.prod(T.y, E)
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T.x.prod(theta, Q.x)
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T.y.prod(lambda, Q.y)
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J.diff(T.x, T.y)
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# EC addition
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T.x.prod(lambda, H)
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T.y.diff(G, H)
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T.y *= theta
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T.y -= I
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T.z *= E
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# Line evaluation
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theta.neg()
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when ECP_ShortW_Proj.F.C.getSexticTwist() == M_Twist:
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lambda *= SexticNonResidue # A = ξ (X₁ - Z₁X₂)
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# Public proc
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# -----------------------------------------------------------------------------
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func line_double*(line: var Line, T: var ECP_ShortW_Proj, P: ECP_ShortW_Aff) =
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## Doubling step of the Miller loop
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## T in G2, P in G1
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##
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## Compute lt,t(P)
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##
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# TODO fused line doubling from Costello 2009, Grewal 2012, Aranha 2013
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line_eval_double(line, T)
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line.line_update(P)
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T.double()
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when true:
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line_eval_fused_double(line, T)
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line.line_update(P)
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else:
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line_eval_double(line, T)
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line.line_update(P)
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T.double()
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func line_add*[C](
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line: var Line,
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@ -225,7 +308,10 @@ func line_add*[C](
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## T and Q in G2, P in G1
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##
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## Compute lt,q(P)
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# TODO fused line addition from Costello 2009, Grewal 2012, Aranha 2013
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line_eval_add(line, T, Q)
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line.line_update(P)
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T += Q
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when true:
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line_eval_fused_add(line, T, Q)
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line.line_update(P)
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else:
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line_eval_add(line, T, Q)
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line.line_update(P)
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T += Q
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@ -41,43 +41,6 @@ import
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# 𝔽p12 by line - Sparse functions
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# ----------------------------------------------------------------
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func mul_sparse_by_y0*[C: static Curve](r: var Fp4[C], a: Fp4[C], b: Fp2[C]) =
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## Sparse multiplication of an Fp4 element
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## with coordinates (a₀, a₁) by (b₀, 0)
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r.c0.prod(a.c0, b)
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r.c1.prod(a.c1, b)
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func mul_sparse_by_0y*[C: static Curve](r: var Fp4[C], a: Fp4[C], b: Fp2[C]) =
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## Sparse multiplication of an Fp4 element
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## with coordinates (a₀, a₁) by (0, b₁)
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r.c0.prod(a.c1, b)
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r.c0 *= NonResidue
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r.c1.prod(a.c0, b)
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func mul_sparse_by_0y0*[C: static Curve](r: var Fp6[C], a: Fp6[C], b: Fp2[C]) =
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## Sparse multiplication of an Fp6 element
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## with coordinates (a₀, a₁, a₂) by (0, b₁, 0)
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# TODO: make generic and move to tower_field_extensions
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# v0 = a0 b0 = 0
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# v1 = a1 b1
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# v2 = a2 b2 = 0
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#
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# r0 = ξ ((a1 + a2) * (b1 + b2) - v1 - v2) + v0
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# = ξ (a1 b1 + a2 b1 - v1)
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# = ξ a2 b1
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# r1 = (a0 + a1) * (b0 + b1) - v0 - v1 + ξ v2
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# = a0 b1 + a1 b1 - v1
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# = a0 b1
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# r2 = (a0 + a2) * (b0 + b2) - v0 - v2 + v1
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# = v1
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# = a1 b1
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r.c0.prod(a.c2, b)
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r.c0 *= ξ
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r.c1.prod(a.c0, b)
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r.c2.prod(a.c1, b)
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func mul_by_line_xy0*[C: static Curve, twist: static SexticTwist](
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r: var Fp6[C],
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a: Fp6[C],
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@ -197,3 +197,49 @@ func `*`*(_: typedesc[γ], a: Fp4): Fp4 {.noInit, inline.} =
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func `*=`*(a: var Fp4, _: typedesc[γ]) {.inline.} =
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a = γ * a
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# Sparse functions
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# ----------------------------------------------------------------
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func `*=`*(a: var Fp2, b: Fp) =
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## Multiply an element of Fp2 by an element of Fp
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# TODO: make generic and move to tower_field_extensions
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a.c0 *= b
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a.c1 *= b
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func mul_sparse_by_y0*[C: static Curve](r: var Fp4[C], a: Fp4[C], b: Fp2[C]) =
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## Sparse multiplication of an Fp4 element
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## with coordinates (a₀, a₁) by (b₀, 0)
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r.c0.prod(a.c0, b)
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r.c1.prod(a.c1, b)
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func mul_sparse_by_0y*[C: static Curve](r: var Fp4[C], a: Fp4[C], b: Fp2[C]) =
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## Sparse multiplication of an Fp4 element
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## with coordinates (a₀, a₁) by (0, b₁)
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r.c0.prod(a.c1, b)
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r.c0 *= NonResidue
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r.c1.prod(a.c0, b)
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func mul_sparse_by_0y0*[C: static Curve](r: var Fp6[C], a: Fp6[C], b: Fp2[C]) =
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## Sparse multiplication of an Fp6 element
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## with coordinates (a₀, a₁, a₂) by (0, b₁, 0)
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# TODO: make generic and move to tower_field_extensions
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# v0 = a0 b0 = 0
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# v1 = a1 b1
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# v2 = a2 b2 = 0
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#
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# r0 = ξ ((a1 + a2) * (b1 + b2) - v1 - v2) + v0
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# = ξ (a1 b1 + a2 b1 - v1)
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# = ξ a2 b1
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# r1 = (a0 + a1) * (b0 + b1) - v0 - v1 + ξ v2
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# = a0 b1 + a1 b1 - v1
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# = a0 b1
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# r2 = (a0 + a2) * (b0 + b2) - v0 - v2 + v1
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# = v1
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# = a1 b1
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r.c0.prod(a.c2, b)
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r.c0 *= ξ
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r.c1.prod(a.c0, b)
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r.c2.prod(a.c1, b)
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|
||||
114
tests/t_pairing_bls12_377_line_functions.nim
Normal file
114
tests/t_pairing_bls12_377_line_functions.nim
Normal file
@ -0,0 +1,114 @@
|
||||
# Constantine
|
||||
# Copyright (c) 2018-2019 Status Research & Development GmbH
|
||||
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
|
||||
# Licensed and distributed under either of
|
||||
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
|
||||
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
|
||||
# at your option. This file may not be copied, modified, or distributed except according to those terms.
|
||||
|
||||
import
|
||||
# Standard library
|
||||
std/[tables, unittest, times],
|
||||
# Internals
|
||||
../constantine/config/common,
|
||||
../constantine/[arithmetic, primitives],
|
||||
../constantine/towers,
|
||||
../constantine/config/curves,
|
||||
../constantine/io/io_towers,
|
||||
../constantine/elliptic/[
|
||||
ec_shortweierstrass_affine,
|
||||
ec_shortweierstrass_projective,
|
||||
ec_scalar_mul],
|
||||
../constantine/pairing/lines_projective,
|
||||
# Test utilities
|
||||
../helpers/[prng_unsafe, static_for]
|
||||
|
||||
const
|
||||
Iters = 4
|
||||
TestCurves = [
|
||||
BLS12_377
|
||||
]
|
||||
|
||||
type
|
||||
RandomGen = enum
|
||||
Uniform
|
||||
HighHammingWeight
|
||||
Long01Sequence
|
||||
|
||||
var rng: RngState
|
||||
let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
|
||||
rng.seed(seed)
|
||||
echo "\n------------------------------------------------------\n"
|
||||
echo "test_pairing_bls12_377_line_functions xoshiro512** seed: ", seed
|
||||
|
||||
func random_point*(rng: var RngState, EC: typedesc, gen: RandomGen): EC {.noInit.} =
|
||||
if gen == Uniform:
|
||||
result = rng.random_unsafe(EC)
|
||||
elif gen == HighHammingWeight:
|
||||
result = rng.random_highHammingWeight(EC)
|
||||
else:
|
||||
result = rng.random_long01Seq(EC)
|
||||
|
||||
func random_point*(rng: var RngState, EC: typedesc, randZ: bool, gen: RandomGen): EC {.noInit.} =
|
||||
if not randZ:
|
||||
if gen == Uniform:
|
||||
result = rng.random_unsafe(EC)
|
||||
elif gen == HighHammingWeight:
|
||||
result = rng.random_highHammingWeight(EC)
|
||||
else:
|
||||
result = rng.random_long01Seq(EC)
|
||||
else:
|
||||
if gen == Uniform:
|
||||
result = rng.random_unsafe_with_randZ(EC)
|
||||
elif gen == HighHammingWeight:
|
||||
result = rng.random_highHammingWeight_with_randZ(EC)
|
||||
else:
|
||||
result = rng.random_long01Seq_with_randZ(EC)
|
||||
|
||||
suite "Pairing - Line Functions on BLS12-377" & " [" & $WordBitwidth & "-bit mode]":
|
||||
test "Line double - lt,t(P)":
|
||||
proc test_line_double(C: static Curve, randZ: bool, gen: RandomGen) =
|
||||
for _ in 0 ..< Iters:
|
||||
let P = rng.random_point(ECP_ShortW_Aff[Fp[C]], gen)
|
||||
var T = rng.random_point(ECP_ShortW_Proj[Fp2[C]], randZ, gen)
|
||||
let Q = rng.random_point(ECP_ShortW_Proj[Fp2[C]], randZ, gen)
|
||||
var l: Line[Fp2[C], C.getSexticTwist()]
|
||||
|
||||
var T2: typeof(Q)
|
||||
T2.double(T)
|
||||
l.line_double(T, P)
|
||||
|
||||
doAssert: bool(T == T2)
|
||||
|
||||
staticFor(curve, TestCurves):
|
||||
test_line_double(curve, randZ = false, gen = Uniform)
|
||||
test_line_double(curve, randZ = true, gen = Uniform)
|
||||
test_line_double(curve, randZ = false, gen = HighHammingWeight)
|
||||
test_line_double(curve, randZ = true, gen = HighHammingWeight)
|
||||
test_line_double(curve, randZ = false, gen = Long01Sequence)
|
||||
test_line_double(curve, randZ = true, gen = Long01Sequence)
|
||||
|
||||
test "Line add - lt,q(P)":
|
||||
proc test_line_add(C: static Curve, randZ: bool, gen: RandomGen) =
|
||||
for _ in 0 ..< Iters:
|
||||
let P = rng.random_point(ECP_ShortW_Aff[Fp[C]], gen)
|
||||
let Q = rng.random_point(ECP_ShortW_Proj[Fp2[C]], randZ, gen)
|
||||
var T = rng.random_point(ECP_ShortW_Proj[Fp2[C]], randZ, gen)
|
||||
var l: Line[Fp2[C], C.getSexticTwist()]
|
||||
|
||||
var TQ{.noInit.}: typeof(T)
|
||||
TQ.sum(T, Q)
|
||||
|
||||
var Qaff{.noInit.}: ECP_ShortW_Aff[Fp2[C]]
|
||||
Qaff.affineFromProjective(Q)
|
||||
l.line_add(T, Qaff, P)
|
||||
|
||||
doAssert: bool(T == TQ)
|
||||
|
||||
staticFor(curve, TestCurves):
|
||||
test_line_add(curve, randZ = false, gen = Uniform)
|
||||
test_line_add(curve, randZ = true, gen = Uniform)
|
||||
test_line_add(curve, randZ = false, gen = HighHammingWeight)
|
||||
test_line_add(curve, randZ = true, gen = HighHammingWeight)
|
||||
test_line_add(curve, randZ = false, gen = Long01Sequence)
|
||||
test_line_add(curve, randZ = true, gen = Long01Sequence)
|
||||
Loading…
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Reference in New Issue
Block a user