Cleanup: consolidate extensions and instantiation + reorg extension module
This commit is contained in:
Mamy André-Ratsimbazafy
parent
8918cabb56
commit
8a7c35af59
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@ -14,9 +14,9 @@ import
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./io_bigints, ./io_fields,
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../primitives,
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../arithmetic/finite_fields,
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../tower_field_extensions/tower_instantiation
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../tower_field_extensions/extension_fields
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export tower_instantiation
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export extension_fields
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# No exceptions allowed
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{.push raises: [].}
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File diff suppressed because it is too large
Load Diff
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@ -7,7 +7,7 @@
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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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./tower_instantiation,
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./extension_fields,
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../arithmetic,
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../primitives,
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../config/[common, curves],
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@ -43,9 +43,9 @@ func isSquare*(a: Fp2): SecretBool =
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result = tv1.isSquare()
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func sqrt_rotate_extension(
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out_sqrt: var QuadraticExt,
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candidate_sqrt: QuadraticExt,
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a: QuadraticExt
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out_sqrt: var Fp2,
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candidate_sqrt: Fp2,
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a: Fp2
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): SecretBool =
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## From a field element `a` and a candidate Fp2 square root
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## Search the actual square root by rotating candidate solution
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@ -57,7 +57,7 @@ func sqrt_rotate_extension(
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## This avoids expensive trial "isSquare" checks (450+ field multiplications)
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## This requires the sqrt of sqrt of the quadratic non-residue
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## to be in Fp2
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var coeff{.noInit.}, cand2{.noInit.}, t{.noInit.}: QuadraticExt
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var coeff{.noInit.}, cand2{.noInit.}, t{.noInit.}: Fp2
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const Curve = typeof(a.c0).C
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# We name µ² the quadratic non-residue
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@ -1,297 +0,0 @@
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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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# Instantiate the actual tower extensions
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# that were described in a "conceptualized" way
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# ----------------------------------------------------------------
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import
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../arithmetic,
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../config/[common, curves],
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../io/io_fields,
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./extension_fields,
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./exponentiations
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export extension_fields, exponentiations
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# We assume that the sextic non-residues used to construct
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# the elliptic curve twists
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# match with the quadratic and cubic non-residues
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# chosen to construct the tower of extension fields.
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# 𝔽p
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# ----------------------------------------------------------------
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func `*=`*(a: var Fp, _: type NonResidue) {.inline.} =
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## Multiply an element of 𝔽p by the quadratic non-residue
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## chosen to construct 𝔽p2
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static: doAssert Fp.C.getNonResidueFp() != -1, "𝔽p2 should be specialized for complex extension"
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a *= Fp.C.getNonResidueFp()
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func prod*(r: var Fp, a: Fp, _: type NonResidue){.inline.} =
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## Multiply an element of 𝔽p by the quadratic non-residue
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## chosen to construct 𝔽p2
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static: doAssert Fp.C.getNonResidueFp() != -1, "𝔽p2 should be specialized for complex extension"
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r.prod(a, Fp.C.getNonResidueFp())
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# 𝔽p2
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# ----------------------------------------------------------------
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type
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Fp2*[C: static Curve] =
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QuadraticExt[Fp[C]]
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template fromComplexExtension*[F](elem: F): static bool =
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## Returns true if the input is a complex extension
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## i.e. the irreducible polynomial chosen is
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## x² - µ with µ = -1
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## and so 𝔽p2 = 𝔽p[x] / x² - µ = 𝔽p[𝑖]
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when F is Fp2 and F.C.getNonResidueFp() == -1:
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true
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else:
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false
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template mulCheckSparse*(a: var Fp2, b: Fp2) =
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when b.isOne().bool:
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discard
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elif b.isMinusOne().bool:
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a.neg()
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elif b.c0.isZero().bool and b.c1.isOne().bool:
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var t {.noInit.}: type(a.c0)
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when fromComplexExtension(b):
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t.neg(a.c1)
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a.c1 = a.c0
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a.c0 = t
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else:
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t.prod(a.c1, NonResidue)
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a.c1 = a.c0
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a.c0 = t
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elif b.c0.isZero().bool and b.c1.isMinusOne().bool:
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var t {.noInit.}: type(a.c0)
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when fromComplexExtension(b):
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t = a.c1
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a.c1.neg(a.c0)
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a.c0 = t
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else:
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t.prod(a.c1, NonResidue)
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a.c1.neg(a.c0)
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a.c0.neg(t)
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elif b.c0.isZero().bool:
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a.mul_sparse_by_0y(b)
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elif b.c1.isZero().bool:
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a.mul_sparse_by_x0(b)
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else:
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a *= b
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func prod*(r: var Fp2, a: Fp2, _: type NonResidue) {.inline.} =
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## Multiply an element of 𝔽p2 by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p4
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## - if cubic non-residue: 𝔽p6
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## - if sextic non-residue: 𝔽p4, 𝔽p6 or 𝔽p12
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# Yet another const tuple unpacking bug
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const u = Fp2.C.getNonResidueFp2()[0]
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const v = Fp2.C.getNonResidueFp2()[1]
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const Beta {.used.} = Fp2.C.getNonResidueFp()
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# ξ = u + v x
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# and x² = β
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#
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# (c0 + c1 x) (u + v x) => u c0 + (u c0 + u c1)x + v c1 x²
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# => u c0 + β v c1 + (v c0 + u c1) x
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when a.fromComplexExtension() and u == 1 and v == 1:
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let t = a.c0
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r.c0.diff(t, a.c1)
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r.c1.sum(t, a.c1)
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else:
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# Case:
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# - BN254_Snarks, QNR_Fp: -1, SNR_Fp2: 9+1𝑖 (𝑖 = √-1)
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# - BLS12_377, QNR_Fp: -5, SNR_Fp2: 0+1j (j = √-5)
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# - BW6_761, SNR_Fp: -4, CNR_Fp2: 0+1j (j = √-4)
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when u == 0:
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# BLS12_377 and BW6_761, use small addition chain
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r.mul_sparse_by_0y(a, v)
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else:
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# BN254_Snarks, u = 9, v = 1, β = -1
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# Even with u = 9, the 2x9 addition chains (8 additions total)
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# are cheaper than full Fp2 multiplication
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var t {.noInit.}: typeof(a.c0)
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t.prod(a.c0, u)
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when v == 1 and Beta == -1: # Case BN254_Snarks
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t -= a.c1 # r0 = u c0 + β v c1
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else:
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{.error: "Unimplemented".}
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r.c1.prod(a.c1, u)
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when v == 1: # r1 = v c0 + u c1
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r.c1 += a.c0
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# aliasing: a.c0 is unused
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r.c0 = t
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else:
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{.error: "Unimplemented".}
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func `*=`*(a: var Fp2, _: type NonResidue) {.inline.} =
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## Multiply an element of 𝔽p2 by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p4
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## - if cubic non-residue: 𝔽p6
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## - if sextic non-residue: 𝔽p4, 𝔽p6 or 𝔽p12
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# Yet another const tuple unpacking bug
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a.prod(a, NonResidue)
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func `/=`*(a: var Fp2, _: type NonResidue) {.inline.} =
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## Divide an element of 𝔽p by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p4
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## - if cubic non-residue: 𝔽p6
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## - if sextic non-residue: 𝔽p4, 𝔽p6 or 𝔽p12
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# Yet another const tuple unpacking bug
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# Yet another const tuple unpacking bug
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const u = Fp2.C.getNonresidueFp2()[0] # Sextic non-residue to construct 𝔽p12
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const v = Fp2.C.getNonresidueFp2()[1]
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const Beta = Fp2.C.getNonResidueFp() # Quadratic non-residue to construct 𝔽p2
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# ξ = u + v x
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# and x² = β
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#
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# (c0 + c1 x) / (u + v x) => (c0 + c1 x)(u - v x) / ((u + vx)(u-vx))
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# => u c0 - v c1 x² + (u c1 - v c0) x / (u² - x²v²)
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# => 1/(u² - βv²) * (uc0 - β v c1, u c1 - v c0)
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# With β = 𝑖 = √-1
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# 1/(u² + v²) * (u c0 + v c1, u c1 - v c0)
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#
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# With β = 𝑖 = √-1 and ξ = 1 + 𝑖
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# 1/2 * (c0 + c1, c1 - c0)
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when a.fromComplexExtension() and u == 1 and v == 1:
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let t = a.c0
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a.c0 += a.c1
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a.c1 -= t
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a.div2()
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else:
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var a0 = a.c0
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let a1 = a.c1
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const u2v2 = u*u - Beta*v*v # (u² - βv²)
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# TODO can be precomputed (or precompute b/µ the twist coefficient)
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# and use faster non-constant-time inversion in the VM
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var u2v2inv {.noInit.}: a.c0.typeof
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u2v2inv.fromUint(u2v2)
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u2v2inv.inv()
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a.c0 *= u
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a.c1 *= Beta * v
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a.c0 -= a.c1
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a.c1 = a1
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a.c1 *= u
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a0 *= v
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a.c1 -= a0
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a.c0 *= u2v2inv
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a.c1 *= u2v2inv
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# 𝔽p4 & 𝔽p6
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# ----------------------------------------------------------------
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type
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Fp4*[C: static Curve] =
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QuadraticExt[Fp2[C]]
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Fp6*[C: static Curve] =
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CubicExt[Fp2[C]]
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func prod*(r: var Fp4, a: Fp4, _: type NonResidue) =
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## Multiply an element of 𝔽p4 by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p8
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## - if cubic non-residue: 𝔽p12
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## - if sextic non-residue: 𝔽p8, 𝔽p12 or 𝔽p24
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##
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## Assumes that it is sqrt(NonResidue_Fp2)
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let t = a.c0
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r.c0.prod(a.c1, NonResidue)
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r.c1 = t
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func `*=`*(a: var Fp4, _: type NonResidue) {.inline.} =
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## Multiply an element of 𝔽p4 by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p8
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## - if cubic non-residue: 𝔽p12
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## - if sextic non-residue: 𝔽p8, 𝔽p12 or 𝔽p24
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##
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## Assumes that it is sqrt(NonResidue_Fp2)
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a.prod(a, NonResidue)
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func prod*(r: var Fp6, a: Fp6, _: type NonResidue) {.inline.} =
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## Multiply an element of 𝔽p6 by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p12
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## - if cubic non-residue: 𝔽p18
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## - if sextic non-residue: 𝔽p12, 𝔽p18 or 𝔽p36
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##
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## Assumes that it is cube_root(NonResidue_Fp2)
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##
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## For all curves γ = v with v the factor for 𝔽p6 coordinate
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## and v³ = ξ
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## (c0 + c1 v + c2 v²) v => ξ c2 + c0 v + c1 v²
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let t = a.c2
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r.c1 = a.c0
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r.c2 = a.c1
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r.c0.prod(t, NonResidue)
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func `*=`*(a: var Fp6, _: type NonResidue) {.inline.} =
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## Multiply an element of 𝔽p6 by the non-residue
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## chosen to construct the next extension or the twist:
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## - if quadratic non-residue: 𝔽p12
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## - if cubic non-residue: 𝔽p18
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## - if sextic non-residue: 𝔽p12, 𝔽p18 or 𝔽p36
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##
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## Assumes that it is cube_root(NonResidue_Fp2)
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##
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## For all curves γ = v with v the factor for 𝔽p6 coordinate
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## and v³ = ξ
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## (c0 + c1 v + c2 v²) v => ξ c2 + c0 v + c1 v²
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a.prod(a, NonResidue)
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# 𝔽p12
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# ----------------------------------------------------------------
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type
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Fp12*[C: static Curve] =
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CubicExt[Fp4[C]]
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# QuadraticExt[Fp6[C]]
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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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a.c0 *= b
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a.c1 *= 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 *= NonResidue
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r.c1.prod(a.c0, b)
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r.c2.prod(a.c1, b)
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@ -8,8 +8,9 @@
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import
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tower_field_extensions/[
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tower_instantiation,
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square_root_fp2
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square_root_fp2,
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exponentiations,
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extension_fields
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]
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export tower_instantiation, square_root_fp2
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export extension_fields, square_root_fp2, exponentiations
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