Consolidated curve-specific Frobenius in a curve folder
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Mamy André-Ratsimbazafy
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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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../config/curves,
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../towers,
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../io/io_towers
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# Frobenius map - on extension fields
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# -----------------------------------------------------------------
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# c = (SNR^((p-1)/6)^coef).
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# Then for frobenius(2): c * conjugate(c)
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# And for frobenius(3): c² * conjugate(c)
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const FrobMapConst_BLS12_377* = [
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# frobenius(1)
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[Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^0
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"0x1",
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"0x0"
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),
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Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^1
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"0x9a9975399c019633c1e30682567f915c8a45e0f94ebc8ec681bf34a3aa559db57668e558eb0188e938a9d1104f2031",
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"0x0"
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),
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Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
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"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000002",
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"0x0"
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),
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Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
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"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
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"0x0"
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),
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Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
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"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000001",
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"0x0"
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),
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Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^5
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"0xcd70cb3fc936348d0351d498233f1fe379531411832232f6648a9a9fc0b9c4e3e21b7467077c05853e2c1be0e9fc32",
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"0x0"
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)],
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# frobenius(2)
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[Fp2[BLS12_377].fromHex( # norm(SNR)^((p-1)/6)^1
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"0x1",
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"0x0"
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),
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Fp2[BLS12_377].fromHex( # norm(SNR)^((p-1)/6)^2
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"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000002",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000001",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000000",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1ae3a4617c510eabc8756ba8f8c524eb8882a75cc9bc8e359064ee822fb5bffd1e945779fffffffffffffffffffffff",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1ae3a4617c510eabc8756ba8f8c524eb8882a75cc9bc8e359064ee822fb5bffd1e94577a00000000000000000000000",
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"0x0"
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)],
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# frobenius(3)
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[Fp2[BLS12_377].fromHex(
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"0x1",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000000",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x4630059e5fd9200575d0e552278a89da1f40fdf62334cd620d1860769e389d7db2d8ea700d82721691ea130ec6e39e",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1",
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"0x0"
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),
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Fp2[BLS12_377].fromHex(
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"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
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"0x0"
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)]]
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# ψ (Psi) - Untwist-Frobenius-Twist Endomorphisms on twisted curves
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# -----------------------------------------------------------------
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# BLS12_377 is a D-Twist: SNR^((p-1)/6)
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const FrobPsiConst_BLS12_377_psi1_coef1* = Fp2[BLS12_377].fromHex(
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"0x9a9975399c019633c1e30682567f915c8a45e0f94ebc8ec681bf34a3aa559db57668e558eb0188e938a9d1104f2031",
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"0x0"
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)
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# SNR^((p-1)/3)
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const FrobPsiConst_BLS12_377_psi1_coef2* = Fp2[BLS12_377].fromHex(
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"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000002",
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"0x0"
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)
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# SNR^((p-1)/2)
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const FrobPsiConst_BLS12_377_psi1_coef3* = Fp2[BLS12_377].fromHex(
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"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
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"0x0"
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)
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# norm(SNR)^((p-1)/3)
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const FrobPsiConst_BLS12_377_psi2_coef2* = Fp2[BLS12_377].fromHex(
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"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000001",
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"0x0"
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)
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@ -0,0 +1,119 @@
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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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../config/curves,
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../towers,
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../io/io_towers
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# Frobenius map - on extension fields
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# -----------------------------------------------------------------
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# c = (SNR^((p-1)/6)^coef).
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# Then for frobenius(2): c * conjugate(c)
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# And for frobenius(3): c² * conjugate(c)
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const FrobMapConst_BLS12_381* = [
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# frobenius(1)
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[Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^0
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"0x1",
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"0x0"
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),
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Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^1
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"0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8",
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"0xfc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3"
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),
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Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
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"0x0",
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"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac"
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),
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Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
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"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09",
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"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09"
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),
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Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
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"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad",
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"0x0"
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),
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Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^5
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"0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116",
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"0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995"
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)],
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# frobenius(2)
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[Fp2[BLS12_381].fromHex( # norm(SNR)^((p-1)/6)^1
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"0x1",
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"0x0"
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),
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Fp2[BLS12_381].fromHex( # norm(SNR)^((p-1)/6)^2
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"0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff",
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"0x0"
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),
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Fp2[BLS12_381].fromHex(
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"0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe",
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"0x0"
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),
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Fp2[BLS12_381].fromHex(
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"0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
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"0x0"
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),
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Fp2[BLS12_381].fromHex(
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"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac",
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"0x0"
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),
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Fp2[BLS12_381].fromHex(
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"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad",
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"0x0"
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)],
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# frobenius(3)
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[Fp2[BLS12_381].fromHex(
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"0x1",
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"0x0"
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),
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Fp2[BLS12_381].fromHex(
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"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2",
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"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09"
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),
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Fp2[BLS12_381].fromHex(
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"0x0",
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"0x1"
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),
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Fp2[BLS12_381].fromHex(
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"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2",
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"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2"
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),
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Fp2[BLS12_381].fromHex(
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"0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
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"0x0"
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),
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Fp2[BLS12_381].fromHex(
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"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09",
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"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2"
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)]]
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# ψ (Psi) - Untwist-Frobenius-Twist Endomorphisms on twisted curves
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# -----------------------------------------------------------------
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# BLS12_381 is a M-twist: (1/SNR)^((p-1)/6)
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const FrobPsiConst_BLS12_381_psi1_coef1* = Fp2[BLS12_381].fromHex(
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"0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116",
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"0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116"
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)
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# (1/SNR)^((p-1)/3)
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const FrobPsiConst_BLS12_381_psi1_coef2* = Fp2[BLS12_381].fromHex(
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"0x0",
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"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad"
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)
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# (1/SNR)^((p-1)/2)
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const FrobPsiConst_BLS12_381_psi1_coef3* = Fp2[BLS12_381].fromHex(
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"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2",
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"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09"
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)
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# norm(SNR)^((p-1)/3)
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const FrobPsiConst_BLS12_381_psi2_coef2* = Fp2[BLS12_381].fromHex(
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"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac",
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"0x0"
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)
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@ -0,0 +1,119 @@
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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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../config/curves,
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../towers,
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../io/io_towers
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# Frobenius map - on extension fields
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# -----------------------------------------------------------------
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# c = (SNR^((p-1)/6)^coef).
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# Then for frobenius(2): c * conjugate(c)
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# And for frobenius(3): c² * conjugate(c)
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const FrobMapConst_BN254_Nogami* = [
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# frobenius(1)
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[Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^0
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"0x1",
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"0x0"
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),
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Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^1
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||||||
|
"0x1b377619212e7c8cb6499b50a846953f850974924d3f77c2e17de6c06f2a6de9",
|
||||||
|
"0x9ebee691ed1837503eab22f57b96ac8dc178b6db2c08850c582193f90d5922a"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
|
||||||
|
"0x0",
|
||||||
|
"0x25236482400000017080eb4000000006181800000000000cd98000000000000b"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
|
||||||
|
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5",
|
||||||
|
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
|
||||||
|
"0x25236482400000017080eb4000000006181800000000000cd98000000000000c",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^5
|
||||||
|
"0x19f3db6884cdca43c2b0d5792cd135accb1baea0b017046e859975ab54b5ef9b",
|
||||||
|
"0xb2f8919bb3235bdf7837806d32eca5b9605515f4fe8fba521668a54ab4a1078"
|
||||||
|
)],
|
||||||
|
# frobenius(2)
|
||||||
|
[Fp2[BN254_Nogami].fromHex( # norm(SNR)^((p-1)/6)^1
|
||||||
|
"0x1",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex( # norm(SNR)^((p-1)/6)^2
|
||||||
|
"0x49b36240000000024909000000000006cd80000000000008",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x49b36240000000024909000000000006cd80000000000007",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x2523648240000001ba344d80000000086121000000000013a700000000000012",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x25236482400000017080eb4000000006181800000000000cd98000000000000b",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x25236482400000017080eb4000000006181800000000000cd98000000000000c",
|
||||||
|
"0x0"
|
||||||
|
)],
|
||||||
|
# frobenius(3)
|
||||||
|
[Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x1",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e",
|
||||||
|
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x0",
|
||||||
|
"0x1"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e",
|
||||||
|
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x2523648240000001ba344d80000000086121000000000013a700000000000012",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5",
|
||||||
|
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e"
|
||||||
|
)]]
|
||||||
|
|
||||||
|
# ψ (Psi) - Untwist-Frobenius-Twist Endomorphisms on twisted curves
|
||||||
|
# -----------------------------------------------------------------
|
||||||
|
|
||||||
|
# BN254_Snarks is a D-Twist: SNR^((p-1)/6)
|
||||||
|
const FrobPsiConst_BN254_Nogami_psi1_coef1* = Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x1b377619212e7c8cb6499b50a846953f850974924d3f77c2e17de6c06f2a6de9",
|
||||||
|
"0x9ebee691ed1837503eab22f57b96ac8dc178b6db2c08850c582193f90d5922a"
|
||||||
|
)
|
||||||
|
# SNR^((p-1)/3)
|
||||||
|
const FrobPsiConst_BN254_Nogami_psi1_coef2* = Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x0",
|
||||||
|
"0x25236482400000017080eb4000000006181800000000000cd98000000000000b"
|
||||||
|
)
|
||||||
|
# SNR^((p-1)/2)
|
||||||
|
const FrobPsiConst_BN254_Nogami_psi1_coef3* = Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5",
|
||||||
|
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5"
|
||||||
|
)
|
||||||
|
# norm(SNR)^((p-1)/3)
|
||||||
|
const FrobPsiConst_BN254_Nogami_psi2_coef2* = Fp2[BN254_Nogami].fromHex(
|
||||||
|
"0x49b36240000000024909000000000006cd80000000000007",
|
||||||
|
"0x0"
|
||||||
|
)
|
||||||
|
|
@ -0,0 +1,119 @@
|
||||||
|
# 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
|
||||||
|
../config/curves,
|
||||||
|
../towers,
|
||||||
|
../io/io_towers
|
||||||
|
|
||||||
|
# Frobenius map - on extension fields
|
||||||
|
# -----------------------------------------------------------------
|
||||||
|
|
||||||
|
# c = (SNR^((p-1)/6)^coef).
|
||||||
|
# Then for frobenius(2): c * conjugate(c)
|
||||||
|
# And for frobenius(3): c² * conjugate(c)
|
||||||
|
const FrobMapConst_BN254_Snarks* = [
|
||||||
|
# frobenius(1)
|
||||||
|
[Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^0
|
||||||
|
"0x1",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^1
|
||||||
|
"0x1284b71c2865a7dfe8b99fdd76e68b605c521e08292f2176d60b35dadcc9e470",
|
||||||
|
"0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
|
||||||
|
"0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d",
|
||||||
|
"0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
|
||||||
|
"0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a",
|
||||||
|
"0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
|
||||||
|
"0x5b54f5e64eea80180f3c0b75a181e84d33365f7be94ec72848a1f55921ea762",
|
||||||
|
"0x2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^5
|
||||||
|
"0x183c1e74f798649e93a3661a4353ff4425c459b55aa1bd32ea2c810eab7692f",
|
||||||
|
"0x12acf2ca76fd0675a27fb246c7729f7db080cb99678e2ac024c6b8ee6e0c2c4b"
|
||||||
|
)],
|
||||||
|
# frobenius(2)
|
||||||
|
[Fp2[BN254_Snarks].fromHex( # norm(SNR)^((p-1)/6)^1
|
||||||
|
"0x1",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex( # norm(SNR)^((p-1)/6)^2
|
||||||
|
"0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff",
|
||||||
|
"0x0"
|
||||||
|
)],
|
||||||
|
# frobenius(3)
|
||||||
|
[Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x1",
|
||||||
|
"0x0"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x19dc81cfcc82e4bbefe9608cd0acaa90894cb38dbe55d24ae86f7d391ed4a67f",
|
||||||
|
"0xabf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x856e078b755ef0abaff1c77959f25ac805ffd3d5d6942d37b746ee87bdcfb6d",
|
||||||
|
"0x4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x2a275b6d9896aa4cdbf17f1dca9e5ea3bbd689a3bea870f45fcc8ad066dce9ed",
|
||||||
|
"0x28a411b634f09b8fb14b900e9507e9327600ecc7d8cf6ebab94d0cb3b2594c64"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0xbc58c6611c08dab19bee0f7b5b2444ee633094575b06bcb0e1a92bc3ccbf066",
|
||||||
|
"0x23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f"
|
||||||
|
),
|
||||||
|
Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x13c49044952c0905711699fa3b4d3f692ed68098967c84a5ebde847076261b43",
|
||||||
|
"0x16db366a59b1dd0b9fb1b2282a48633d3e2ddaea200280211f25041384282499"
|
||||||
|
)]]
|
||||||
|
|
||||||
|
# ψ (Psi) - Untwist-Frobenius-Twist Endomorphisms on twisted curves
|
||||||
|
# -----------------------------------------------------------------
|
||||||
|
|
||||||
|
# BN254_Snarks is a D-Twist: SNR^((p-1)/6)
|
||||||
|
const FrobPsiConst_BN254_Snarks_psi1_coef1* = Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x1284b71c2865a7dfe8b99fdd76e68b605c521e08292f2176d60b35dadcc9e470",
|
||||||
|
"0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac"
|
||||||
|
)
|
||||||
|
# SNR^((p-1)/3)
|
||||||
|
const FrobPsiConst_BN254_Snarks_psi1_coef2* = Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d",
|
||||||
|
"0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2"
|
||||||
|
)
|
||||||
|
# SNR^((p-1)/2)
|
||||||
|
const FrobPsiConst_BN254_Snarks_psi1_coef3* = Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a",
|
||||||
|
"0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3"
|
||||||
|
)
|
||||||
|
# norm(SNR)^((p-1)/3)
|
||||||
|
const FrobPsiConst_BN254_Snarks_psi2_coef2* = Fp2[BN254_Snarks].fromHex(
|
||||||
|
"0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48",
|
||||||
|
"0x0"
|
||||||
|
)
|
||||||
|
|
@ -0,0 +1,19 @@
|
||||||
|
# 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
|
||||||
|
./bls12_377_frobenius,
|
||||||
|
./bls12_381_frobenius,
|
||||||
|
./bn254_nogami_frobenius,
|
||||||
|
./bn254_snarks_frobenius
|
||||||
|
|
||||||
|
export
|
||||||
|
bls12_377_frobenius,
|
||||||
|
bls12_381_frobenius,
|
||||||
|
bn254_nogami_frobenius,
|
||||||
|
bn254_snarks_frobenius
|
||||||
|
|
@ -8,9 +8,10 @@
|
||||||
|
|
||||||
import
|
import
|
||||||
std/macros,
|
std/macros,
|
||||||
../config/[common, curves],
|
../config/curves,
|
||||||
../io/io_towers,
|
../arithmetic,
|
||||||
../towers, ../arithmetic
|
../towers,
|
||||||
|
../curves/constants_frobenius
|
||||||
|
|
||||||
# Frobenius Map
|
# Frobenius Map
|
||||||
# ------------------------------------------------------------
|
# ------------------------------------------------------------
|
||||||
|
|
@ -66,320 +67,6 @@ template mulCheckSparse[Fp2](a: var Fp2, b: Fp2) =
|
||||||
# Frobenius map - on extension fields
|
# Frobenius map - on extension fields
|
||||||
# -----------------------------------------------------------------
|
# -----------------------------------------------------------------
|
||||||
|
|
||||||
# c = (SNR^((p-1)/6)^coef).
|
|
||||||
# Then for frobenius(2): c * conjugate(c)
|
|
||||||
# And for frobenius(3): c² * conjugate(c)
|
|
||||||
const FrobMapConst_BLS12_377 = [
|
|
||||||
# frobenius(1)
|
|
||||||
[Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^0
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^1
|
|
||||||
"0x9a9975399c019633c1e30682567f915c8a45e0f94ebc8ec681bf34a3aa559db57668e558eb0188e938a9d1104f2031",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
|
|
||||||
"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000002",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
|
|
||||||
"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
|
|
||||||
"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000001",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex( # SNR^((p-1)/6)^5
|
|
||||||
"0xcd70cb3fc936348d0351d498233f1fe379531411832232f6648a9a9fc0b9c4e3e21b7467077c05853e2c1be0e9fc32",
|
|
||||||
"0x0"
|
|
||||||
)],
|
|
||||||
# frobenius(2)
|
|
||||||
[Fp2[BLS12_377].fromHex( # norm(SNR)^((p-1)/6)^1
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex( # norm(SNR)^((p-1)/6)^2
|
|
||||||
"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000002",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000001",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000000",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1ae3a4617c510eabc8756ba8f8c524eb8882a75cc9bc8e359064ee822fb5bffd1e945779fffffffffffffffffffffff",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1ae3a4617c510eabc8756ba8f8c524eb8882a75cc9bc8e359064ee822fb5bffd1e94577a00000000000000000000000",
|
|
||||||
"0x0"
|
|
||||||
)],
|
|
||||||
# frobenius(3)
|
|
||||||
[Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000000",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x4630059e5fd9200575d0e552278a89da1f40fdf62334cd620d1860769e389d7db2d8ea700d82721691ea130ec6e39e",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
|
|
||||||
"0x0"
|
|
||||||
)]]
|
|
||||||
|
|
||||||
# c = (SNR^((p-1)/6)^coef).
|
|
||||||
# Then for frobenius(2): c * conjugate(c)
|
|
||||||
# And for frobenius(3): c² * conjugate(c)
|
|
||||||
const FrobMapConst_BLS12_381 = [
|
|
||||||
# frobenius(1)
|
|
||||||
[Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^0
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^1
|
|
||||||
"0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8",
|
|
||||||
"0xfc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
|
|
||||||
"0x0",
|
|
||||||
"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
|
|
||||||
"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09",
|
|
||||||
"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
|
|
||||||
"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex( # SNR^((p-1)/6)^5
|
|
||||||
"0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116",
|
|
||||||
"0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995"
|
|
||||||
)],
|
|
||||||
# frobenius(2)
|
|
||||||
[Fp2[BLS12_381].fromHex( # norm(SNR)^((p-1)/6)^1
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex( # norm(SNR)^((p-1)/6)^2
|
|
||||||
"0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffff",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffe",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad",
|
|
||||||
"0x0"
|
|
||||||
)],
|
|
||||||
# frobenius(3)
|
|
||||||
[Fp2[BLS12_381].fromHex(
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2",
|
|
||||||
"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x0",
|
|
||||||
"0x1"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2",
|
|
||||||
"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BLS12_381].fromHex(
|
|
||||||
"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09",
|
|
||||||
"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2"
|
|
||||||
)]]
|
|
||||||
|
|
||||||
const FrobMapConst_BN254_Nogami = [
|
|
||||||
# frobenius(1)
|
|
||||||
[Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^0
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^1
|
|
||||||
"0x1b377619212e7c8cb6499b50a846953f850974924d3f77c2e17de6c06f2a6de9",
|
|
||||||
"0x9ebee691ed1837503eab22f57b96ac8dc178b6db2c08850c582193f90d5922a"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
|
|
||||||
"0x0",
|
|
||||||
"0x25236482400000017080eb4000000006181800000000000cd98000000000000b"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
|
|
||||||
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5",
|
|
||||||
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
|
|
||||||
"0x25236482400000017080eb4000000006181800000000000cd98000000000000c",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex( # SNR^((p-1)/6)^5
|
|
||||||
"0x19f3db6884cdca43c2b0d5792cd135accb1baea0b017046e859975ab54b5ef9b",
|
|
||||||
"0xb2f8919bb3235bdf7837806d32eca5b9605515f4fe8fba521668a54ab4a1078"
|
|
||||||
)],
|
|
||||||
# frobenius(2)
|
|
||||||
[Fp2[BN254_Nogami].fromHex( # norm(SNR)^((p-1)/6)^1
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex( # norm(SNR)^((p-1)/6)^2
|
|
||||||
"0x49b36240000000024909000000000006cd80000000000008",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x49b36240000000024909000000000006cd80000000000007",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x2523648240000001ba344d80000000086121000000000013a700000000000012",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x25236482400000017080eb4000000006181800000000000cd98000000000000b",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x25236482400000017080eb4000000006181800000000000cd98000000000000c",
|
|
||||||
"0x0"
|
|
||||||
)],
|
|
||||||
# frobenius(3)
|
|
||||||
[Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e",
|
|
||||||
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x0",
|
|
||||||
"0x1"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e",
|
|
||||||
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x2523648240000001ba344d80000000086121000000000013a700000000000012",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5",
|
|
||||||
"0x1439ab09c60b248f398c5d77b755f92b9edc5f19d2873545be471151a747e4e"
|
|
||||||
)]]
|
|
||||||
|
|
||||||
const FrobMapConst_BN254_Snarks = [
|
|
||||||
# frobenius(1)
|
|
||||||
[Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^0
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^1
|
|
||||||
"0x1284b71c2865a7dfe8b99fdd76e68b605c521e08292f2176d60b35dadcc9e470",
|
|
||||||
"0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^2 = SNR^((p-1)/3)
|
|
||||||
"0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d",
|
|
||||||
"0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^3 = SNR^((p-1)/2)
|
|
||||||
"0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a",
|
|
||||||
"0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^4 = SNR^(2(p-1)/3)
|
|
||||||
"0x5b54f5e64eea80180f3c0b75a181e84d33365f7be94ec72848a1f55921ea762",
|
|
||||||
"0x2c145edbe7fd8aee9f3a80b03b0b1c923685d2ea1bdec763c13b4711cd2b8126"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex( # SNR^((p-1)/6)^5
|
|
||||||
"0x183c1e74f798649e93a3661a4353ff4425c459b55aa1bd32ea2c810eab7692f",
|
|
||||||
"0x12acf2ca76fd0675a27fb246c7729f7db080cb99678e2ac024c6b8ee6e0c2c4b"
|
|
||||||
)],
|
|
||||||
# frobenius(2)
|
|
||||||
[Fp2[BN254_Snarks].fromHex( # norm(SNR)^((p-1)/6)^1
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex( # norm(SNR)^((p-1)/6)^2
|
|
||||||
"0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd49",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd46",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177fffffe",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x59e26bcea0d48bacd4f263f1acdb5c4f5763473177ffffff",
|
|
||||||
"0x0"
|
|
||||||
)],
|
|
||||||
# frobenius(3)
|
|
||||||
[Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x1",
|
|
||||||
"0x0"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x19dc81cfcc82e4bbefe9608cd0acaa90894cb38dbe55d24ae86f7d391ed4a67f",
|
|
||||||
"0xabf8b60be77d7306cbeee33576139d7f03a5e397d439ec7694aa2bf4c0c101"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x856e078b755ef0abaff1c77959f25ac805ffd3d5d6942d37b746ee87bdcfb6d",
|
|
||||||
"0x4f1de41b3d1766fa9f30e6dec26094f0fdf31bf98ff2631380cab2baaa586de"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x2a275b6d9896aa4cdbf17f1dca9e5ea3bbd689a3bea870f45fcc8ad066dce9ed",
|
|
||||||
"0x28a411b634f09b8fb14b900e9507e9327600ecc7d8cf6ebab94d0cb3b2594c64"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0xbc58c6611c08dab19bee0f7b5b2444ee633094575b06bcb0e1a92bc3ccbf066",
|
|
||||||
"0x23d5e999e1910a12feb0f6ef0cd21d04a44a9e08737f96e55fe3ed9d730c239f"
|
|
||||||
),
|
|
||||||
Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x13c49044952c0905711699fa3b4d3f692ed68098967c84a5ebde847076261b43",
|
|
||||||
"0x16db366a59b1dd0b9fb1b2282a48633d3e2ddaea200280211f25041384282499"
|
|
||||||
)]]
|
|
||||||
|
|
||||||
{.experimental: "dynamicBindSym".}
|
{.experimental: "dynamicBindSym".}
|
||||||
|
|
||||||
macro frobMapConst(C: static Curve): untyped =
|
macro frobMapConst(C: static Curve): untyped =
|
||||||
|
|
@ -418,96 +105,11 @@ func frobenius_map*[C](r: var Fp12[C], a: Fp12[C], k: static int = 1) {.inline.}
|
||||||
|
|
||||||
# ψ (Psi) - Untwist-Frobenius-Twist Endomorphisms on twisted curves
|
# ψ (Psi) - Untwist-Frobenius-Twist Endomorphisms on twisted curves
|
||||||
# -----------------------------------------------------------------
|
# -----------------------------------------------------------------
|
||||||
# TODO: generate those constants via Sage in a Json file
|
|
||||||
# and parse at compile-time
|
|
||||||
|
|
||||||
# Constants:
|
# Constants:
|
||||||
# Assuming embedding degree of 12 and a sextic twist
|
# Assuming embedding degree of 12 and a sextic twist
|
||||||
# with SNR the sextic non-residue
|
# with SNR the sextic non-residue
|
||||||
#
|
#
|
||||||
# BN254_Snarks is a D-Twist: SNR^((p-1)/6)
|
|
||||||
const FrobPsiConst_BN254_Snarks_psi1_coef1 = Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x1284b71c2865a7dfe8b99fdd76e68b605c521e08292f2176d60b35dadcc9e470",
|
|
||||||
"0x246996f3b4fae7e6a6327cfe12150b8e747992778eeec7e5ca5cf05f80f362ac"
|
|
||||||
)
|
|
||||||
# SNR^((p-1)/3)
|
|
||||||
const FrobPsiConst_BN254_Snarks_psi1_coef2 = Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x2fb347984f7911f74c0bec3cf559b143b78cc310c2c3330c99e39557176f553d",
|
|
||||||
"0x16c9e55061ebae204ba4cc8bd75a079432ae2a1d0b7c9dce1665d51c640fcba2"
|
|
||||||
)
|
|
||||||
# SNR^((p-1)/2)
|
|
||||||
const FrobPsiConst_BN254_Snarks_psi1_coef3 = Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x63cf305489af5dcdc5ec698b6e2f9b9dbaae0eda9c95998dc54014671a0135a",
|
|
||||||
"0x7c03cbcac41049a0704b5a7ec796f2b21807dc98fa25bd282d37f632623b0e3"
|
|
||||||
)
|
|
||||||
# norm(SNR)^((p-1)/3)
|
|
||||||
const FrobPsiConst_BN254_Snarks_psi2_coef2 = Fp2[BN254_Snarks].fromHex(
|
|
||||||
"0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
|
|
||||||
# BN254_Nogami is a D-Twist: SNR^((p-1)/6)
|
|
||||||
const FrobPsiConst_BN254_Nogami_psi1_coef1 = Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x1b377619212e7c8cb6499b50a846953f850974924d3f77c2e17de6c06f2a6de9",
|
|
||||||
"0x9ebee691ed1837503eab22f57b96ac8dc178b6db2c08850c582193f90d5922a"
|
|
||||||
)
|
|
||||||
# SNR^((p-1)/3)
|
|
||||||
const FrobPsiConst_BN254_Nogami_psi1_coef2 = Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x0",
|
|
||||||
"0x25236482400000017080eb4000000006181800000000000cd98000000000000b"
|
|
||||||
)
|
|
||||||
# SNR^((p-1)/2)
|
|
||||||
const FrobPsiConst_BN254_Nogami_psi1_coef3 = Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5",
|
|
||||||
"0x23dfc9d1a39f4db8c69b87a8848aa075a7333a0e62d78cbf4b1b8eeae58b81c5"
|
|
||||||
)
|
|
||||||
# norm(SNR)^((p-1)/3)
|
|
||||||
const FrobPsiConst_BN254_Nogami_psi2_coef2 = Fp2[BN254_Nogami].fromHex(
|
|
||||||
"0x49b36240000000024909000000000006cd80000000000007",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
|
|
||||||
# BLS12_377 is a D-Twist: SNR^((p-1)/6)
|
|
||||||
const FrobPsiConst_BLS12_377_psi1_coef1 = Fp2[BLS12_377].fromHex(
|
|
||||||
"0x9a9975399c019633c1e30682567f915c8a45e0f94ebc8ec681bf34a3aa559db57668e558eb0188e938a9d1104f2031",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
# SNR^((p-1)/3)
|
|
||||||
const FrobPsiConst_BLS12_377_psi1_coef2 = Fp2[BLS12_377].fromHex(
|
|
||||||
"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000002",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
# SNR^((p-1)/2)
|
|
||||||
const FrobPsiConst_BLS12_377_psi1_coef3 = Fp2[BLS12_377].fromHex(
|
|
||||||
"0x1680a40796537cac0c534db1a79beb1400398f50ad1dec1bce649cf436b0f6299588459bff27d8e6e76d5ecf1391c63",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
# norm(SNR)^((p-1)/3)
|
|
||||||
const FrobPsiConst_BLS12_377_psi2_coef2 = Fp2[BLS12_377].fromHex(
|
|
||||||
"0x9b3af05dd14f6ec619aaf7d34594aabc5ed1347970dec00452217cc900000008508c00000000001",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
|
|
||||||
# BLS12_381 is a M-twist: (1/SNR)^((p-1)/6)
|
|
||||||
const FrobPsiConst_BLS12_381_psi1_coef1 = Fp2[BLS12_381].fromHex(
|
|
||||||
"0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116",
|
|
||||||
"0x5b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116"
|
|
||||||
)
|
|
||||||
# (1/SNR)^((p-1)/3)
|
|
||||||
const FrobPsiConst_BLS12_381_psi1_coef2 = Fp2[BLS12_381].fromHex(
|
|
||||||
"0x0",
|
|
||||||
"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaad"
|
|
||||||
)
|
|
||||||
# (1/SNR)^((p-1)/2)
|
|
||||||
const FrobPsiConst_BLS12_381_psi1_coef3 = Fp2[BLS12_381].fromHex(
|
|
||||||
"0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2",
|
|
||||||
"0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09"
|
|
||||||
)
|
|
||||||
# norm(SNR)^((p-1)/3)
|
|
||||||
const FrobPsiConst_BLS12_381_psi2_coef2 = Fp2[BLS12_381].fromHex(
|
|
||||||
"0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac",
|
|
||||||
"0x0"
|
|
||||||
)
|
|
||||||
|
|
||||||
macro frobPsiConst(C: static Curve, psipow, coefpow: static int): untyped =
|
macro frobPsiConst(C: static Curve, psipow, coefpow: static int): untyped =
|
||||||
return bindSym("FrobPsiConst_" & $C & "_psi" & $psipow & "_coef" & $coefpow)
|
return bindSym("FrobPsiConst_" & $C & "_psi" & $psipow & "_coef" & $coefpow)
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue