157 lines
3.9 KiB
Python
157 lines
3.9 KiB
Python
#!/usr/bin/sage
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# vim: syntax=python
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# vim: set ts=2 sw=2 et:
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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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# ############################################################
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#
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# Curves configuration
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#
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# ############################################################
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import inspect
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# Accelerate arithmetic by accepting probabilistic proofs
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from sage.structure.proof.all import arithmetic
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arithmetic(False)
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def derive_BN_field(x):
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params = {
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'param': x,
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'modulus': 36*x^4 + 36*x^3 + 24*x^2 + 6*x + 1,
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'order': 36*x^4 + 36*x^3 + 18*x^2 + 6*x + 1,
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'trace': 6*x^2 + 1,
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'family': 'BN'
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}
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return params
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def derive_BLS12_field(x):
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params = {
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'param': x,
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'modulus': (x - 1)^2 * (x^4 - x^2 + 1)//3 + x,
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'order': x^4 - x^2 + 1,
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'trace': x + 1,
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'family': 'BLS12'
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}
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return params
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def derive_BW6_compose_BLS12_field(x, cofactor_trace, cofactor_y):
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# Brezing-Weng input
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r = (x^6 - 2*x^5 + 2*x^3 + x + 1) // 3 # BLS12 modulus
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# 6-th root of unity output + cofactors
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t = x^5 - 3*x^4 + 3*x^3 - x + 3 + cofactor_trace*r
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y = (x^5 - 3*x^4 + 3*x^3 - x + 3)//3 + cofactor_y*r
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# Curve parameters
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p = (t^2 + 3*y^2)/4
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trace = p+1-r # (3*y+t)/2
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params = {
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'param': x,
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'modulus': p,
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'order': r,
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'trace': trace,
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'family': 'BW6'
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}
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return params
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def copyright():
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return inspect.cleandoc("""
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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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""")
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Curves = {
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'BN254_Nogami': {
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'field': derive_BN_field(-(2^62 + 2^55 + 1)),
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'curve': {
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'form': 'short_weierstrass',
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'a': 0,
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'b': 2
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},
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'tower': {
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'embedding_degree': 12,
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'twist_degree': 6,
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'QNR_Fp': -1,
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'SNR_Fp2': [1, 1],
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'twist': 'D_Twist'
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}
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},
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'BN254_Snarks': {
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'field': derive_BN_field(Integer('0x44e992b44a6909f1')),
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'curve': {
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'form': 'short_weierstrass',
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'a': 0,
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'b': 3
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},
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'tower': {
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'embedding_degree': 12,
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'twist_degree': 6,
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'QNR_Fp': -1,
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'SNR_Fp2': [9, 1],
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'twist': 'D_Twist'
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}
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},
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'BLS12_377': {
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'field': derive_BLS12_field(3 * 2^46 * (7 * 13 * 499) + 1),
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'curve': {
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'form': 'short_weierstrass',
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'a': 0,
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'b': 1
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},
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'tower': {
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'embedding_degree': 12,
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'twist_degree': 6,
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'QNR_Fp': -5,
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'SNR_Fp2': [0, 1],
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'twist': 'D_Twist'
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}
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},
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'BLS12_381': {
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'field': derive_BLS12_field(-(2^63 + 2^62 + 2^60 + 2^57 + 2^48 + 2^16)),
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'curve': {
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'form': 'short_weierstrass',
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'a': 0,
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'b': 4
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},
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'tower': {
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'embedding_degree': 12,
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'twist_degree': 6,
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'QNR_Fp': -1,
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'SNR_Fp2': [1, 1],
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'twist': 'M_Twist'
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}
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},
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'BW6_761': {
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'field': derive_BW6_compose_BLS12_field(
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3 * 2^46 * (7 * 13 * 499) + 1,
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cofactor_trace = 13,
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cofactor_y = 9
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),
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'curve': {
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'form': 'short_weierstrass',
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'a': 0,
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'b': -1
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},
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'tower': {
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'embedding_degree': 6,
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'twist_degree': 6,
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'SNR_Fp': -4,
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'twist': 'M_Twist'
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}
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}
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}
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