149 lines
4.1 KiB
Python
149 lines
4.1 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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# Frobenius constants
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#
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# ############################################################
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# Imports
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# ---------------------------------------------------------
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import os
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import inspect, textwrap
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# Working directory
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# ---------------------------------------------------------
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os.chdir(os.path.dirname(__file__))
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# Sage imports
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# ---------------------------------------------------------
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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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load('curves.sage')
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# Utilities
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# ---------------------------------------------------------
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def fp2_to_hex(a):
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v = vector(a)
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return '0x' + Integer(v[0]).hex() + ' + β * ' + '0x' + Integer(v[1]).hex()
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def field_to_nim(value, field, curve, prefix = "", comment_above = "", comment_right = ""):
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result = '# ' + comment_above + '\n' if comment_above else ''
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comment_right = ' # ' + comment_right if comment_right else ''
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if field == 'Fp2':
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v = vector(value)
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result += inspect.cleandoc(f"""
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{prefix}Fp2[{curve}].fromHex( {comment_right}
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"0x{Integer(v[0]).hex()}",
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"0x{Integer(v[1]).hex()}"
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)""")
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elif field == 'Fp':
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result += inspect.cleandoc(f"""
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{prefix}Fp[{curve}].fromHex( {comment_right}
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"0x{Integer(value).hex()}")
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""")
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else:
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raise NotImplementedError()
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return result
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# Code generators
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# ---------------------------------------------------------
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def genSqrtFp2Constants(curve_name, curve_config):
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embdeg = curve_config[curve_name]['tower']['embedding_degree']
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twdeg = curve_config[curve_name]['tower']['twist_degree']
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g2field = f'Fp{embdeg//twdeg}' if (embdeg//twdeg) > 1 else 'Fp'
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p = curve_config[curve_name]['field']['modulus']
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Fp = GF(p)
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K.<u> = PolynomialRing(Fp)
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if g2field == 'Fp2':
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QNR_Fp = curve_config[curve_name]['tower']['QNR_Fp']
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Fp2.<beta> = Fp.extension(u^2 - QNR_Fp)
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else:
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SNR_Fp = curve_config[curve_name]['tower']['SNR_Fp']
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Fp2.<beta> = Fp.extension(u^2 - SNR_Fp)
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sqrt_QNR = Fp2([0, 1])
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sqrt_sqrt_QNR = sqrt_QNR.sqrt()
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sqrt_minus_sqrt_QNR = (-sqrt_QNR).sqrt()
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print('\n----> Square root on Fp2 constants <----\n')
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buf = inspect.cleandoc(f"""
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# Square Root Fp2 constants
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# -----------------------------------------------------------------
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""")
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buf += '\n'
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buf += f'const {curve_name}_sqrt_QNR* = '
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buf += field_to_nim(sqrt_QNR, 'Fp2', curve_name)
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buf += '\n'
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buf += f'const {curve_name}_sqrt_sqrt_QNR* = '
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buf += field_to_nim(sqrt_sqrt_QNR, 'Fp2', curve_name)
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buf += '\n'
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buf += f'const {curve_name}_sqrt_minus_sqrt_QNR* = '
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buf += field_to_nim(sqrt_minus_sqrt_QNR, 'Fp2', curve_name)
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buf += '\n'
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return buf
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# CLI
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# ---------------------------------------------------------
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if __name__ == "__main__":
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# Usage
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# BLS12-381
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# sage sage/derive_sqrt.sage BLS12_381
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from argparse import ArgumentParser
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parser = ArgumentParser()
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parser.add_argument("curve",nargs="+")
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args = parser.parse_args()
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curve = args.curve[0]
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if curve not in Curves:
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raise ValueError(
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curve +
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' is not one of the available curves: ' +
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str(Curves.keys())
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)
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else:
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sqrt = genSqrtFp2Constants(curve, Curves)
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with open(f'{curve.lower()}_square_root.nim', 'w') as f:
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f.write(copyright())
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f.write('\n\n')
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f.write(inspect.cleandoc("""
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import
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../config/curves,
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../io/io_towers
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"""))
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f.write('\n\n')
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f.write(sqrt)
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print(f'Successfully created {curve}_sqrt_fp2.nim')
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