2020-03-21 16:42:06 +00:00
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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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# BN Curves parameters
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# (Barreto-Naehrig curves)
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#
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# ############################################################
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#
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# This module derives a BN curve parameters from
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# its base parameter u
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2020-03-21 14:50:39 +00:00
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def compute_curve_characteristic(u_str):
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u = sage_eval(u_str)
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p = 36*u^4 + 36*u^3 + 24*u^2 + 6*u + 1
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r = 36*u^4 + 36*u^3 + 18*u^2 + 6*u + 1
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print(f'BN family - {p.nbits()} bits')
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print(' Prime modulus: 0x' + p.hex())
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print(' Curve order: 0x' + r.hex())
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print(' Parameter u: ' + u_str)
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if u < 0:
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print(' Parameter u (hex): -0x' + (-u).hex())
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else:
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print(' Parameter u (hex): 0x' + u.hex())
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if __name__ == "__main__":
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# Usage
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# sage sage/curve_family_bn.sage '-(2^62 + 2^55 + 1)'
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from argparse import ArgumentParser
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parser = ArgumentParser()
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parser.add_argument("curve_param",nargs="+")
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args = parser.parse_args()
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compute_curve_characteristic(args.curve_param[0])
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