56 lines
2.8 KiB
C++
56 lines
2.8 KiB
C++
// Copyright (c) 2021-2022 Zano Project
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// Copyright (c) 2021-2022 sowle (val@zano.org, crypto.sowle@gmail.com)
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// Distributed under the MIT/X11 software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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//
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#pragma once
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//
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// Tosion elements of ed25519 group in canonical and non-canonical form
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//
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// (partly inspired by "Taming the many EdDSAs" by Chalkias et al https://eprint.iacr.org/2020/1244.pdf)
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//
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namespace crypto
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{
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// let ty = -sqrt((-sqrt(D+1)-1) / D), is_neg(ty) == false
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// canonical serialization sig order EC point
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// 26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05 0 8 (sqrt(-1)*ty, ty)
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// 0000000000000000000000000000000000000000000000000000000000000000 0 4 (sqrt(-1), 0)
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// c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a 0 8 (sqrt(-1)*ty, -ty)
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// ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f 0 2 (0, -1)
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// c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa 1 8 (-sqrt(-1)*ty, -ty)
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// 0000000000000000000000000000000000000000000000000000000000000080 1 4 (-sqrt(-1), 0)
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// 26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85 1 8 (-sqrt(-1)*ty, ty)
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struct canonical_torsion_elements_t
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{
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const char* string;
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bool sign;
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uint8_t order;
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uint8_t incorrect_order_0;
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uint8_t incorrect_order_1;
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};
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canonical_torsion_elements_t canonical_torsion_elements[] = {
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{"26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc05", false, 8, 4, 2},
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{"0000000000000000000000000000000000000000000000000000000000000000", false, 4, 2, 6},
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{"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a", false, 8, 4, 2},
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{"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f", false, 2, 5, 3},
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{"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa", true, 8, 4, 2},
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{"0000000000000000000000000000000000000000000000000000000000000080", true, 4, 2, 6},
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{"26e8958fc2b227b045c3f489f2ef98f0d5dfac05d3c63339b13802886d53fc85", true, 8, 4, 2}
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};
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// non-canonical elements (should not load at all thanks to the checks in ge_frombytes_vartime)
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const char* noncanonical_torsion_elements[] = {
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"0100000000000000000000000000000000000000000000000000000000000080", // (-0, 1)
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"ECFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", // (-0, -1)
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"EEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F", // (0, 2*255-18)
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"EEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", // (-0, 2*255-18)
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"EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7F", // (sqrt(-1), 2*255-19)
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"EDFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" // (-sqrt(-1), 2*255-19)
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};
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} // namespace crypto
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