648 lines
24 KiB
C#
648 lines
24 KiB
C#
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/*
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* Secucore
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*
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* Copyright (C) 2023 Trevor Hall
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* All rights reserved.
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*
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* This software may be modified and distributed under the terms
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* of the MIT license.
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*
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*/
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using System;
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using System.Security.Cryptography;
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namespace SecuCore.Curves
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{
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public class Curve25519
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{
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public const int KeySize = 32;
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static readonly byte[] Order = { 237, 211, 245, 92, 26, 99, 18, 88, 214, 156, 247, 162, 222, 249, 222, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16 };
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public static void ClampPrivateKeyInline(byte[] key)
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{
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if (key == null)
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throw new ArgumentNullException("key");
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if (key.Length != 32)
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throw new ArgumentException(String.Format("key must be 32 bytes long (but was {0} bytes long)", key.Length));
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key[31] &= 0x7F;
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key[31] |= 0x40;
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key[0] &= 0xF8;
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}
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public static byte[] ClampPrivateKey(byte[] rawKey)
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{
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if (rawKey == null)
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throw new ArgumentNullException("rawKey");
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if (rawKey.Length != 32)
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throw new ArgumentException(String.Format("rawKey must be 32 bytes long (but was {0} bytes long)", rawKey.Length), "rawKey");
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var res = new byte[32];
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Array.Copy(rawKey, res, 32);
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res[31] &= 0x7F;
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res[31] |= 0x40;
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res[0] &= 0xF8;
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return res;
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}
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public static byte[] CreateRandomPrivateKey()
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{
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var privateKey = new byte[32];
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privateKey = RandomNumberGenerator.GetBytes(32);
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ClampPrivateKeyInline(privateKey);
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return privateKey;
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}
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public static void KeyGenInline(byte[] publicKey, byte[] signingKey, byte[] privateKey)
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{
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if (publicKey == null)
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throw new ArgumentNullException("publicKey");
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if (publicKey.Length != 32)
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throw new ArgumentException(String.Format("publicKey must be 32 bytes long (but was {0} bytes long)", publicKey.Length), "publicKey");
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if (signingKey == null)
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throw new ArgumentNullException("signingKey");
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if (signingKey.Length != 32)
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throw new ArgumentException(String.Format("signingKey must be 32 bytes long (but was {0} bytes long)", signingKey.Length), "signingKey");
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if (privateKey == null)
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throw new ArgumentNullException("privateKey");
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if (privateKey.Length != 32)
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throw new ArgumentException(String.Format("privateKey must be 32 bytes long (but was {0} bytes long)", privateKey.Length), "privateKey");
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privateKey = RandomNumberGenerator.GetBytes(32);
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ClampPrivateKeyInline(privateKey);
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Core(publicKey, signingKey, privateKey, null);
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}
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public static byte[] GetPublicKey(byte[] privateKey)
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{
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var publicKey = new byte[32];
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Core(publicKey, null, privateKey, null);
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return publicKey;
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}
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public static byte[] GetSigningKey(byte[] privateKey)
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{
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var signingKey = new byte[32];
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var publicKey = new byte[32];
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Core(publicKey, signingKey, privateKey, null);
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return signingKey;
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}
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public static byte[] GetSharedSecret(byte[] privateKey, byte[] peerPublicKey)
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{
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var sharedSecret = new byte[32];
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Core(sharedSecret, null, privateKey, peerPublicKey);
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return sharedSecret;
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}
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private sealed class Long10
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{
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public Long10() { }
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public Long10(long n0, long n1, long n2, long n3, long n4, long n5, long n6, long n7, long n8, long n9)
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{
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N0 = n0;
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N1 = n1;
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N2 = n2;
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N3 = n3;
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N4 = n4;
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N5 = n5;
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N6 = n6;
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N7 = n7;
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N8 = n8;
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N9 = n9;
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}
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public long N0, N1, N2, N3, N4, N5, N6, N7, N8, N9;
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}
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static void Copy32(byte[] source, byte[] destination) { Array.Copy(source, 0, destination, 0, 32); }
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static int
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MultiplyArraySmall(byte[] p, byte[] q, int m, byte[] x, int n, int z)
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{
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int v = 0;
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for (int i = 0; i < n; ++i)
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{
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v += (q[i + m] & 0xFF) + z * (x[i] & 0xFF);
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p[i + m] = (byte)v;
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v >>= 8;
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}
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return v;
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}
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static void
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MultiplyArray32(byte[] p, byte[] x, byte[] y, int t, int z)
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{
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const int n = 31;
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int w = 0;
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int i = 0;
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for (; i < t; i++)
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{
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int zy = z * (y[i] & 0xFF);
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w += MultiplyArraySmall(p, p, i, x, n, zy) + (p[i + n] & 0xFF) + zy * (x[n] & 0xFF);
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p[i + n] = (byte)w;
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w >>= 8;
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}
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p[i + n] = (byte)(w + (p[i + n] & 0xFF));
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}
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static void
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DivMod(byte[] q, byte[] r, int n, byte[] d, int t)
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{
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int rn = 0;
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int dt = ((d[t - 1] & 0xFF) << 8);
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if (t > 1)
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{
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dt |= (d[t - 2] & 0xFF);
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}
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while (n-- >= t)
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{
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int z = (rn << 16) | ((r[n] & 0xFF) << 8);
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if (n > 0)
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{
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z |= (r[n - 1] & 0xFF);
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}
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z /= dt;
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rn += MultiplyArraySmall(r, r, n - t + 1, d, t, -z);
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q[n - t + 1] = (byte)((z + rn) & 0xFF);
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MultiplyArraySmall(r, r, n - t + 1, d, t, -rn);
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rn = (r[n] & 0xFF);
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r[n] = 0;
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}
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r[t - 1] = (byte)rn;
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}
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static int
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GetNumSize(byte[] num, int maxSize)
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{
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for (int i = maxSize; i >= 0; i++)
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{
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if (num[i] == 0)
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return i + 1;
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}
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return 0;
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}
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static byte[] Egcd32(byte[] x, byte[] y, byte[] a, byte[] b)
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{
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int bn = 32;
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int i;
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for (i = 0; i < 32; i++)
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x[i] = y[i] = 0;
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x[0] = 1;
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int an = GetNumSize(a, 32);
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if (an == 0)
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return y;
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var temp = new byte[32];
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while (true)
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{
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int qn = bn - an + 1;
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DivMod(temp, b, bn, a, an);
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bn = GetNumSize(b, bn);
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if (bn == 0)
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return x;
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MultiplyArray32(y, x, temp, qn, -1);
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qn = an - bn + 1;
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DivMod(temp, a, an, b, bn);
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an = GetNumSize(a, an);
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if (an == 0)
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return y;
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MultiplyArray32(x, y, temp, qn, -1);
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}
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}
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private const int P25 = 33554431;
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private const int P26 = 67108863;
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static void
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Unpack(Long10 x, byte[] m)
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{
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x.N0 = ((m[0] & 0xFF)) | ((m[1] & 0xFF)) << 8 | (m[2] & 0xFF) << 16 | ((m[3] & 0xFF) & 3) << 24;
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x.N1 = ((m[3] & 0xFF) & ~3) >> 2 | (m[4] & 0xFF) << 6 | (m[5] & 0xFF) << 14 | ((m[6] & 0xFF) & 7) << 22;
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x.N2 = ((m[6] & 0xFF) & ~7) >> 3 | (m[7] & 0xFF) << 5 | (m[8] & 0xFF) << 13 | ((m[9] & 0xFF) & 31) << 21;
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x.N3 = ((m[9] & 0xFF) & ~31) >> 5 | (m[10] & 0xFF) << 3 | (m[11] & 0xFF) << 11 | ((m[12] & 0xFF) & 63) << 19;
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x.N4 = ((m[12] & 0xFF) & ~63) >> 6 | (m[13] & 0xFF) << 2 | (m[14] & 0xFF) << 10 | (m[15] & 0xFF) << 18;
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x.N5 = (m[16] & 0xFF) | (m[17] & 0xFF) << 8 | (m[18] & 0xFF) << 16 | ((m[19] & 0xFF) & 1) << 24;
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x.N6 = ((m[19] & 0xFF) & ~1) >> 1 | (m[20] & 0xFF) << 7 | (m[21] & 0xFF) << 15 | ((m[22] & 0xFF) & 7) << 23;
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x.N7 = ((m[22] & 0xFF) & ~7) >> 3 | (m[23] & 0xFF) << 5 | (m[24] & 0xFF) << 13 | ((m[25] & 0xFF) & 15) << 21;
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x.N8 = ((m[25] & 0xFF) & ~15) >> 4 | (m[26] & 0xFF) << 4 | (m[27] & 0xFF) << 12 | ((m[28] & 0xFF) & 63) << 20;
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x.N9 = ((m[28] & 0xFF) & ~63) >> 6 | (m[29] & 0xFF) << 2 | (m[30] & 0xFF) << 10 | (m[31] & 0xFF) << 18;
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}
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static bool
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IsOverflow(Long10 x)
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{
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return (((x.N0 > P26 - 19)) & ((x.N1 & x.N3 & x.N5 & x.N7 & x.N9) == P25) & ((x.N2 & x.N4 & x.N6 & x.N8) == P26)) || (x.N9 > P25);
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}
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static void
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Pack(Long10 x, byte[] m)
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{
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int ld = (IsOverflow(x) ? 1 : 0) - ((x.N9 < 0) ? 1 : 0);
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int ud = ld * -(P25 + 1);
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ld *= 19;
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long t = ld + x.N0 + (x.N1 << 26);
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m[0] = (byte)t;
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m[1] = (byte)(t >> 8);
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m[2] = (byte)(t >> 16);
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m[3] = (byte)(t >> 24);
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t = (t >> 32) + (x.N2 << 19);
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m[4] = (byte)t;
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m[5] = (byte)(t >> 8);
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m[6] = (byte)(t >> 16);
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m[7] = (byte)(t >> 24);
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t = (t >> 32) + (x.N3 << 13);
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m[8] = (byte)t;
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m[9] = (byte)(t >> 8);
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m[10] = (byte)(t >> 16);
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m[11] = (byte)(t >> 24);
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t = (t >> 32) + (x.N4 << 6);
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m[12] = (byte)t;
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m[13] = (byte)(t >> 8);
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m[14] = (byte)(t >> 16);
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m[15] = (byte)(t >> 24);
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t = (t >> 32) + x.N5 + (x.N6 << 25);
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m[16] = (byte)t;
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m[17] = (byte)(t >> 8);
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m[18] = (byte)(t >> 16);
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m[19] = (byte)(t >> 24);
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t = (t >> 32) + (x.N7 << 19);
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m[20] = (byte)t;
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m[21] = (byte)(t >> 8);
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m[22] = (byte)(t >> 16);
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m[23] = (byte)(t >> 24);
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t = (t >> 32) + (x.N8 << 12);
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m[24] = (byte)t;
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m[25] = (byte)(t >> 8);
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m[26] = (byte)(t >> 16);
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m[27] = (byte)(t >> 24);
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t = (t >> 32) + ((x.N9 + ud) << 6);
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m[28] = (byte)t;
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m[29] = (byte)(t >> 8);
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m[30] = (byte)(t >> 16);
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m[31] = (byte)(t >> 24);
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}
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static void
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Copy(Long10 numOut, Long10 numIn)
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{
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numOut.N0 = numIn.N0;
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numOut.N1 = numIn.N1;
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numOut.N2 = numIn.N2;
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numOut.N3 = numIn.N3;
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numOut.N4 = numIn.N4;
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numOut.N5 = numIn.N5;
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numOut.N6 = numIn.N6;
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numOut.N7 = numIn.N7;
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numOut.N8 = numIn.N8;
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numOut.N9 = numIn.N9;
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}
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static void
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Set(Long10 numOut, int numIn)
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{
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numOut.N0 = numIn;
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numOut.N1 = 0;
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numOut.N2 = 0;
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numOut.N3 = 0;
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numOut.N4 = 0;
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numOut.N5 = 0;
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numOut.N6 = 0;
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numOut.N7 = 0;
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numOut.N8 = 0;
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numOut.N9 = 0;
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}
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static void
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Add(Long10 xy, Long10 x, Long10 y)
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{
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xy.N0 = x.N0 + y.N0;
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xy.N1 = x.N1 + y.N1;
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xy.N2 = x.N2 + y.N2;
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xy.N3 = x.N3 + y.N3;
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|
|
xy.N4 = x.N4 + y.N4;
|
|||
|
|
xy.N5 = x.N5 + y.N5;
|
|||
|
|
xy.N6 = x.N6 + y.N6;
|
|||
|
|
xy.N7 = x.N7 + y.N7;
|
|||
|
|
xy.N8 = x.N8 + y.N8;
|
|||
|
|
xy.N9 = x.N9 + y.N9;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static void
|
|||
|
|
Sub(Long10 xy, Long10 x, Long10 y)
|
|||
|
|
{
|
|||
|
|
xy.N0 = x.N0 - y.N0;
|
|||
|
|
xy.N1 = x.N1 - y.N1;
|
|||
|
|
xy.N2 = x.N2 - y.N2;
|
|||
|
|
xy.N3 = x.N3 - y.N3;
|
|||
|
|
xy.N4 = x.N4 - y.N4;
|
|||
|
|
xy.N5 = x.N5 - y.N5;
|
|||
|
|
xy.N6 = x.N6 - y.N6;
|
|||
|
|
xy.N7 = x.N7 - y.N7;
|
|||
|
|
xy.N8 = x.N8 - y.N8;
|
|||
|
|
xy.N9 = x.N9 - y.N9;
|
|||
|
|
}
|
|||
|
|
static void
|
|||
|
|
MulSmall(Long10 xy, Long10 x, long y)
|
|||
|
|
{
|
|||
|
|
long temp = (x.N8 * y);
|
|||
|
|
xy.N8 = (temp & ((1 << 26) - 1));
|
|||
|
|
temp = (temp >> 26) + (x.N9 * y);
|
|||
|
|
xy.N9 = (temp & ((1 << 25) - 1));
|
|||
|
|
temp = 19 * (temp >> 25) + (x.N0 * y);
|
|||
|
|
xy.N0 = (temp & ((1 << 26) - 1));
|
|||
|
|
temp = (temp >> 26) + (x.N1 * y);
|
|||
|
|
xy.N1 = (temp & ((1 << 25) - 1));
|
|||
|
|
temp = (temp >> 25) + (x.N2 * y);
|
|||
|
|
xy.N2 = (temp & ((1 << 26) - 1));
|
|||
|
|
temp = (temp >> 26) + (x.N3 * y);
|
|||
|
|
xy.N3 = (temp & ((1 << 25) - 1));
|
|||
|
|
temp = (temp >> 25) + (x.N4 * y);
|
|||
|
|
xy.N4 = (temp & ((1 << 26) - 1));
|
|||
|
|
temp = (temp >> 26) + (x.N5 * y);
|
|||
|
|
xy.N5 = (temp & ((1 << 25) - 1));
|
|||
|
|
temp = (temp >> 25) + (x.N6 * y);
|
|||
|
|
xy.N6 = (temp & ((1 << 26) - 1));
|
|||
|
|
temp = (temp >> 26) + (x.N7 * y);
|
|||
|
|
xy.N7 = (temp & ((1 << 25) - 1));
|
|||
|
|
temp = (temp >> 25) + xy.N8;
|
|||
|
|
xy.N8 = (temp & ((1 << 26) - 1));
|
|||
|
|
xy.N9 += (temp >> 26);
|
|||
|
|
}
|
|||
|
|
static void
|
|||
|
|
Multiply(Long10 xy, Long10 x, Long10 y)
|
|||
|
|
{
|
|||
|
|
long x0 = x.N0, x1 = x.N1, x2 = x.N2, x3 = x.N3, x4 = x.N4, x5 = x.N5, x6 = x.N6, x7 = x.N7, x8 = x.N8, x9 = x.N9;
|
|||
|
|
long y0 = y.N0, y1 = y.N1, y2 = y.N2, y3 = y.N3, y4 = y.N4, y5 = y.N5, y6 = y.N6, y7 = y.N7, y8 = y.N8, y9 = y.N9;
|
|||
|
|
long t = (x0 * y8) + (x2 * y6) + (x4 * y4) + (x6 * y2) + (x8 * y0) + 2 * ((x1 * y7) + (x3 * y5) + (x5 * y3) + (x7 * y1)) + 38 * (x9 * y9);
|
|||
|
|
xy.N8 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + (x0 * y9) + (x1 * y8) + (x2 * y7) + (x3 * y6) + (x4 * y5) + (x5 * y4) + (x6 * y3) + (x7 * y2) + (x8 * y1) + (x9 * y0);
|
|||
|
|
xy.N9 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (x0 * y0) + 19 * ((t >> 25) + (x2 * y8) + (x4 * y6) + (x6 * y4) + (x8 * y2)) + 38 * ((x1 * y9) + (x3 * y7) + (x5 * y5) + (x7 * y3) + (x9 * y1));
|
|||
|
|
xy.N0 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + (x0 * y1) + (x1 * y0) + 19 * ((x2 * y9) + (x3 * y8) + (x4 * y7) + (x5 * y6) + (x6 * y5) + (x7 * y4) + (x8 * y3) + (x9 * y2));
|
|||
|
|
xy.N1 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + (x0 * y2) + (x2 * y0) + 19 * ((x4 * y8) + (x6 * y6) + (x8 * y4)) + 2 * (x1 * y1) + 38 * ((x3 * y9) + (x5 * y7) + (x7 * y5) + (x9 * y3));
|
|||
|
|
xy.N2 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + (x0 * y3) + (x1 * y2) + (x2 * y1) + (x3 * y0) + 19 * ((x4 * y9) + (x5 * y8) + (x6 * y7) + (x7 * y6) + (x8 * y5) + (x9 * y4));
|
|||
|
|
xy.N3 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + (x0 * y4) + (x2 * y2) + (x4 * y0) + 19 * ((x6 * y8) + (x8 * y6)) + 2 * ((x1 * y3) + (x3 * y1)) + 38 * ((x5 * y9) + (x7 * y7) + (x9 * y5));
|
|||
|
|
xy.N4 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + (x0 * y5) + (x1 * y4) + (x2 * y3) + (x3 * y2) + (x4 * y1) + (x5 * y0) + 19 * ((x6 * y9) + (x7 * y8) + (x8 * y7) + (x9 * y6));
|
|||
|
|
xy.N5 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + (x0 * y6) + (x2 * y4) + (x4 * y2) + (x6 * y0) + 19 * (x8 * y8) + 2 * ((x1 * y5) + (x3 * y3) + (x5 * y1)) + 38 * ((x7 * y9) + (x9 * y7));
|
|||
|
|
xy.N6 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + (x0 * y7) + (x1 * y6) + (x2 * y5) + (x3 * y4) + (x4 * y3) + (x5 * y2) + (x6 * y1) + (x7 * y0) + 19 * ((x8 * y9) + (x9 * y8));
|
|||
|
|
xy.N7 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + xy.N8;
|
|||
|
|
xy.N8 = (t & ((1 << 26) - 1));
|
|||
|
|
xy.N9 += (t >> 26);
|
|||
|
|
}
|
|||
|
|
static void
|
|||
|
|
Square(Long10 xsqr, Long10 x)
|
|||
|
|
{
|
|||
|
|
long x0 = x.N0, x1 = x.N1, x2 = x.N2, x3 = x.N3, x4 = x.N4, x5 = x.N5, x6 = x.N6, x7 = x.N7, x8 = x.N8, x9 = x.N9;
|
|||
|
|
|
|||
|
|
long t = (x4 * x4) + 2 * ((x0 * x8) + (x2 * x6)) + 38 * (x9 * x9) + 4 * ((x1 * x7) + (x3 * x5));
|
|||
|
|
|
|||
|
|
xsqr.N8 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + 2 * ((x0 * x9) + (x1 * x8) + (x2 * x7) + (x3 * x6) + (x4 * x5));
|
|||
|
|
xsqr.N9 = (t & ((1 << 25) - 1));
|
|||
|
|
t = 19 * (t >> 25) + (x0 * x0) + 38 * ((x2 * x8) + (x4 * x6) + (x5 * x5)) + 76 * ((x1 * x9) + (x3 * x7));
|
|||
|
|
xsqr.N0 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + 2 * (x0 * x1) + 38 * ((x2 * x9) + (x3 * x8) + (x4 * x7) + (x5 * x6));
|
|||
|
|
xsqr.N1 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + 19 * (x6 * x6) + 2 * ((x0 * x2) + (x1 * x1)) + 38 * (x4 * x8) + 76 * ((x3 * x9) + (x5 * x7));
|
|||
|
|
xsqr.N2 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + 2 * ((x0 * x3) + (x1 * x2)) + 38 * ((x4 * x9) + (x5 * x8) + (x6 * x7));
|
|||
|
|
xsqr.N3 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + (x2 * x2) + 2 * (x0 * x4) + 38 * ((x6 * x8) + (x7 * x7)) + 4 * (x1 * x3) + 76 * (x5 * x9);
|
|||
|
|
xsqr.N4 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + 2 * ((x0 * x5) + (x1 * x4) + (x2 * x3)) + 38 * ((x6 * x9) + (x7 * x8));
|
|||
|
|
xsqr.N5 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + 19 * (x8 * x8) + 2 * ((x0 * x6) + (x2 * x4) + (x3 * x3)) + 4 * (x1 * x5) + 76 * (x7 * x9);
|
|||
|
|
xsqr.N6 = (t & ((1 << 26) - 1));
|
|||
|
|
t = (t >> 26) + 2 * ((x0 * x7) + (x1 * x6) + (x2 * x5) + (x3 * x4)) + 38 * (x8 * x9);
|
|||
|
|
xsqr.N7 = (t & ((1 << 25) - 1));
|
|||
|
|
t = (t >> 25) + xsqr.N8;
|
|||
|
|
xsqr.N8 = (t & ((1 << 26) - 1));
|
|||
|
|
xsqr.N9 += (t >> 26);
|
|||
|
|
}
|
|||
|
|
static void
|
|||
|
|
Reciprocal(Long10 y, Long10 x, bool sqrtAssist)
|
|||
|
|
{
|
|||
|
|
Long10 t0 = new Long10(), t1 = new Long10(), t2 = new Long10(), t3 = new Long10(), t4 = new Long10();
|
|||
|
|
int i;
|
|||
|
|
|
|||
|
|
Square(t1, x);
|
|||
|
|
Square(t2, t1);
|
|||
|
|
Square(t0, t2);
|
|||
|
|
Multiply(t2, t0, x);
|
|||
|
|
Multiply(t0, t2, t1);
|
|||
|
|
Square(t1, t0);
|
|||
|
|
Multiply(t3, t1, t2);
|
|||
|
|
Square(t1, t3);
|
|||
|
|
Square(t2, t1);
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Square(t2, t1);
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Multiply(t2, t1, t3);
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Square(t3, t1);
|
|||
|
|
for (i = 1; i < 5; i++)
|
|||
|
|
{
|
|||
|
|
Square(t1, t3);
|
|||
|
|
Square(t3, t1);
|
|||
|
|
}
|
|||
|
|
Multiply(t1, t3, t2);
|
|||
|
|
Square(t3, t1);
|
|||
|
|
Square(t4, t3);
|
|||
|
|
for (i = 1; i < 10; i++)
|
|||
|
|
{
|
|||
|
|
Square(t3, t4);
|
|||
|
|
Square(t4, t3);
|
|||
|
|
}
|
|||
|
|
Multiply(t3, t4, t1);
|
|||
|
|
for (i = 0; i < 5; i++)
|
|||
|
|
{
|
|||
|
|
Square(t1, t3);
|
|||
|
|
Square(t3, t1);
|
|||
|
|
}
|
|||
|
|
Multiply(t1, t3, t2);
|
|||
|
|
Square(t2, t1);
|
|||
|
|
Square(t3, t2);
|
|||
|
|
for (i = 1; i < 25; i++)
|
|||
|
|
{
|
|||
|
|
Square(t2, t3);
|
|||
|
|
Square(t3, t2);
|
|||
|
|
}
|
|||
|
|
Multiply(t2, t3, t1);
|
|||
|
|
Square(t3, t2);
|
|||
|
|
Square(t4, t3);
|
|||
|
|
for (i = 1; i < 50; i++)
|
|||
|
|
{
|
|||
|
|
Square(t3, t4);
|
|||
|
|
Square(t4, t3);
|
|||
|
|
}
|
|||
|
|
Multiply(t3, t4, t2);
|
|||
|
|
for (i = 0; i < 25; i++)
|
|||
|
|
{
|
|||
|
|
Square(t4, t3);
|
|||
|
|
Square(t3, t4);
|
|||
|
|
}
|
|||
|
|
Multiply(t2, t3, t1);
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Square(t2, t1);
|
|||
|
|
if (sqrtAssist)
|
|||
|
|
{
|
|||
|
|
Multiply(y, x, t2);
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Square(t2, t1);
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Multiply(y, t1, t0);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static int
|
|||
|
|
IsNegative(Long10 x)
|
|||
|
|
{
|
|||
|
|
return (int)(((IsOverflow(x) | (x.N9 < 0)) ? 1 : 0) ^ (x.N0 & 1));
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static void
|
|||
|
|
MontyPrepare(Long10 t1, Long10 t2, Long10 ax, Long10 az)
|
|||
|
|
{
|
|||
|
|
Add(t1, ax, az);
|
|||
|
|
Sub(t2, ax, az);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static void
|
|||
|
|
MontyAdd(Long10 t1, Long10 t2, Long10 t3, Long10 t4, Long10 ax, Long10 az, Long10 dx)
|
|||
|
|
{
|
|||
|
|
Multiply(ax, t2, t3);
|
|||
|
|
Multiply(az, t1, t4);
|
|||
|
|
Add(t1, ax, az);
|
|||
|
|
Sub(t2, ax, az);
|
|||
|
|
Square(ax, t1);
|
|||
|
|
Square(t1, t2);
|
|||
|
|
Multiply(az, t1, dx);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static void
|
|||
|
|
MontyDouble(Long10 t1, Long10 t2, Long10 t3, Long10 t4, Long10 bx, Long10 bz)
|
|||
|
|
{
|
|||
|
|
Square(t1, t3);
|
|||
|
|
Square(t2, t4);
|
|||
|
|
Multiply(bx, t1, t2);
|
|||
|
|
Sub(t2, t1, t2);
|
|||
|
|
MulSmall(bz, t2, 121665);
|
|||
|
|
Add(t1, t1, bz);
|
|||
|
|
Multiply(bz, t1, t2);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static void
|
|||
|
|
CurveEquationInline(Long10 y2, Long10 x, Long10 temp)
|
|||
|
|
{
|
|||
|
|
Square(temp, x);
|
|||
|
|
MulSmall(y2, x, 486662);
|
|||
|
|
Add(temp, temp, y2);
|
|||
|
|
temp.N0++;
|
|||
|
|
Multiply(y2, temp, x);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static void Core(byte[] publicKey, byte[] signingKey, byte[] privateKey, byte[] peerPublicKey)
|
|||
|
|
{
|
|||
|
|
if (publicKey == null)
|
|||
|
|
throw new ArgumentNullException("publicKey");
|
|||
|
|
if (publicKey.Length != 32)
|
|||
|
|
throw new ArgumentException(String.Format("publicKey must be 32 bytes long (but was {0} bytes long)", publicKey.Length), "publicKey");
|
|||
|
|
|
|||
|
|
if (signingKey != null && signingKey.Length != 32)
|
|||
|
|
throw new ArgumentException(String.Format("signingKey must be null or 32 bytes long (but was {0} bytes long)", signingKey.Length), "signingKey");
|
|||
|
|
|
|||
|
|
if (privateKey == null)
|
|||
|
|
throw new ArgumentNullException("privateKey");
|
|||
|
|
if (privateKey.Length != 32)
|
|||
|
|
throw new ArgumentException(String.Format("privateKey must be 32 bytes long (but was {0} bytes long)", privateKey.Length), "privateKey");
|
|||
|
|
|
|||
|
|
if (peerPublicKey != null && peerPublicKey.Length != 32)
|
|||
|
|
throw new ArgumentException(String.Format("peerPublicKey must be null or 32 bytes long (but was {0} bytes long)", peerPublicKey.Length), "peerPublicKey");
|
|||
|
|
|
|||
|
|
Long10 dx = new Long10(), t1 = new Long10(), t2 = new Long10(), t3 = new Long10(), t4 = new Long10();
|
|||
|
|
Long10[] x = { new Long10(), new Long10() }, z = { new Long10(), new Long10() };
|
|||
|
|
|
|||
|
|
if (peerPublicKey != null)
|
|||
|
|
Unpack(dx, peerPublicKey);
|
|||
|
|
else
|
|||
|
|
Set(dx, 9);
|
|||
|
|
|
|||
|
|
Set(x[0], 1);
|
|||
|
|
Set(z[0], 0);
|
|||
|
|
|
|||
|
|
Copy(x[1], dx);
|
|||
|
|
Set(z[1], 1);
|
|||
|
|
|
|||
|
|
for (int i = 32; i-- != 0;)
|
|||
|
|
{
|
|||
|
|
for (int j = 8; j-- != 0;)
|
|||
|
|
{
|
|||
|
|
int bit1 = (privateKey[i] & 0xFF) >> j & 1;
|
|||
|
|
int bit0 = ~(privateKey[i] & 0xFF) >> j & 1;
|
|||
|
|
Long10 ax = x[bit0];
|
|||
|
|
Long10 az = z[bit0];
|
|||
|
|
Long10 bx = x[bit1];
|
|||
|
|
Long10 bz = z[bit1];
|
|||
|
|
|
|||
|
|
MontyPrepare(t1, t2, ax, az);
|
|||
|
|
MontyPrepare(t3, t4, bx, bz);
|
|||
|
|
MontyAdd(t1, t2, t3, t4, ax, az, dx);
|
|||
|
|
MontyDouble(t1, t2, t3, t4, bx, bz);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
Reciprocal(t1, z[0], false);
|
|||
|
|
Multiply(dx, x[0], t1);
|
|||
|
|
Pack(dx, publicKey);
|
|||
|
|
|
|||
|
|
if (signingKey != null)
|
|||
|
|
{
|
|||
|
|
CurveEquationInline(t1, dx, t2);
|
|||
|
|
Reciprocal(t3, z[1], false);
|
|||
|
|
Multiply(t2, x[1], t3);
|
|||
|
|
Add(t2, t2, dx);
|
|||
|
|
t2.N0 += 9 + 486662;
|
|||
|
|
dx.N0 -= 9;
|
|||
|
|
Square(t3, dx);
|
|||
|
|
Multiply(dx, t2, t3);
|
|||
|
|
Sub(dx, dx, t1);
|
|||
|
|
dx.N0 -= 39420360;
|
|||
|
|
Multiply(t1, dx, BaseR2Y);
|
|||
|
|
if (IsNegative(t1) != 0)
|
|||
|
|
Copy32(privateKey, signingKey);
|
|||
|
|
else
|
|||
|
|
MultiplyArraySmall(signingKey, OrderTimes8, 0, privateKey, 32, -1);
|
|||
|
|
|
|||
|
|
var temp1 = new byte[32];
|
|||
|
|
var temp2 = new byte[64];
|
|||
|
|
var temp3 = new byte[64];
|
|||
|
|
Copy32(Order, temp1);
|
|||
|
|
Copy32(Egcd32(temp2, temp3, signingKey, temp1), signingKey);
|
|||
|
|
if ((signingKey[31] & 0x80) != 0)
|
|||
|
|
MultiplyArraySmall(signingKey, signingKey, 0, Order, 32, 1);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static readonly byte[] OrderTimes8 = { 104, 159, 174, 231, 210, 24, 147, 192, 178, 230, 188, 23, 245, 206, 247, 166, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128 };
|
|||
|
|
|
|||
|
|
static readonly Long10 BaseR2Y = new Long10(5744, 8160848, 4790893, 13779497, 35730846, 12541209, 49101323, 30047407, 40071253, 6226132);
|
|||
|
|
}
|
|||
|
|
}
|