331 lines
8.3 KiB
C#
331 lines
8.3 KiB
C#
using System;
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using System.Collections;
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using Org.BouncyCastle.Crypto;
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using Org.BouncyCastle.Crypto.Parameters;
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using Org.BouncyCastle.Math;
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using Org.BouncyCastle.Security;
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using Org.BouncyCastle.Utilities;
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namespace Org.BouncyCastle.Crypto.Generators
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{
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/**
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* Key generation parameters for NaccacheStern cipher. For details on this cipher, please see
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*
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* http://www.gemplus.com/smart/rd/publications/pdf/NS98pkcs.pdf
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*/
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public class NaccacheSternKeyPairGenerator
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: IAsymmetricCipherKeyPairGenerator
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{
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private static readonly int[] smallPrimes =
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{
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3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67,
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71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
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151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
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239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
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337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431,
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433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523,
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541, 547, 557
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};
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private NaccacheSternKeyGenerationParameters param;
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/*
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* (non-Javadoc)
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*
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* @see org.bouncycastle.crypto.AsymmetricCipherKeyPairGenerator#init(org.bouncycastle.crypto.KeyGenerationParameters)
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*/
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public void Init(KeyGenerationParameters parameters)
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{
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this.param = (NaccacheSternKeyGenerationParameters)parameters;
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}
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/*
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* (non-Javadoc)
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*
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* @see org.bouncycastle.crypto.AsymmetricCipherKeyPairGenerator#generateKeyPair()
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*/
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public AsymmetricCipherKeyPair GenerateKeyPair()
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{
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int strength = param.Strength;
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SecureRandom rand = param.Random;
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int certainty = param.Certainty;
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bool debug = param.IsDebug;
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if (debug)
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{
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Console.WriteLine("Fetching first " + param.CountSmallPrimes + " primes.");
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}
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ArrayList smallPrimes = findFirstPrimes(param.CountSmallPrimes);
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smallPrimes = permuteList(smallPrimes, rand);
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BigInteger u = BigInteger.One;
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BigInteger v = BigInteger.One;
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for (int i = 0; i < smallPrimes.Count / 2; i++)
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{
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u = u.Multiply((BigInteger)smallPrimes[i]);
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}
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for (int i = smallPrimes.Count / 2; i < smallPrimes.Count; i++)
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{
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v = v.Multiply((BigInteger)smallPrimes[i]);
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}
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BigInteger sigma = u.Multiply(v);
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// n = (2 a u p_ + 1 ) ( 2 b v q_ + 1)
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// -> |n| = strength
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// |2| = 1 in bits
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// -> |a| * |b| = |n| - |u| - |v| - |p_| - |q_| - |2| -|2|
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// remainingStrength = strength - sigma.bitLength() - p_.bitLength() -
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// q_.bitLength() - 1 -1
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int remainingStrength = strength - sigma.BitLength - 48;
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BigInteger a = generatePrime(remainingStrength / 2 + 1, certainty, rand);
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BigInteger b = generatePrime(remainingStrength / 2 + 1, certainty, rand);
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BigInteger p_;
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BigInteger q_;
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BigInteger p;
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BigInteger q;
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long tries = 0;
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if (debug)
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{
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Console.WriteLine("generating p and q");
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}
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BigInteger _2au = a.Multiply(u).ShiftLeft(1);
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BigInteger _2bv = b.Multiply(v).ShiftLeft(1);
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for (;;)
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{
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tries++;
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p_ = generatePrime(24, certainty, rand);
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p = p_.Multiply(_2au).Add(BigInteger.One);
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if (!p.IsProbablePrime(certainty))
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continue;
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for (;;)
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{
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q_ = generatePrime(24, certainty, rand);
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if (p_.Equals(q_))
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continue;
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q = q_.Multiply(_2bv).Add(BigInteger.One);
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if (q.IsProbablePrime(certainty))
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break;
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}
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if (!sigma.Gcd(p_.Multiply(q_)).Equals(BigInteger.One))
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{
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Console.WriteLine("sigma.gcd(p_.mult(q_)) != 1!\n p_: " + p_ +"\n q_: "+ q_ );
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continue;
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}
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if (p.Multiply(q).BitLength < strength)
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{
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if (debug)
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{
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Console.WriteLine("key size too small. Should be " + strength + " but is actually "
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+ p.Multiply(q).BitLength);
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}
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continue;
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}
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break;
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}
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if (debug)
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{
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Console.WriteLine("needed " + tries + " tries to generate p and q.");
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}
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BigInteger n = p.Multiply(q);
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BigInteger phi_n = p.Subtract(BigInteger.One).Multiply(q.Subtract(BigInteger.One));
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BigInteger g;
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tries = 0;
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if (debug)
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{
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Console.WriteLine("generating g");
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}
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for (;;)
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{
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// TODO After the first loop, just regenerate one randomly-selected gPart each time?
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ArrayList gParts = new ArrayList();
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for (int ind = 0; ind != smallPrimes.Count; ind++)
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{
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BigInteger i = (BigInteger)smallPrimes[ind];
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BigInteger e = phi_n.Divide(i);
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for (;;)
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{
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tries++;
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g = generatePrime(strength, certainty, rand);
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if (!g.ModPow(e, n).Equals(BigInteger.One))
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{
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gParts.Add(g);
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break;
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}
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}
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}
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g = BigInteger.One;
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for (int i = 0; i < smallPrimes.Count; i++)
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{
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BigInteger gPart = (BigInteger) gParts[i];
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BigInteger smallPrime = (BigInteger) smallPrimes[i];
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g = g.Multiply(gPart.ModPow(sigma.Divide(smallPrime), n)).Mod(n);
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}
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// make sure that g is not divisible by p_i or q_i
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bool divisible = false;
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for (int i = 0; i < smallPrimes.Count; i++)
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{
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if (g.ModPow(phi_n.Divide((BigInteger)smallPrimes[i]), n).Equals(BigInteger.One))
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{
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if (debug)
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{
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Console.WriteLine("g has order phi(n)/" + smallPrimes[i] + "\n g: " + g);
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}
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divisible = true;
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break;
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}
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}
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if (divisible)
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{
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continue;
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}
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// make sure that g has order > phi_n/4
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//if (g.ModPow(phi_n.Divide(BigInteger.ValueOf(4)), n).Equals(BigInteger.One))
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if (g.ModPow(phi_n.ShiftRight(2), n).Equals(BigInteger.One))
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{
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if (debug)
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{
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Console.WriteLine("g has order phi(n)/4\n g:" + g);
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}
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continue;
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}
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if (g.ModPow(phi_n.Divide(p_), n).Equals(BigInteger.One))
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{
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if (debug)
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{
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Console.WriteLine("g has order phi(n)/p'\n g: " + g);
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}
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continue;
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}
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if (g.ModPow(phi_n.Divide(q_), n).Equals(BigInteger.One))
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{
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if (debug)
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{
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Console.WriteLine("g has order phi(n)/q'\n g: " + g);
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}
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continue;
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}
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if (g.ModPow(phi_n.Divide(a), n).Equals(BigInteger.One))
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{
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if (debug)
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{
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Console.WriteLine("g has order phi(n)/a\n g: " + g);
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}
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continue;
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}
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if (g.ModPow(phi_n.Divide(b), n).Equals(BigInteger.One))
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{
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if (debug)
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{
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Console.WriteLine("g has order phi(n)/b\n g: " + g);
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}
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continue;
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}
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break;
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}
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if (debug)
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{
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Console.WriteLine("needed " + tries + " tries to generate g");
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Console.WriteLine();
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Console.WriteLine("found new NaccacheStern cipher variables:");
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Console.WriteLine("smallPrimes: " + Arrays.ToString(smallPrimes.ToArray()));
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Console.WriteLine("sigma:...... " + sigma + " (" + sigma.BitLength + " bits)");
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Console.WriteLine("a:.......... " + a);
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Console.WriteLine("b:.......... " + b);
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Console.WriteLine("p':......... " + p_);
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Console.WriteLine("q':......... " + q_);
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Console.WriteLine("p:.......... " + p);
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Console.WriteLine("q:.......... " + q);
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Console.WriteLine("n:.......... " + n);
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Console.WriteLine("phi(n):..... " + phi_n);
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Console.WriteLine("g:.......... " + g);
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Console.WriteLine();
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}
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return new AsymmetricCipherKeyPair(new NaccacheSternKeyParameters(false, g, n, sigma.BitLength),
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new NaccacheSternPrivateKeyParameters(g, n, sigma.BitLength, smallPrimes, phi_n));
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}
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private static BigInteger generatePrime(
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int bitLength,
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int certainty,
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SecureRandom rand)
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{
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return new BigInteger(bitLength, certainty, rand);
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}
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/**
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* Generates a permuted ArrayList from the original one. The original List
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* is not modified
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*
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* @param arr
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* the ArrayList to be permuted
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* @param rand
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* the source of Randomness for permutation
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* @return a new ArrayList with the permuted elements.
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*/
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private static ArrayList permuteList(
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ArrayList arr,
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SecureRandom rand)
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{
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ArrayList retval = new ArrayList(arr.Count);
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foreach (object element in arr)
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{
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int index = rand.Next(retval.Count + 1);
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retval.Insert(index, element);
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}
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return retval;
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}
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/**
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* Finds the first 'count' primes starting with 3
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*
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* @param count
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* the number of primes to find
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* @return a vector containing the found primes as Integer
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*/
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private static ArrayList findFirstPrimes(
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int count)
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{
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ArrayList primes = new ArrayList(count);
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for (int i = 0; i != count; i++)
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{
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primes.Add(BigInteger.ValueOf(smallPrimes[i]));
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}
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return primes;
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}
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}
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}
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