static void BenchmarkLiu <T>(LiuScheme <T> lsag, int participants) where T : ILinkableSignature
{
Console.WriteLine("Benchmark for {0} participants", participants);
lsag.GroupParameters = KnownGroupParameters.RFC5114_2_1_160;
var message = "hi";
var messageBytes = Encoding.UTF8.GetBytes(message);
var keys = Enumerable.Range(0, participants).Select(i => lsag.GenerateKeyPair()).ToArray();
var publicKeys = keys.Select(k => k[1]).ToArray();
Console.WriteLine("Computing signatures");
Stopwatch timer = new Stopwatch();
timer.Start();
var signatures = Enumerable.Range(0, participants).
Select(i => lsag.GenerateSignature(messageBytes, publicKeys, keys[i][0], i)).ToArray();
timer.Stop();
Console.WriteLine("Generation took {0}, {1}s / participant, {2}s / participant^2", timer.Elapsed,
timer.Elapsed.TotalSeconds / participants, timer.Elapsed.TotalSeconds / participants / participants);
Console.WriteLine("Verifying signatures");
timer.Restart();
var cache = new MultiExponentiation(lsag.GroupParameters.Prime, publicKeys);
if (signatures.All(s => lsag.VerifySignature(messageBytes, s, cache)))
{
Console.WriteLine("OK");
}
else
{
Console.WriteLine("FAIL");
}
timer.Stop();
Console.WriteLine("Verification took {0}, {1}s / participant, {2}s / participant^2", timer.Elapsed,
timer.Elapsed.TotalSeconds / participants, timer.Elapsed.TotalSeconds / participants / participants);
}
// This is a simple check that the implementation is not completely broken
static void TestLiu <T>(LiuScheme <T> lsag) where T : ILinkableSignature
{
Console.WriteLine("Testing " + lsag);
lsag.GroupParameters = KnownGroupParameters.ExampleDsa_160;
Random rand = new Random();
int participants = 5;
var messages = new[] { "hi", "hi again", "this is another message" }.Select(Encoding.UTF8.GetBytes).ToArray();
var keys = Enumerable.Range(0, participants).Select(i => lsag.GenerateKeyPair()).ToArray();
foreach (var key in keys)
{
if (BigInteger.ModPow(lsag.GroupParameters.Generator, key[0], lsag.GroupParameters.Prime) != key[1])
{
Console.WriteLine("Key generation failed");
}
}
var publicKeys = keys.Select(k => k[1]).ToArray();
var signatures = new T[participants, messages.Length];
for (int i = 0; i < participants; ++i)
{
for (int j = 0; j < messages.Length; ++j)
{
signatures[i, j] = lsag.GenerateSignature(messages[j], publicKeys, keys[i][0], i);
if (!lsag.VerifySignature(messages[j], publicKeys, signatures[i, j]))
{
Console.WriteLine("Signature generation failed");
}
for (int k = 0; k < messages.Length; ++k)
{
if (lsag.VerifySignature(messages[k], publicKeys, signatures[i, j]) != (k == j))
{
Console.WriteLine("Verification failed");
}
}
if (signatures[i, j] is Liu2004.Signature)
{
var orig = (Liu2004.Signature)(ILinkableSignature) signatures[i, j];
var tampered = new Liu2004.Signature(orig.C1.FlipBit(rand.Next(orig.C1.BitLength())), orig.S, orig.Ytilda);
if (lsag.VerifySignature(messages[j], publicKeys, (T)(ILinkableSignature)tampered))
{
Console.WriteLine("Tampering test failed");
}
tampered = new Liu2004.Signature(orig.C1, orig.S, orig.Ytilda.FlipBit(rand.Next(orig.Ytilda.BitLength())));
if (lsag.VerifySignature(messages[j], publicKeys, (T)(ILinkableSignature)tampered))
{
Console.WriteLine("Tampering test failed");
}
var s = (BigInteger[])orig.S.Clone();
var t = rand.Next(s.Length);
s[t] = s[t].FlipBit(rand.Next(s[t].BitLength()));
tampered = new Liu2004.Signature(orig.C1, s, orig.Ytilda);
if (lsag.VerifySignature(messages[j], publicKeys, (T)(ILinkableSignature)tampered))
{
Console.WriteLine("Tampering test failed");
}
}
if (signatures[i, j] is Liu2005.Signature)
{
var orig = (Liu2005.Signature)(ILinkableSignature) signatures[i, j];
var tampered = new Liu2005.Signature(orig.Y0, orig.S.FlipBit(rand.Next(orig.S.BitLength())), orig.C);
if (lsag.VerifySignature(messages[j], publicKeys, (T)(ILinkableSignature)tampered))
{
Console.WriteLine("Tampering test failed");
}
tampered = new Liu2005.Signature(orig.Y0.FlipBit(rand.Next(orig.Y0.BitLength())), orig.S, orig.C);
if (lsag.VerifySignature(messages[j], publicKeys, (T)(ILinkableSignature)tampered))
{
Console.WriteLine("Tampering test failed");
}
var s = (BigInteger[])orig.C.Clone();
var t = rand.Next(s.Length);
s[t] = s[t].FlipBit(rand.Next(s[t].BitLength()));
tampered = new Liu2005.Signature(orig.Y0, orig.S, s);
if (lsag.VerifySignature(messages[j], publicKeys, (T)(ILinkableSignature)tampered))
{
Console.WriteLine("Tampering test failed");
}
}
}
}
for (int i = 0; i < participants; ++i)
{
for (int j = 0; j < messages.Length; ++j)
{
for (int k = 0; k < participants; ++k)
{
for (int l = 0; l < messages.Length; ++l)
{
if (signatures[i, j].IsLinked(signatures[k, l]) != (i == k))
{
Console.WriteLine("Linking failed");
}
}
}
}
}
Console.WriteLine("Tests complete");
}
