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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
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package org.bouncycastle.math.ec.tools;

import java.math.BigInteger;
import java.security.SecureRandom;
import java.util.ArrayList;
import java.util.Enumeration;
import java.util.Iterator;
import java.util.SortedSet;
import java.util.TreeSet;

import org.bouncycastle.asn1.x9.ECNamedCurveTable;
import org.bouncycastle.asn1.x9.X9ECParameters;
import org.bouncycastle.crypto.ec.CustomNamedCurves;
import org.bouncycastle.math.ec.ECAlgorithms;
import org.bouncycastle.math.ec.ECCurve;
import org.bouncycastle.math.ec.ECFieldElement;
import org.bouncycastle.util.Integers;

public class TraceOptimizer
{
    private static final BigInteger ONE = BigInteger.valueOf(1);

    private static final SecureRandom R = new SecureRandom();

    public static void main(String[] args)
    {
        SortedSet names = new TreeSet(enumToList(ECNamedCurveTable.getNames()));
        names.addAll(enumToList(CustomNamedCurves.getNames()));

        Iterator it = names.iterator();
        while (it.hasNext())
        {
            String name = (String)it.next();
            X9ECParameters x9 = CustomNamedCurves.getByName(name);
            if (x9 == null)
            {
                x9 = ECNamedCurveTable.getByName(name);
            }
            if (x9 != null && ECAlgorithms.isF2mCurve(x9.getCurve()))
            {
                System.out.print(name + ":");
                implPrintNonZeroTraceBits(x9);
            }
        }
    }

    public static void printNonZeroTraceBits(X9ECParameters x9)
    {
        if (!ECAlgorithms.isF2mCurve(x9.getCurve()))
        {
            throw new IllegalArgumentException("Trace only defined over characteristic-2 fields");
        }

        implPrintNonZeroTraceBits(x9);
    }

    public static void implPrintNonZeroTraceBits(X9ECParameters x9)
    {
        ECCurve c = x9.getCurve();
        int m = c.getFieldSize();

        ArrayList nonZeroTraceBits = new ArrayList();

        /*
         * Determine which of the bits contribute to the trace.
         * 
         * See section 3.6.2 of "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone)
         */
        {
            for (int i = 0; i < m; ++i)
            {
                BigInteger zi = ONE.shiftLeft(i);
                ECFieldElement fe = c.fromBigInteger(zi);
                int tr = calculateTrace(fe);
                if (tr != 0)
                {
                    nonZeroTraceBits.add(Integers.valueOf(i));
                    System.out.print(" " + i);
                }
            }
            System.out.println();
        }

        /*
         *  Check calculation based on the non-zero-trace bits against explicit calculation, for random field elements
         */
        {
            for (int i = 0; i < 1000; ++i)
            {
                BigInteger x = new BigInteger(m, R);
                ECFieldElement fe = c.fromBigInteger(x);
                int check = calculateTrace(fe);

                int tr = 0;
                for (int j = 0; j < nonZeroTraceBits.size(); ++j)
                {
                    int bit = ((Integer)nonZeroTraceBits.get(j)).intValue();
                    if (x.testBit(bit))
                    {
                        tr ^= 1;
                    }
                }
                
                if (check != tr)
                {
                    throw new IllegalStateException("Optimized-trace sanity check failed");
                }
            }
        }
    }

    private static int calculateTrace(ECFieldElement fe)
    {
        int m = fe.getFieldSize();
        ECFieldElement tr = fe;
        for (int i = 1; i < m; ++i)
        {
            fe = fe.square();
            tr = tr.add(fe);
        }
        BigInteger b = tr.toBigInteger();
        if (b.bitLength() > 1)
        {
            throw new IllegalStateException();
        }
        return b.intValue();
    }

    private static ArrayList enumToList(Enumeration en)
    {
        ArrayList rv = new ArrayList();
        while (en.hasMoreElements())
        {
            rv.add(en.nextElement());
        }
        return rv;
    }
}