Estoy implementando la operación aritmética de punto de curva elíptica en la curva especificada por NIST "p192". Para propósitos de prueba he tomado ejemplos de los puntos mostrados enDocumento de rutina del NIST para la curva p192.. Recibo respuestas correctas para la suma de puntos y la duplicación de puntos, pero para la multiplicación escalar mis respuestas no son correctas. Debido a esta razón no puedo llegar a si

$ k^{-1}(kP) = P $

dónde

$ k^{-1}.k = 1 mod p $

Por favor, ayúdame a entender dónde estoy cometiendo errores.

package a;
import java.math.BigInteger;
import java.security.spec.ECPoint;
public class ScalarMultiply {
private static final BigInteger ONE = new BigInteger("1");;
static BigInteger TWO = new BigInteger("2");
    static BigInteger p = new BigInteger("6277101735386680763835789423207666416083908700390324961279");


public static ECPoint scalmult(ECPoint P, BigInteger k){
    ECPoint R =P,S = P;
    int length = k.bitLength();
    //System.out.println("length is" + length);
    byte[] binarray = new byte[length];
    for(int i=0;i<=length-1;i++){
        binarray[i] = k.mod(TWO).byteValue();
        k = k.divide(TWO);

    }
    for(int i=0;i<=length-1;i++){
        System.out.print("" + binarray[i]); 
    }

    for(int i = length - 2;i > 0;i--){
        R = doublePoint(R);
        if(binarray[i]== 1) 
            R = addPoint(R, S);
    }
return R;
}

public static ECPoint addPoint(ECPoint r, ECPoint s) {

    BigInteger slope = (r.getAffineY().subtract(s.getAffineY())).multiply(r.getAffineX().subtract(s.getAffineX()).modInverse(p)).mod(p);
    BigInteger Xout = (slope.modPow(TWO, p).subtract(r.getAffineX())).subtract(s.getAffineX()).mod(p);
    BigInteger Yout = r.getAffineY().negate().mod(p);
    Yout = Yout.add(slope.multiply(r.getAffineX().subtract(Xout))).mod(p);
    ECPoint out = new ECPoint(Xout, Yout);
    return out;
}

public static ECPoint doublePoint(ECPoint r) {
    // TODO Auto-generated method stub
    BigInteger slope = (r.getAffineX().pow(2)).multiply(new BigInteger("3"));
    slope = slope.add(new BigInteger("3"));
    slope = slope.multiply((r.getAffineY().multiply(TWO)).modInverse(p));
    BigInteger Xout = slope.pow(2).subtract(r.getAffineX().multiply(new BigInteger("2"))).mod(p);
    BigInteger Yout = (r.getAffineY().negate()).add(slope.multiply(r.getAffineX().subtract(Xout))).mod(p);
    ECPoint out = new ECPoint(Xout, Yout);
    return out;
}
}

La clase principal es

    package a;
    import java.math.BigInteger;
    import java.security.spec.ECPoint;

    public class EccArithmetic {

    /**
     * @param args
     */
    public static void main(String[] args) {

             BigInteger xs = new BigInteger("d458e7d127ae671b0c330266d246769353a012073e97acf8", 16);
             BigInteger ys = new BigInteger
("325930500d851f336bddc050cf7fb11b5673a1645086df3b", 16);
             BigInteger xt = new BigInteger

("f22c4395213e9ebe67ddecdd87fdbd01be16fb059b9753a4", 16);
             BigInteger yt = new BigInteger

("264424096af2b3597796db48f8dfb41fa9cecc97691a9c79", 16);
             ECPoint S = new ECPoint(xs,ys);
             ECPoint T = new ECPoint(xt,yt);
             // Verifying addition 

             ECPoint Rst = ScalarMultiply.addPoint(S, T);
             BigInteger xst = new BigInteger

("48e1e4096b9b8e5ca9d0f1f077b8abf58e843894de4d0290", 16);   // Specified value of x of point R for addition  in NIST Routine example
             System.out.println("\nx-coordinate of point Rst is : " + Rst.getAffineX()); 
             System.out.println("\ny-coordinate of point Rst is : " + Rst.getAffineY());
             if(Rst.getAffineX().equals(xst))
                 System.out.println("Adding is correct");

//Verifying Doubling
BigInteger xr = new BigInteger

("30c5bc6b8c7da25354b373dc14dd8a0eba42d25a3f6e6962", 16);  // Specified value of x of point R for doubling  in NIST Routine example
             BigInteger yr = new BigInteger

("0dde14bc4249a721c407aedbf011e2ddbbcb2968c9d889cf", 16);
             ECPoint R2s = new ECPoint(xr, yr);  // Specified value of y of point R for doubling  in NIST Routine example
             System.out.println("\nx-coordinate of point R2s is : " + R2s.getAffineX()); 
             System.out.println("\ny-coordinate of point R2s is : " + R2s.getAffineY());
             System.out.println("\nx-coordinate of calculated point is : " + 

ScalarMultiply.doublePoint(S).getAffineX()); 
             System.out.println("\ny-coordinate of calculated point is : " + 

ScalarMultiply.doublePoint(S).getAffineY());
             if(R2s.getAffineX().equals(ScalarMultiply.doublePoint(S).getAffineX()))
                 System.out.println("Doubling is correct");

             xr = new BigInteger("1faee4205a4f669d2d0a8f25e3bcec9a62a6952965bf6d31", 16);  // Specified value of x of point R for scalar Multiplication  in NIST Routine example
             yr = new BigInteger("5ff2cdfa508a2581892367087c696f179e7a4d7e8260fb06", 16);   // Specified value of y of point R for scalar Multiplication  in NIST Routine example
             ECPoint Rds = new ECPoint(xr, yr);
             BigInteger d = new BigInteger

("a78a236d60baec0c5dd41b33a542463a8255391af64c74ee", 16);
             //Rs = new ECPoint(ScalarMultiply.scalmult(S, d).getAffineX(), yr);
             System.out.println("\nx-coordinate of point Rds is : " + Rds.getAffineX());
            System.out.println("\nx-coordinate of point Rds is : " + Rds.getAffineY());
            System.out.println("\nx-coordinate of calculated point is : " + ScalarMultiply.scalmult(S, 

            d).getAffineX());
            System.out.println("\nx-coordinate of calculated point is : " + ScalarMultiply.scalmult(S, 

            d).getAffineY());            
            if(Rds.getAffineX().equals(ScalarMultiply.scalmult(S, d).getAffineX()))
                 System.out.println("Scalar Multiplication is correct");

    }
}