使用RSA进行模乘会导致Java卡出错

你好，我正在做一个Java卡上的项目，这意味着很多模乘。我使用RSA密码系统在这个平台上实现了模乘，但它似乎适用于某些数字

public byte[] modMultiply(byte[] x, short xOffset, short xLength, byte[] y,
        short yOffset, short yLength, short tempOutoffset) {

    //copy x value to temporary rambuffer
    Util.arrayCopy(x, xOffset, tempBuffer, tempOutoffset, xLength);


    // copy the y value to match th size of rsa_object
    Util.arrayFillNonAtomic(eempromTempBuffer, (short)0, (byte) (Configuration.LENGTH_RSAOBJECT_MODULUS-1),(byte)0x00);
    Util.arrayCopy(y,yOffset,eempromTempBuffer,(short)(Configuration.LENGTH_RSAOBJECT_MODULUS - yLength),yLength);

    // x+y
    if (JBigInteger.add(x,xOffset,xLength, eempromTempBuffer,
            (short)0,Configuration.LENGTH_MODULUS)) ;
    if(this.isGreater(x, xOffset, xLength, tempBuffer,Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS)>0)
    {
        JBigInteger.subtract(x,xOffset,xLength, tempBuffer,
                Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
    }

    //(x+y)2
    mRsaCipherForSquaring.init(mRsaPublicKekForSquare, Cipher.MODE_ENCRYPT);

    mRsaCipherForSquaring.doFinal(x, xOffset, Configuration.LENGTH_RSAOBJECT_MODULUS, x,
            xOffset); // OK

    mRsaCipherForSquaring.doFinal(tempBuffer, tempOutoffset, Configuration.LENGTH_RSAOBJECT_MODULUS, tempBuffer, tempOutoffset); // OK


    if (JBigInteger.subtract(x, xOffset, Configuration.LENGTH_MODULUS, tempBuffer, tempOutoffset,
            Configuration.LENGTH_MODULUS)) {
        JBigInteger.add(x, xOffset, Configuration.LENGTH_MODULUS, tempBuffer,
                Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
    } 

    mRsaCipherForSquaring.doFinal(eempromTempBuffer, yOffset, Configuration.LENGTH_RSAOBJECT_MODULUS, eempromTempBuffer, yOffset); //OK 


    if (JBigInteger.subtract(x, xOffset, Configuration.LENGTH_MODULUS, eempromTempBuffer, yOffset,
            Configuration.LENGTH_MODULUS)) {

        JBigInteger.add(x, xOffset, Configuration.LENGTH_MODULUS, tempBuffer,
                Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);

    }
    // ((x+y)^2 - x^2 -y^2)/2
    JBigInteger.modular_division_by_2(x, xOffset,Configuration. LENGTH_MODULUS, tempBuffer, Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
    return x;
}


public static boolean add(byte[] x, short xOffset, short xLength, byte[] y,
        short yOffset, short yLength) {
    short digit_mask = 0xff;
    short digit_len = 0x08;
    short result = 0;
    short i = (short) (xLength + xOffset - 1);
    short j = (short) (yLength + yOffset - 1);

    for (; i >= xOffset; i--, j--) {
        result = (short) (result + (short) (x[i] & digit_mask) + (short) (y[j] & digit_mask));

        x[i] = (byte) (result & digit_mask);
        result = (short) ((result >> digit_len) & digit_mask);
    }
    while (result > 0 && i >= xOffset) {
        result = (short) (result + (short) (x[i] & digit_mask));
        x[i] = (byte) (result & digit_mask);
        result = (short) ((result >> digit_len) & digit_mask);
        i--;
    }

    return result != 0;
}
public static boolean subtract(byte[] x, short xOffset, short xLength, byte[] y,
        short yOffset, short yLength) {
    short digit_mask = 0xff;
    short i = (short) (xLength + xOffset - 1);
    short j = (short) (yLength + yOffset - 1);
    short carry = 0;
    short subtraction_result = 0;

    for (; i >= xOffset && j >= yOffset; i--, j--) {
        subtraction_result = (short) ((x[i] & digit_mask)
                - (y[j] & digit_mask) - carry);
        x[i] = (byte) (subtraction_result & digit_mask);
        carry = (short) (subtraction_result < 0 ? 1 : 0);
    }
    for (; i >= xOffset && carry > 0; i--) {
        if (x[i] != 0)
            carry = 0;
        x[i] -= 1;
    }

    return carry > 0;
}



 public short isGreater(byte[] x,short xOffset,short xLength,byte[] y ,short yOffset,short yLength)
    {
        if(xLength > yLength)
            return (short)1;
        if(xLength < yLength)
            return (short)(-1);
        short digit_mask = 0xff;
        short digit_len = 0x08;
        short result = 0;
        short i = (short) (xLength + xOffset - 1);
        short j = (short) (yLength + yOffset - 1);

        for (; i >= xOffset; i--, j--) {
            result = (short) (result + (short) (x[i] & digit_mask) - (short) (y[j] & digit_mask));
            if(result > 0)
                return (short)1;
            if(result < 0)
                return (short)-1;
        }
        return 0;
    }

public byte[]modMultiply（byte[]x，short xOffset，short xLength，byte[]y，
短Y偏移、短Y长度、短tempOutoffset）{
//将x值复制到临时rambuffer
Util.arrayCopy（x，xOffset，tempBuffer，tempOutoffset，xLength）；
//复制y值以匹配rsa_对象的大小
Util.arrayFillNonAtomic（eempromTempBuffer，（短）0，（字节）（Configuration.LENGTH\u RSAOBJECT\u module-1，（字节）0x00）；
Util.arrayCopy（y，yOffset，eempromTempBuffer，（short）（Configuration.LENGTH\u RSAOBJECT\u modules-yllength），yllength）；
//x+y
如果（JBigInteger.add）（x，xOffset，xLength，eempromTempBuffer，
（短）0，配置。长度（模量））；
如果（该值大于（x，xOffset，xLength，tempBuffer，Configuration.TEMP_OFFSET_模数，Configuration.LENGTH_模数）>0）
{
减法（x，xOffset，xLength，tempBuffer，
配置。温度偏移量（模数）、配置。长度（模数）；
}
//（x+y）2
mrsaciipherforsquare.init（mrsaPublicekforsquare，Cipher.MODE_ENCRYPT）；
mRsaCipherForSquaring.doFinal（x，xOffset，Configuration.LENGTH\u RSAOBJECT\u模数，x，
xOffset）；//好的
mrsaciipherforsquaring.doFinal（tempBuffer，tempOutoffset，Configuration.LENGTH_RSAOBJECT_modules，tempBuffer，tempOutoffset）；//确定
if（JBigInteger.subtract（x，xOffset，Configuration.LENGTH_模数，tempBuffer，tempOutoffset，
配置。长度（单位模量）{
JBigInteger.add（x，xOffset，Configuration.LENGTH_模数，tempBuffer，
配置。温度偏移量（模数）、配置。长度（模数）；
} 
mrsaciipherforsquaring.doFinal（eempromTempBuffer，yOffset，Configuration.LENGTH_RSAOBJECT_modules，eempromTempBuffer，yOffset）；//确定
if（JBigInteger.subtract（x，xOffset，Configuration.LENGTH_模数，eempromTempBuffer，yOffset，
配置。长度（单位模量）{
JBigInteger.add（x，xOffset，Configuration.LENGTH_模数，tempBuffer，
配置。温度偏移量（模数）、配置。长度（模数）；
}
//（（x+y）^2-x^2-y^2）/2
JBigInteger.modular_除以_2（x，xOffset，Configuration.LENGTH_modules，tempBuffer，Configuration.TEMP_OFFSET_modules，Configuration.LENGTH_modules）；
返回x；
}
公共静态布尔加法（字节[]x，短xOffset，短xLength，字节[]y，
短Y偏移，短Y长度）{
短数字屏蔽=0xff；
短数字_len=0x08；
短结果=0；
短i=（短）（xLength+xOffset-1）；
短j=（短）（Y长度+Y偏移-1）；
对于（；i>=xOffset；i--，j--）{
结果=（短）（结果+（短）（x[i]和数字屏蔽）+（短）（y[j]和数字屏蔽））；
x[i]=（字节）（结果和数字屏蔽）；
结果=（短）（（结果>>数字长度）和数字掩码）；
}
而（结果>0&&i>=xOffset）{
结果=（短）（结果+（短）（x[i]&数字屏蔽）；
x[i]=（字节）（结果和数字屏蔽）；
结果=（短）（（结果>>数字长度）和数字掩码）；
我--；
}
返回结果！=0；
}
公共静态布尔减法（字节[]x，短xOffset，短xLength，字节[]y，
短Y偏移，短Y长度）{
短数字屏蔽=0xff；
短i=（短）（xLength+xOffset-1）；
短j=（短）（Y长度+Y偏移-1）；
短进位=0；
短减法结果=0；
对于（；i>=xOffset&&j>=yOffset；i--，j--）{
减法结果=（短）（（x[i]&数字掩码）
-（y[j]&数字掩码-进位）；
x[i]=（字节）（减法结果和数字掩码）；
进位=（短）（减法结果<0？1:0）；
}
对于（；i>=xOffset&&carry>0；i--）{
如果（x[i]！=0）
进位=0；
x[i]=1；
}
返回进位>0；
}
公共短路大于（字节[]x，短xOffset，短xLength，字节[]y，短yOffset，短yLength）
{
如果（X长度>Y长度）
返回（短）1；
if（X长度=xOffset；i--，j--）{
结果=（短）（结果+（短）（x[i]和数字屏蔽）-（短）（y[j]和数字屏蔽））；
如果（结果>0）
返回（短）1；
如果（结果<0）
返回（短）-1；
}
返回0；
}

---

这段代码适用于少量代码，但适用于较大的代码时会失败。下面是一个非常简单的单元测试，其中包含（希望）代码的工作变体：

package test.java.so;

import java.math.BigInteger;
import java.util.Random;

import javacard.framework.JCSystem;
import javacard.framework.Util;
import javacard.security.KeyBuilder;
import javacard.security.RSAPublicKey;
import javacardx.crypto.Cipher;

import org.apache.commons.lang3.ArrayUtils;
import org.bouncycastle.util.Arrays;
import org.junit.Assert;
import org.junit.Test;

import sutil.test.AbstractTest;

public class So36966764_Test extends AbstractTest {

    private static final int NUM_BITS = 1024;

    // Dummy
    static class Configuration {
        public static final short LENGTH_MODULUS = NUM_BITS/8;
        public static final short LENGTH_RSAOBJECT_MODULUS = LENGTH_MODULUS;
        public static final short TEMP_OFFSET_MODULUS = 0;
        public static final short TEMP_OFFSET_RESULT = LENGTH_MODULUS;
    }

    private byte[] tempBuffer = JCSystem.makeTransientByteArray((short)(Configuration.TEMP_OFFSET_RESULT+Configuration.LENGTH_MODULUS), JCSystem.CLEAR_ON_DESELECT);
    private byte[] eempromTempBuffer = new byte[Configuration.LENGTH_MODULUS]; // Why EEPROM?
    private RSAPublicKey mRsaPublicKekForSquare = (RSAPublicKey)KeyBuilder.buildKey(KeyBuilder.TYPE_RSA_PUBLIC, (short)NUM_BITS, false);
    private Cipher mRsaCipherForSquaring = Cipher.getInstance(Cipher.ALG_RSA_NOPAD, false);

    // Assuming xLength==yLength==LENGTH_MODULUS
    public byte[] modMultiply(byte[] x, short xOffset, short xLength, byte[] y, short yOffset, short yLength, short tempOutoffset) {

        //copy x value to temporary rambuffer
        Util.arrayCopy(x, xOffset, tempBuffer, tempOutoffset, xLength);

        // copy the y value to match th size of rsa_object
        Util.arrayFillNonAtomic(eempromTempBuffer, (short)0, (short) (Configuration.LENGTH_RSAOBJECT_MODULUS-1),(byte)0x00);
        Util.arrayCopy(y,yOffset,eempromTempBuffer,(short)(Configuration.LENGTH_RSAOBJECT_MODULUS - yLength),yLength);

        // x+y
        if(add(x,xOffset,xLength, eempromTempBuffer, (short)0,Configuration.LENGTH_MODULUS)) {
            subtract(x,xOffset,xLength, tempBuffer, Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
        }
        while(isGreater(x, xOffset, xLength, tempBuffer,Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS)>0) {
            subtract(x,xOffset,xLength, tempBuffer,Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
        }

        //(x+y)2
        mRsaCipherForSquaring.init(mRsaPublicKekForSquare, Cipher.MODE_ENCRYPT);
        mRsaCipherForSquaring.doFinal(x, xOffset, Configuration.LENGTH_RSAOBJECT_MODULUS, x, xOffset); // OK

        mRsaCipherForSquaring.doFinal(tempBuffer, tempOutoffset, Configuration.LENGTH_RSAOBJECT_MODULUS, tempBuffer, tempOutoffset); // OK

        if (subtract(x, xOffset, Configuration.LENGTH_MODULUS, tempBuffer, tempOutoffset,
                Configuration.LENGTH_MODULUS)) {
            add(x, xOffset, Configuration.LENGTH_MODULUS, tempBuffer,
                    Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
        }

        /*WRONG OFFSET mRsaCipherForSquaring.doFinal(eempromTempBuffer, yOffset, Configuration.LENGTH_RSAOBJECT_MODULUS, eempromTempBuffer, yOffset); */
        mRsaCipherForSquaring.doFinal(eempromTempBuffer, (short)0, Configuration.LENGTH_RSAOBJECT_MODULUS, eempromTempBuffer, (short)0); //OK

        /*WRONG OFFSET if (subtract(x, xOffset, Configuration.LENGTH_MODULUS, eempromTempBuffer, yOffset,*/
        if (subtract(x, xOffset, Configuration.LENGTH_MODULUS, eempromTempBuffer, (short)0,Configuration.LENGTH_MODULUS)) {
            add(x, xOffset, Configuration.LENGTH_MODULUS, tempBuffer,
                    Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
        }
        // ((x+y)^2 - x^2 -y^2)/2
        modular_division_by_2(x, xOffset,Configuration. LENGTH_MODULUS, tempBuffer, Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
        return x;
    }

    public static boolean add(byte[] x, short xOffset, short xLength, byte[] y, short yOffset, short yLength) {
        short digit_mask = 0xff;
        short digit_len = 0x08;
        short result = 0;
        short i = (short) (xLength + xOffset - 1);
        short j = (short) (yLength + yOffset - 1);

        for (; i >= xOffset; i--, j--) {
            result = (short) (result + (short) (x[i] & digit_mask) + (short) (y[j] & digit_mask));

            x[i] = (byte) (result & digit_mask);
            result = (short) ((result >> digit_len) & digit_mask);
        }
        while (result > 0 && i >= xOffset) {
            result = (short) (result + (short) (x[i] & digit_mask));
            x[i] = (byte) (result & digit_mask);
            result = (short) ((result >> digit_len) & digit_mask);
            i--;
        }

        return result != 0;
    }

    public static boolean subtract(byte[] x, short xOffset, short xLength, byte[] y, short yOffset, short yLength) {
        short digit_mask = 0xff;
        short i = (short) (xLength + xOffset - 1);
        short j = (short) (yLength + yOffset - 1);
        short carry = 0;
        short subtraction_result = 0;

        for (; i >= xOffset && j >= yOffset; i--, j--) {
            subtraction_result = (short) ((x[i] & digit_mask)
                    - (y[j] & digit_mask) - carry);
            x[i] = (byte) (subtraction_result & digit_mask);
            carry = (short) (subtraction_result < 0 ? 1 : 0);
        }
        for (; i >= xOffset && carry > 0; i--) {
            if (x[i] != 0)
                carry = 0;
            x[i] -= 1;
        }

        return carry > 0;
    }

    public short isGreater(byte[] x,short xOffset,short xLength,byte[] y ,short yOffset,short yLength)
    {
        // Beware: this part is not tested
        while(xLength>yLength) {
            if(x[xOffset++]!=0x00) {
                return 1; // x is greater
            }
            xLength--;
        }
        while(yLength>xLength) {
            if(y[yOffset++]!=0x00) {
                return -1; // y is greater
            }
            yLength--;
        }
        // Beware: this part is not tested END
        for(short i = 0; i < xLength; i++) {
            if (x[xOffset] != y[yOffset]) {
                short srcShort = (short)(x[xOffset]&(short)0xFF);
                short dstShort = (short)(y[yOffset]&(short)0xFF);
                return ( ((srcShort > dstShort) ? (byte)1 : (byte)-1));
            }
            xOffset++;
            yOffset++;
        }
        return 0;
    }

    private void modular_division_by_2(byte[] input, short inOffset, short inLength, byte[] modulus, short modulusOffset, short modulusLength) {
        short carry = 0;
        short digit_mask = 0xff;
        short digit_first_bit_mask = 0x80;
        short lastIndex = (short) (inOffset + inLength - 1);

        short i = inOffset;
        if ((byte) (input[lastIndex] & 0x01) != 0) {
            if (add(input, inOffset, inLength, modulus, modulusOffset,
                    modulusLength)) {
                carry = digit_first_bit_mask;
            }
        }

        for (; i <= lastIndex; i++) {
            if ((input[i] & 0x01) == 0) {
                input[i] = (byte) (((input[i] & digit_mask) >> 1) | carry);
                carry = 0;
            } else {
                input[i] = (byte) (((input[i] & digit_mask) >> 1) | carry);
                carry = digit_first_bit_mask;
            }
        }
    }

    @Test
    public void testModMultiply() {
        Random r = new Random(12345L);
        for(int iiii=0;iiii<10;iiii++) {
            BigInteger modulus = BigInteger.probablePrime(NUM_BITS, r);
            System.out.println(" M = " + modulus);
            byte[] modulusBytes = normalize(modulus.toByteArray());
            Util.arrayCopyNonAtomic(modulusBytes, (short)0, tempBuffer, Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);

            mRsaPublicKekForSquare.setModulus(modulusBytes, (short)0, (short)modulusBytes.length);
            mRsaPublicKekForSquare.setExponent(new byte[] {0x02}, (short)0, (short)1);

            for(int iii=0;iii<1000;iii++) {
                BigInteger x = new BigInteger(NUM_BITS, r).mod(modulus);
                System.out.println(" x = " + x);
                BigInteger y = new BigInteger(NUM_BITS, r).mod(modulus);
                System.out.println(" y = " + y);
                BigInteger accResult;
                {
                    byte[] xBytes = normalize(x.toByteArray());
                    byte[] yBytes = normalize(y.toByteArray());
                    byte[] accResultBytes = modMultiply(xBytes, (short)0, (short)xBytes.length, yBytes, (short)0, (short)yBytes.length, Configuration.TEMP_OFFSET_RESULT);
                    accResult = new BigInteger(1, accResultBytes);
                }
                System.out.println(" Qr = " + accResult);
                BigInteger realResult = x.multiply(y).mod(modulus);
                System.out.println(" Rr = " + realResult);
                Assert.assertEquals(realResult, accResult);
            }
        }
    }

    private byte[] normalize(byte[] xBytes) {
        if(xBytes.length<Configuration.LENGTH_MODULUS) {
            xBytes = ArrayUtils.addAll(new byte[Configuration.LENGTH_MODULUS-xBytes.length], xBytes);
        }
        if(xBytes.length>Configuration.LENGTH_MODULUS) {
            Assert.assertEquals(xBytes[0], 0x00);
            xBytes=Arrays.copyOfRange(xBytes, 1, xBytes.length);
        }
        return xBytes;
    }
}

package test.java.so；
导入java.math.biginger；
导入java.util.Random；
导入javacard.framework.JCSystem；
导入javacard.framework.Util；
导入javacard.security.KeyBuilder；
导入javacard.security.RSAPublicKey；
导入javacardx.crypto.Cipher；
导入org.apache.commons.lang3.ArrayUtils；
导入org.bouncycastle.util.Arrays；
导入org.junit.Assert；
导入org.junit.Test；
导入sutil.test.AbstractTest；
公共类So36966764_测试扩展了抽象测试{
专用静态最终int NUM_位=1024；
//假人
静态类配置{
公共静态最终短长度\u模数=NUM\u位/8；
公共静态最终短长度物体模量=长度模量；
公共静态最终短温度偏移模数=0；
公共静态最终短温度偏移结果=长度模数；
}
私有字节[]tempBuffer=JCSystem.makeTransientByteArray（（短）（Configuration.TEMP\u OFFSET\u RESULT+Configuration.LENGTH\u modules），JCSystem.CLEAR\u ON\u DESELECT）；
私有字节[]eempromTempBuffer=新字节[Configuration.L]
private byte[] multiply(byte[] x, short xOffset, short xLength, byte[] y,
        short yOffset, short yLength,short tempOutoffset)
{
    normalize();
    //copy x value to temporary rambuffer
    Util.arrayFillNonAtomic(tempBuffer, tempOutoffset,(short) (Configuration.LENGTH_RSAOBJECT_MODULUS+tempOutoffset),(byte)0x00);
    Util.arrayCopy(x, xOffset, tempBuffer, (short)(Configuration.LENGTH_RSAOBJECT_MODULUS - xLength), xLength);

    // copy the y value to match th size of rsa_object
    Util.arrayFillNonAtomic(ram_y, IConsts.OFFSET_START, (short) (Configuration.LENGTH_RSAOBJECT_MODULUS-1),(byte)0x00);
    Util.arrayCopy(y,yOffset,ram_y,(short)(Configuration.LENGTH_RSAOBJECT_MODULUS - yLength),yLength);

    Util.arrayFillNonAtomic(ram_y_prime, IConsts.OFFSET_START, (short) (Configuration.LENGTH_RSAOBJECT_MODULUS-1),(byte)0x00);
    Util.arrayCopy(y,yOffset,ram_y_prime,(short)(Configuration.LENGTH_RSAOBJECT_MODULUS - yLength),yLength);

    Util.arrayFillNonAtomic(ram_x, IConsts.OFFSET_START, (short) (Configuration.LENGTH_RSAOBJECT_MODULUS-1),(byte)0x00);
    Util.arrayCopy(x,xOffset,ram_x,(short)(Configuration.LENGTH_RSAOBJECT_MODULUS - xLength),xLength);

    // if x>y
    if(this.isGreater(ram_x, IConsts.OFFSET_START, Configuration.LENGTH_RSAOBJECT_MODULUS, ram_y,IConsts.OFFSET_START, Configuration.LENGTH_MODULUS)>0)
    {

        // x <- x-y
        JBigInteger.subtract(ram_x,IConsts.OFFSET_START,Configuration.LENGTH_RSAOBJECT_MODULUS, ram_y,
                IConsts.OFFSET_START, Configuration.LENGTH_RSAOBJECT_MODULUS);
    }
    else
    {

        // y <- y-x
        JBigInteger.subtract(ram_y_prime,IConsts.OFFSET_START,Configuration.LENGTH_RSAOBJECT_MODULUS, ram_x,
                IConsts.OFFSET_START, Configuration.LENGTH_MODULUS);
         // ramy stores the (y-x) values copy value to ram_x
        Util.arrayCopy(ram_y_prime, IConsts.OFFSET_START,ram_x,IConsts.OFFSET_START,Configuration.LENGTH_RSAOBJECT_MODULUS);

    }

        //|x-y|2
        mRsaCipherForSquaring.init(mRsaPublicKekForSquare, Cipher.MODE_ENCRYPT);
        mRsaCipherForSquaring.doFinal(ram_x, IConsts.OFFSET_START, Configuration.LENGTH_RSAOBJECT_MODULUS, ram_x,
                IConsts.OFFSET_START); // OK

        // x^2
        mRsaCipherForSquaring.doFinal(tempBuffer, tempOutoffset, Configuration.LENGTH_RSAOBJECT_MODULUS, tempBuffer, tempOutoffset); // OK

        // y^2
        mRsaCipherForSquaring.doFinal(ram_y,IConsts.OFFSET_START, Configuration.LENGTH_RSAOBJECT_MODULUS, ram_y,IConsts.OFFSET_START); //OK 



        if (JBigInteger.add(ram_y, IConsts.OFFSET_START, Configuration.LENGTH_MODULUS, tempBuffer, tempOutoffset,
                Configuration.LENGTH_MODULUS)) {
              // y^2 + x^2 
            JBigInteger.subtract(ram_y, IConsts.OFFSET_START, Configuration.LENGTH_MODULUS, tempBuffer,
                    Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
        } 


        //  x^2 + y^2
        if (JBigInteger.subtract(ram_y, IConsts.OFFSET_START, Configuration.LENGTH_MODULUS, ram_x, IConsts.OFFSET_START,
                Configuration.LENGTH_MODULUS)) {

            JBigInteger.add(ram_y, IConsts.OFFSET_START, Configuration.LENGTH_MODULUS, tempBuffer,
                    Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
    }
    // (x^2 + y^2 - (x-y)^2)/2
   JBigInteger.modular_division_by_2(ram_y, IConsts.OFFSET_START,Configuration. LENGTH_MODULUS, tempBuffer, Configuration.TEMP_OFFSET_MODULUS, Configuration.LENGTH_MODULUS);
   return ram_y;
}