下面是一个非常简单的单元测试,其中包含代码的(希望)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;
}
}
什么(恕我直言)错了:
The isGreater()
方法——虽然可以使用减法来比较数字,但从最高有效字节开始比较相应的字节并在第一个不匹配时停止比较更容易(也更快)。 (在减法情况下,您需要完成减法并返回最终结果的符号 - 您的原始代码以第一个“不匹配”结束。)
x+y
溢出——您应该保留加法溢出情况的模减法(即当add()
返回 true) 在您的最后一次编辑中。
偏移量为eempromTempBuffer
-- 在你使用过的两个地方yOffset
并且应该使用0
(用“错误的偏移量”注释掉)。
Casting Configuration.LENGTH_RSAOBJECT_MODULUS-1
to byte
对于较大的模长度值来说不是一个好主意
一些(随机)评论:
测试使用已经提到的jcardsim to work
该代码假设长度为x
and y
都是LENGTH_MODULUS
(也LENGTH_RSAOBJECT_MODULUS
等于LENGTH_MODULUS
)
这不是一个好主意eempromTempBuffer
在非易失性存储器中
你的代码非常类似于这段代码这很有趣
关于这个主题的有趣读物是here(第 4.2.3 节)。
祝你好运!
免责声明:我不是加密专家也不是数学家,所以请验证我的想法