Multiplying without the * key

I got asked, once, how to multiply two numbers without the '*' key on my keyboard working. My first reaction was "get a new keyboard" but apparently that didn't cut it in this hyper theoretical situation. Hence I came up with the following Java solution using BigIntegers

private static BigInteger shiftMultiply(final BigInteger a, final BigInteger b) {

BigInteger bBuff = new BigInteger(b.toString());

//now for the real calculation

BigInteger product = BigInteger.ZERO;

//for(int i = 0; i < requiredBitSize(b); i++) {

int bShift = 0;

while(bBuff.compareTo(BigInteger.ZERO) > 0)

{

if( bBuff.and(BigInteger.ONE).compareTo(BigInteger.ZERO) != 0) {

BigInteger aBuff = new BigInteger(a.toString());

int aShift = 0;

while(aBuff.compareTo(BigInteger.ZERO) > 0)

{

if( aBuff.and(BigInteger.ONE).compareTo(BigInteger.ZERO) != 0 ){

//product += bitMasks[bMaskPos + aMaskPos];

product = product.add(BigInteger.ONE.shiftLeft(bShift + aShift));

}

aBuff = aBuff.shiftRight(1);

aShift++;

}

}

bBuff = bBuff.shiftRight(1);

bShift++;

}