Efficient Privacy-Preserving Fingerprint-Based Authentication System Using Fully Homomorphic Encryption

Algorithm 1

Homomorphic addition.

	program HomAddition (LweSample ∗x, LweSample ∗y, int numberofbits, CloudKeySet ∗evalkey)
	//two carries
	LweSample ∗carry = new_LweSample_array(2);
	//the first carry is intialized to 1
	bootsCONSTANT(carry, 1, evalkey);
	//two temps
	LweSample ∗temp = new_LweSample_array(2);
	For int i: 0 to (numberofbits − 1)
	temp = bootsXOR(x + i, y + i, evalkey);
	//sum[i] = x[i] XOR y[i] XOR carryin
	sum + i = boots XOR(temp, carry, evalkey);
	temp + 1 = boots AND(x + i, y + i, evalkey);
	//carry out
	carry + 1 = boots MUX(temp, carry, temp + 1, evalkey);
	carry = carry + 1;
	end
	sum + numberofbits = carry;
	return sum;
	end