# Homomorphic Encryption with Addition and Exponentiation

Is there any homomorphic encryption scheme which supports addition and power over cipher text ? Paillier is close but it supports addition and multiplication with a constant.

I am getting an output like this:

1 0 1 0 -1 1


My goal is to make -1 positive by any means. As it will encrypted so I cannot know if it is -1 or 1. This (similar) output is being generated by subtracting binary streams.

For example:

101101 -- A1
111001 --- A2
----------------------------
2 1 2 1 1 0 2 --- A+A2=A3
----------------------------
1 0 1 0 -1 1 ---- A3-1


A1 and A2 bits can be replaced to any other integers. Also, can I perform AND operation in additive mode ? Please note that this question is link to my previous question

Primary Objective: To be able to check any of following

1. How many same bits occurs that is 1ns in A1 and A2 in the same position
2. How many zero bits on the same positions in A1 and A2
3. How many different bit locations in A1 and A2
• Is the plaintext space limited to -1,0,1? – mikeazo Nov 6 '15 at 14:09
• plain text space is not limited to any value. To achieve my result i can use any values. – Umer Nov 6 '15 at 14:11
• If it were limited to -1,0,1 I could see where squaring the ciphertext would ensure that $-1\to 1$. If it is not limited, as you say, how does exponentiation help you achieve your goal of making the value positive? – mikeazo Nov 6 '15 at 14:12
• by taking square of each bit result. – Umer Nov 6 '15 at 14:18
• I have a suggestion for you, as it seems like you aren't getting anywhere with your questions. You have some problem you are trying to solve and you have some direction on a solution (i.e., use homomorphic encryption). You are asking us about a problem with the possible solution, and that is going nowhere. I suggest you better explain the problem you are trying to solve. That context would be very helpful. – mikeazo Nov 6 '15 at 14:24