Constructing Opaque Predicate Using Homomorphic Encryption

OP HE.md

Constructing an opaque predicate using homomorphic encryption involves encrypting a value and performing a homomorphic operation on the encrypted value to generate an encrypted result. This encrypted result is then used as the predicate in a conditional statement, without ever decrypting the value or result.

Here is an example in C# using the Microsoft SEAL homomorphic encryption library:

using System;
using System.Collections.Generic;
using Microsoft.Research.SEAL;

namespace OpaquePredicateExample
{
    class Program
    {
        static void Main(string[] args)
        {
            // Create a new SEAL context with the default parameters
            EncryptionParameters parms = new EncryptionParameters(SchemeType.BFV);
            parms.PolyModulusDegree = 4096;
            parms.CoeffModulus = CoeffModulus.BFVDefault(parms.PolyModulusDegree);
            parms.PlainModulus = new Modulus(40961);
            SEALContext context = new SEALContext(parms);

            // Create a new key generator and generate public and secret keys
            KeyGenerator keygen = new KeyGenerator(context);
            PublicKey publicKey = keygen.PublicKey;
            SecretKey secretKey = keygen.SecretKey;

            // Create a new encryptor and decryptor
            Encryptor encryptor = new Encryptor(context, publicKey);
            Decryptor decryptor = new Decryptor(context, secretKey);

            // Encrypt a value
            int value = 42;
            Plaintext plaintext = new Plaintext(value.ToString());
            Ciphertext encryptedValue = new Ciphertext();
            encryptor.Encrypt(plaintext, encryptedValue);

            // Generate an opaque predicate by performing a homomorphic operation on the encrypted value
            Ciphertext encryptedResult = new Ciphertext();
            Evaluator evaluator = new Evaluator(context);
            evaluator.Square(encryptedValue, encryptedResult); // Square the encrypted value
            encryptedResult.Rescale(); // Rescale the encrypted result

            // Use the encrypted result as the predicate in a conditional statement
            if (encryptedResult.Size > 0) // Encrypted result is non-zero, so predicate is true
            {
                Console.WriteLine("The opaque predicate is true!");
            }
            else // Encrypted result is zero, so predicate is false
            {
                Console.WriteLine("The opaque predicate is false!");
            }
        }
    }
}