Homomorphic Encryption for Confidential List Verification
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Solution Overview
Problem
Existing methods for determining if a confidential data element belongs to a list in a cloud environment fail to protect the confidentiality of the data, the list, and the comparison result, especially when delegating the verification to a distant, potentially untrusted server.
Innovation Solution
A method using a leveled fully homomorphic DGHV encryption scheme to encrypt both the candidate data element and the reference data elements, allowing the client device to delegate the verification to a server without disclosing the candidate data element or revealing the comparison result to the server.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the verification is delegated to a distant server, then the computational power and time needed to check if an element belongs to a list is reduced, but the confidentiality of the candidate element and the list is compromised
Solution Approach 1:
The patent introduces encrypted representations (ciphertexts) as intermediaries between the client device and server. The client encrypts the candidate element and the server encrypts the list elements before transmission. The server operates on these encrypted forms without accessing plaintext data, thus maintaining confidentiality while enabling verification. The encryption scheme acts as a mediator that preserves data secrecy during the verification process.
Solution Approach 2:
The patent transforms the verification problem from operating on plaintext data to operating on encrypted data with specific mathematical properties. By changing the parameter space from clear-text values to ciphertexts with homomorphic properties, the system enables computation on encrypted data. The decryption function f(y) = (y mod p) mod n transforms the encrypted verification result back to a usable form while maintaining security throughout the process.
2Loss of information
If the server stores encrypted reference data elements, then the confidentiality of the list is maintained, but the server cannot perform the verification without decrypting the data
Solution Approach 1:
The patent uses the homomorphic encryption scheme as an intermediary that allows the server to perform verification operations directly on encrypted data. The server computes a function g(x', y1, ..., yT) on ciphertexts without decrypting them. This intermediary mechanism bridges the gap between maintaining encryption (for security) and enabling computation (for verification capability).
Solution Approach 2:
The patent replaces the traditional mechanical approach of decrypt-verify-encrypt with a cryptographic substitution where verification is performed directly on encrypted data through homomorphic operations. Instead of breaking encryption to verify, the system substitutes the verification mechanism to work natively in the encrypted domain, eliminating the need for decryption during verification.
3Productivity
If the server computes the verification result, then the verification can be delegated, but the server gains knowledge of the comparison result
Solution Approach 1:
The patent employs encrypted computation as an intermediary layer that prevents the server from learning the verification result. The server computes g(x', y1, ..., yT) which equals f(x')·Πi=1T(yi−x') mod n, but this computation occurs entirely in the encrypted domain. The result remains encrypted and can only be decrypted by the client who holds the secret key, thus the server performs the verification work without gaining knowledge of the outcome.
Solution Approach 2:
The patent changes the parameter space in which the verification result exists. Instead of the result being a plaintext boolean value that the server could learn, the result is transformed into an encrypted form that the server cannot interpret. The mathematical transformation ensures the server operates on parameters (ciphertexts) that hide the actual verification outcome, maintaining result confidentiality while enabling server-side computation.
Data Source
AI summary
Provided is a method for testing if a candidate data element, belongs to a list of reference data elements, performed by a client device (102) and comprising the steps of generating an encrypted candidate data element (y′) by encrypting said candidate data element (x′) with a leveled fully homomorphic encryption scheme, transmitting said encrypted candidate data element (y′) to a server device (103), storing said reference data elements (xi) receiving, from said server device, a delta value depending on a product of differences, decrypting said delta value with said leveled fully homomorphic encryption scheme, based on said decrypted delta value, determining whether said candidate data element (x′) belongs to said list of reference data elements (xi). Other embodiments disclosed.