Feature Homomorphism -- A Cryptographic Scheme For Data Verification Under Ciphertext-Only Conditions

TL;DR

This paper introduces Feature Homomorphism, a cryptographic scheme enabling data verification and integrity checks directly on encrypted data using eigenvalues, enhancing privacy, tamper resistance, and searchable encryption.

Contribution

It proposes a novel homomorphism based on eigenvalues, allowing data verification under ciphertext-only conditions without decrypting the data.

Findings

Enables verification of data consistency via eigenvalues

Supports tamper resistance and non-repudiation

Facilitates searchable encryption using eigenvalues

Abstract

Privacy computing involves the extensive exchange and processing of encrypted data. For the parties involved in these interactions, how to determine the consistency of exchanged data without accessing the original data, ensuring tamper resistance, non-repudiation, quality traceability, indexing, and retrieval during the use of encrypted data, which is a key topic of achieving "Data Availability versus Visibility". This paper proposes a new type of homomorphism: Feature Homomorphism, and based on this feature, introduces a cryptographic scheme for data verification under ciphertext-only conditions. The proposed scheme involves designing a group of algorithms that meet the requirements outlined in this paper, including encryption/decryption algorithms and Feature Homomorphic Algorithm. This group of algorithms not only allows for the encryption and decryption of data but also ensures that the plaintext and its corresponding ciphertext, encrypted using the specified encryption algorithm, satisfy the following property: the eigenvalue of the plaintext obtained using the Feature Homomorphic Algorithm is equal to the eigenvalue of the ciphertext obtained using the same algorithm. With this group of algorithms, it is possible to verify data consistency directly by comparing the eigenvalues of the plaintext and ciphertext without accessing the original data (i.e., under ciphertext-only conditions). This can be used for tamper resistance, non-repudiation, and quality traceability. Additionally, the eigenvalue can serve as a ciphertext index, enabling searchable encryption. This scheme completes a piece of the puzzle in homomorphic encryption. Keywords: Privacy Computing, Data Consistency, Searchable Encryption, Zero-Knowledge Proof, Feature Homomorphism