Perfect Confidentiality through Unconditionally Secure Homomorphic Encryption Using OTP With a Single Pre-Shared Key

Unconditional security means that knowledge of an encrypted text does not provide any information about the corresponding plaintext; or more, regardless of the number of ciphertexts available to an attacker, no amount of cryptanalysis can break the cipher. Until now, only the One-Time Pad (OTP) method meets this condition with well-defined assumptions. The design of a Homomorphic Encryption scheme that allows operations over the encrypted data is required in current applications to reach the highest possible level of privacy. However, existing symmetric solutions that use OTP have a key management problem; they are not linear encryption, which means that they have high computational complexity, and some of them do not meet all homomorphic properties. This article simulates the OTP taking into consideration these issues and achieving the maximum resistance to cryptanalysis, even when the attacker has great computing power. The first major advantage of the proposed OTP-based method is that it only uses a single pre-shared key. The key is composed of two sections, a fixed number of bits followed by random bits; the size of each section is dependent on the robustness of the system. Analysis of the proposed technique shows that it provides perfect privacy by using a different key for each message to be encrypted.