Paper 2025/1140

Unconditionally secure encryption algorithm with unified confidentiality and integrity

Abstract

One-Time Pad (OTP), introduced by Shannon, is well-known as an unconditionally secure encryption algorithm and has become the cornerstone of modern cryptography. However, the unconditional security of OTP applies solely to confidentiality and does not extend to integrity. Hash functions such as SHA2, SHA3 or SM3 applies only to integrity but not to confidentiality and also can not obtain unconditional security. Encryption and digital signatures based on asymmetric cryptography can provide confidentiality, integrity and authentication, but they can only achieve computational security. Leveraging the fundamental principles of quantum mechanics，Quantum key distribution（QKD）can achieve unconditional security in theory. However, due to limitations in eavesdropping detection, the use of classical channels and imperfections in quantum devices, it cannot reach unconditional security in practical applications. In this paper, based on polynomial rings and the theory of probability, we propose an unconditionally secure encryption algorithm with unified confidentiality and integrity. The main calculation of the encryption algorithm is Cyclic Redundancy Check(CRC). Theoretical analysis proves that the encryption algorithm not only meets the unconditional security of confidentiality, but also guarantees the unconditional security of integrity, especially suitable for high-security communications such as finance, military, government and other fields.