Shannon's perfect-secrecy theorem states that a perfect encryption system that yields zero information to the adversary must be a one-time pad (OTP) with the keys randomly generated and never reused. In this work we design the first encryption method (classical or quantum) that overcomes Shannon's theorem to achieve perfect secrecy with reusable keys. Because the mechanisms used are fundamentally quantum, Shannon's theorem remains true in the classical regime. Consequently, the quantum encryption design demonstrates decisive quantum advantage by achieving a goal impossible for classical systems. Finally, the design has major practical advantages by not requiring authentication and having silent tampering detection.
Shannon's perfect-secrecy theorem states that a perfect encryption system that yields zero information to the adversary must be a one-time pad (OTP) with the keys randomly generated and never reused. In this work we design the first encryption method (classical or quantum) that overcomes Shannon's theorem to achieve perfect secrecy with reusable keys. Because the mechanisms used are fundamentally quantum, Shannon's theorem remains true in the classical regime. Consequently, the quantum encryption design demonstrates decisive quantum advantage by achieving a goal impossible for classical systems. Finally, the design has major practical advantages by not requiring authentication and having silent tampering detection.
The One-time-pad (OTP) was mathematically proven to be perfectly secure by Shannon in 1949. We propose to extend the classical OTP from an n-bit finite field to the entire symmetric group over the finite field. Within this context the symmetric group can be represented by a discrete Hilbert sphere (DHS) over an n-bit computational basis. Unlike the continuous Hilbert space defined over a complex field in quantum computing, a DHS is defined over the finite field GF(2). Within this DHS, the entire symmetric group can be completely described by the complete set of n-bit binary permutation matrices. Encoding of a plaintext can be done by randomly selecting a permutation matrix from the symmetric group to multiply with the computational basis vector associated with the state corresponding to the data to be encoded. Then, the resulting vector is converted to an output state as the ciphertext. The decoding is the same procedure but with the transpose of the pre-shared permutation matrix. We demonstrate that under this extension, the 1-to-1 mapping in the classical OTP is equally likely decoupled in Discrete Hilbert Space. The uncertainty relationship between permutation matrices protects the selected pad, consisting of M permutation matrices (also called Quantum permutation pad, or QPP). QPP not only maintains the perfect secrecy feature of the classical formulation but is also reusable without invalidating the perfect secrecy property. The extended Shannon perfect secrecy is then stated such that the ciphertext C gives absolutely no information about the plaintext P and the pad.
Quantum cryptography-the application of quantum information processing and quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the success of the QKD, the development of quantum encryption algorithms is limited to designs of mostly one-time pads (OTP) that are unsuitable for most communication needs. In this work we propose a non-OTP quantum encryption design utilizing a quantum state creation process to encrypt messages. As essentially a non-OTP quantum block cipher the method stands out against existing methods with the following features: 1. complex key-ciphertext relation (i.e. confusion) and complex plaintext-ciphertext relation (i.e. diffusion); 2. mode of operation design for practical encryption on multiple blocks. These features provide key reusability and protection against eavesdropping and standard cryptanalytic attacks.
Modern cryptography offers three goals of Confidentiality, Integrity and Availability, known as CIA triad. Confidentiality of any message or communication is secrecy of its content. All the modern cryptosystems provide cryptographic secrecy and not perfect secrecy. Two ingredients of perfect secrecy are truly random source and secure communication channel. Both are available in quantum computing paradigm. However, Quantum Computers are not yet commercially available. Certain time-tested cryptographic techniques in classical computing can be combined with principles of quantum computing to to achieve the goal of perfect secrecy. Theoretically, One Time Pad (OTP) is proven to be unconditionally secure. The paper suggests an hybrid approach to cryptography by generating OTP using quantum superposition states. The results of OTP generation are corroborated with theoretical values. The OTP so generated by realization of the suggested approach on a classical system is found to pass the test for randomness.
One of the key aspects of Shannon theory is that it provides guidance for designing the most efficient systems, such as minimizing errors and clarifying the limits of coding. This theory has seen great developments in the 50 years since 1948. It has played a vital role in enabling the development of modern ultra-fast, stable, and highly dependable information and communication systems. Shannon theory is supported by statistical communication theories such as detection and estimation theory. The theory of communication systems that transmit Shannon information using quantum media is called quantum Shannon information theory, and research began in the 1960s. The theoretical formulation comparable to conventional Shannon theory has been completed. Its important role is to suggest that application of quantum effects will surpass existing communication performance. It would be meaningless if performance, efficiency, and utility were to deteriorate due to quantum effects, even if a certain new function is given. This paper suggests that there are various limitations to utilizing quantum Shannon information theory to benefit real-world communication systems and presents a theoretical framework for achieving the ultimate goal. Finally, we present the perfect secure cipher that overcomes the Shannon impossibility theorem without degrading communication performance and sensors as an example.
One of the key aspects of Shannon's theory is that it provides guidance for designing the most efficient systems, such as minimizing errors and clarifying the limits of coding. Such theories have made great developments in the 50 years since 1948. It has played a vital role in enabling the development of modern ultra-fast, stable, and highly dependable information and communication systems. The Shannon theory is supported by the statistical communication theory such as detection and estimation theory. The theory of communication systems that transmit Shannon information using quantum media is called quantum Shannon information theory, and research began in the 1960s. The theoretical formulation comparable to conventional Shannon theory has been completed. Its important role is to suggest that application of quantum effect will surpass existing communication performance. It would be meaningless if performance, efficiency, and utility were to deteriorate due to quantum effects, even if certain new function is given. This paper suggests that there are various limitations to utilizing quantum Shannon information theory to benefit real-world communication systems and presents a theoretical framework for achieving the ultimate goal. Finally, we introduce the perfect secure cipher that overcome the Shannon impossibility theorem without degrading communication performance and sensor et al as the examples.
In this thesis, a new practical method to realize one-time pad perfect secrecy for wireless \ncommunication is presented. Most commonly used security methods are based on cryp- tographic \ntechniques employed at the upper layers of a wireless network. These methods basically rely on the \ncomputational hardness of some mathematical problems. This com- putational complexity is vulnerable \nin nature due to fast-growing computational power of hardware technology, yet not taking into \naccount the revolution of Quantum computing in further future. Another core problematic issue \nexists in symmetric security systems; there is a deadlock between securing the channel and \nestablishing the shared key. We need the key for securing the channel, on the other hand, for \nsharing the key we need a secure channel. \n \nTo address such vulnerabilities, Physical Layer Security (PLS) has been widely studied in recent \nyears. PLS schemes build on the idea of turning unpredictable and random wire- less channel \ncharacteristics into a source for information-theoretic security. Information- theoretic security \nitself, relies on Shannon’s pioneer work . Shannon, inspired by one-time pad, also known as Vernam \ncipher, theoretically showed that the only unconditional per- fect secrecy system is a one-time pad \nwith a key at least as random as the plaintext, i.e., a system that uses a different random key to \ncipher any new plaintext. In PLS key genera- tion methods, legitimate parties alternately send \nprobe signals and estimate Channel State Information (CSI) of common random channel and then \nconvert enough amount of these estimates to secure shared keys. To achieve perfect secrecy, the key \ngeneration methods must meet the key randomness and Key Generation Rate (KGR) requirements of \ntheir specific cryptographic applications. \n \nIn this research a new practical system for achieving unconditional perfect secrecy is presented. \nOur system uses channel phase as the probing parameter to fully benefit from its uniform \ndistribution over [0, 2π]. It also uses an encryption method based on modulo- \n2π addition of phase values which is the perfect counterpart of XOR addition in binary one-time \npad. Moreover, by intentionally perturbing the wireless channel in vicinity of the transceiver \nantenna based on RF-mirrors structure, it produces different random phase values in each channel \nprobing, much faster than the inherent channel variation would do, resulting in dramatically higher \nKGR than any wide-band PLS scheme presented so far and realizing true perfect secrecy. Most \nimportantly, the focus of this research is a detailed practical algorithm for implementing the \nsystem as well as empirical results which makes \nour system the first channel-phase-based PLS scheme implementation, reported so far.