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arXiv:1511.02338

Towards Quantum Enigma Cipher II-A protocol based on quantum illumination-

Osamu Hirota

Published Nov 7, 2015• 2 citations
arXivHTMLPDF

Abstract

This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security analysis and ability of computers. This kind of cipher can be decrypted with probability one in principle by the Brute force attack in which an eavesdropper tries all the possible keys based on the correct ciphertext and some known plaintext. A cipher with quantum effects in physical layer may protect the system from the Brute force attack by means of the quantum no cloning theorem and randomizations based on quantum noise effect. The randomizations for the ciphertext which is the output from the mathematical encryption box is crucial to realize a quantum enigma cipher. Especially, by randomizations, it is necessary to make a substantial difference in accuracy of ciphertext in eavesdropper's observation and legitimate user's observation. The quantum illumination protocol can make a difference in error performance of the legitimate's receiver and the eavesdropper's receiver. This difference is due to differences in ability of the legitimate's receiver with entanglement and the eavesdropper's receiver without entanglement. It is shown in this note that the quantum illumination can be employed as an element of the most simple quantum enigma cipher.

DOI
10.48550/arxiv.1511.02338

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This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security analysis and ability of computers. This kind of cipher can be decrypted with probability one in principle by the Brute force attack in which an eavesdropper tries all the possible keys based on the correct ciphertext and some known plaintext. A cipher with quantum effects in physical layer may protect the system from the Brute force attack by means of the quantum no cloning theorem and randomizations based on quantum noise effect. The randomizations for the ciphertext which is the output from the mathematical encryption box is crucial to realize a quantum enigma cipher. Especially, by randomizations, it is necessary to make a substantial difference in accuracy of ciphertext in eavesdropper's observation and legitimate user's observation. The quantum illumination protocol can make a difference in error performance of the legitimate's receiver and the eavesdropper's receiver. This difference is due to differences in ability of the legitimate's receiver with entanglement and the eavesdropper's receiver without entanglement. It is shown in this note that the quantum illumination can be employed as an element of the most simple quantum enigma cipher.
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm for cryptanalysis and ability of computers. This kind of cipher cannot exceed the Shannon limit of cryptography,and it can be decrypted with probability one in principle by trying all the possible keys against the data length equal to the secret key length. A cipher with quantum effect in physical layer may exceed the Shannon limit of cryptography. The quantum stream cipher by α/ηα/ηα/η or Yuen-2000 protocol (Y-00) which operates at Gbit/sec is a typical example of such a cipher. That is, ciphertext of mathematical cipher with a secret key is masked by quantum noise of laser light when an eavesdropper observes optical signals as a ciphertext of the mathematical cipher, while the legitimate receiver does not suffer the quantum noise effect. As a result, the inherent difference of accuracy of ciphertext between eavesdropper and legitimate receiver arises. This is a necessary condition to exceed the Shannon limit of cryptography. In this note, we present a new method to generate an inherent difference of accuracy of the ciphertext, taking into account a fundamental properties of quantum detection schemes.
This research note suggests a new way to realize a high speed direct encryption based on quantum detection theory. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm for cryptanalysis and ability of computers. This kind of cipher cannot exceed the Shannon limit of cryptography, and it can be decrypted with proba- bility one in principle by trying all the possible keys against the data length equal to the secret key length. A cipher with quantum effect in physical layer may exceed the Shannon limit of cryptography. The quantum stream cipher by α/η or Yuen-2000 protocol (Y-00) which operates at Gbit/sec is a typical example of such a cipher. That is, ciphertext of mathematical cipher with a secret key is masked by quantum noise of laser light when an eavesdropper observes optical signals as a ciphertext of the mathematical cipher, while the legitimate receiver does not suffer the quantum noise effect. As a result, the inherent difference of accuracy of ciphertext between eavesdropper and legitimate receiver arises. This is a necessary condition to exceed the Shannon limit of cryptography. In this note, we present a new method to generate an inherent difference of accuracy of the ciphertext, taking into account a fundamental properties of quantum detection schemes.
This paper is dedicated to the late Professor H.P. Yuen in commemoration to our 50-year friendship. He invented the concept of quantum stream cipher. It is designed based on a completely different concept from conventional ciphers. The purpose of this cipher is to provide information-theoretic security of long data and secret key with short key length. It is based on hiding the ciphertext of mathematical cipher with quantum noise, achieving unprecedented information-theoretic security in any cipher. The protocol corresponds to randomizing the ciphertext by means of differentiating the receiving performance of Bob with key and Eve without key according to the principle of quantum communication theory. In this paper, we introduce some progress on the specific method to develop from the standard type to generalized quantum stream cipher (Quantum Enigma Cipher). There are two methods for generalization. One is the additional randomization method by the product cipher form and the other is the M-th order extended quantum coding method. Here we discuss the former. The results proved that it has sufficient information-theoretic security against known plaintext attack on key in comparison with quantum data locking. The latter method will be reported in Part II.
We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as $\ensuremath{\alpha}\ensuremath{\eta}$ and show that it is equivalent to a random cipher in which the required randomization is affected by coherent-state quantum noise. We describe the currently known security features of $\ensuremath{\alpha}\ensuremath{\eta}$ and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how $\ensuremath{\alpha}\ensuremath{\eta}$ used in conjunction with any standard stream cipher such as the Advanced Encryption Standard provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that $\ensuremath{\alpha}\ensuremath{\eta}$ is equivalent to a nonrandom stream cipher.
Cryptographic protocols can be classified by the type of security against eavesdropping which they provide. There exist mathematically secure schemes whose security relies on mathematical proofs (like the Vernam cipher discussed below) or conjectures (like public key RSA encryption) about the complexity of deciphering the message without possessing the correct key. The majority of current secure public Internet connections rely on such schemes. Alternatively, a cryptographic setup may provide a physically secure method for communicating. In these setups the security is provided by the physical laws governing the communication protocol. Here we first discuss a provably secure classical communication protocol and then quantum methods for distributing the necessary keys. The BB84 protocol relies on the impossibility of perfectly distinguishing non-orthogonal quantum states from one copy of the quantum system. The scheme was invented in 1984 and is the first of its kind. In contrast, the Ekert91 protocol makes use of Bell correlations between entangled pairs of photons. These correlations are destroyed when Eve attempts to make a measurement on one of the particles but also when imperfections, such as decoherence processes, affect the scheme. As long as no such “elements of reality” are introduced, and Bell correlations violating local realism can be generated by Alice and Bob, no eavesdropper can be present. One-time pads and the Vernam cipher The Vernam cipher is a cryptographic protocol which allows the encryption and decryption protocol to be publicly known. The security of the protocol relies entirely on the key which is private and not publicly known. Alice and Bob share identical n -bit secret key strings (one-time pad).
Based on the principles of both classical and quantum computation primitives, a new symmetric key quantum cryptographic algorithm is proposed. This algorithm can be used to encrypt classical binary messages as well as quantum information. Encryption and decryption are implemented by the aid of classical and quantum computation which can be realized by suitable technology. Because each encryption process is under the control of the key which is dynamically and recursively changed through each round in both encryption and decryption and the final ciphertext states are non-orthogonal, the eavesdropper can not acquire fixed ciphertext without the keys so the eavesdropping attack is invalid, which is guaranteed with the no-cloning theory in quantum mechanics. Similarly, the non-orthogonality of the ciphertext renders the Trojan horse attack strategy impossible. Also the algorithm applies a pseudo random process from stage to stage. This pseudo randomness hinders the ability of Eve to attack such a cryptographic scheme.