Osamu Hirota

Osamu Hirota

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.

Osamu Hirota

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 $α/η$ 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.