The fundamental security and efficiency considerations for fresh key generation will be described. It is shown that the attacker's optimal probability of finding the generated key is an indispensable measure of security and that this probability limits the possibility of privacy amplification and the amount of fresh key that can be generated. A new approach to quantum cryptography to be called keyed communication in quantum noise (KCQ) is developed on the basis of quantum detection and communication theory for classical information transmission. KCQ key generation schemes with coherent states of considerable energy will be described. The possibility of fresh key generation is demonstrated for binary and N-ary detection systems under heterodyne attacks. The security issues of these schemes will be discussed and compared with BB84. The emphasis throughout is on concrete finite bit-length protocols.

Key Generation: Foundations and a New Quantum Approach

There exists a great gap between one-time pad with perfect secrecy and conventional mathematical encryption. The Yuen 2000 (Y00) protocol or $\ensuremath{\alpha}\ensuremath{\eta}$ scheme may provide a protocol which covers from the conventional security to the ultimate one, depending on implementations. This paper presents the complexity-theoretic security analysis on some models of the Y00 protocol with nonlinear pseudo-random-number-generator and quantum noise diffusion mapping (QDM). Algebraic attacks and fast correlation attacks are applied with a model of the Y00 protocol with nonlinear filtering like the Toyocrypt stream cipher as the running key generator, and it is shown that these attacks in principle do not work on such models even when the mapping between running key and quantum state signal is fixed. In addition, a security property of the Y00 protocol with QDM is clarified. Consequently, we show that the Y00 protocol has a potential which cannot be realized by conventional cryptography and that it goes beyond mathematical encryption with physical encryption.

Practical security analysis of a quantum stream cipher by the Yuen 2000 protocol

We describe an emerging method of encryption suitable for high-speed optical communication networks. This encryption protocol combines traditional electronic cryptographic algorithms with the physical effect of optical noise of quantum origin to create a highly secure method of secret communications. The resulting optical signal is compatible with today's high speed fiber optic infrastructure including optical amplification and add/drop multiplexing. Systems implementing this protocol can be constructed with common commercially available components. We describe experimental results obtained with a 2.5 Gb/s system. The encrypted signal is shown to travel error-free through >500 km of optical fiber. Simulations show that reaches and data rates consistent with modern long haul optical networks are attainable.

Practical physical-layer encryption: The marriage of optical noise with traditional cryptography

We adapt a physical-layer modulation scheme previously used for enhancing security in the optical domain to an OFDM radio link. The method relies on manipulating the signal constellation according to a cryptographic pseudo-random number generator and adding a small amount of truly random noise at the transmitter. We test the ultra-secure format by generating modified 802.11a packets offline and transmitting them over-the-air using a radio board designed for software defined radio applications. Our initial test system uses an underlying QPSK data format with a 12Mb/s burst-mode data rate. No performance penalty was observed by adding the noise-enhanced encryption function.

Noise-enhanced encryption for physical layer security in an OFDM radio

Security is an important topic of research for future 4G applications employing OFDM modulation. Physical layer security is an emerging candidate, based on the concept of perfect secrecy. In this paper we present a symmetric key physical layer encryption for OFDM systems, termed Masked-OFDM (MOFDM). The OFDM signal becomes practically undetectable by a potential eavesdropper by being masked in a non-orthogonal FDM signal of approximately the same overall bandwidth. This is equivalent to the transmission of roughly twice as much data as the channel degrees of freedom. For the OFDM symbol, a positive secrecy capacity can be achieved in AWGN even in cases where the wiretap channel has a better SNR than the main channel. The system secrecy capacity due to using a structured helping interferer is higher than compared to using a noise-like mask signal. The proposed scheme does not compromise either the bandwidth efficiency, or the error performance of the OFDM system, at the cost of increased transmission power.

Masked-OFDM: A physical layer encryption for future OFDM applications

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.

Takami Eguchi

Papers

Quantum Noise Randomized Ciphers