Secret Key Bits Research Articles

Practical Physical Layer Security Schemes for MIMO-OFDM Systems Using Precoding Matrix Indices

In physical-layer security, secret bits are extracted from wireless channels. With the assumption of channel reciprocity, the legitimate users share the same channel which is independent of the channels between the legitimate users and the eavesdropper, leading to secure transmissions. However, practical implementation of the physical layer security faces many challenges. First, for the correlated channel such as the multiple-input and multiple-output (MIMO) channel, the security is decreased due to the correlation between the generated secret bits. Second, the nearby eavesdropper posts a security threat due to observing the same channel as the legitimate user's. Third, the eavesdroppers might try to reconstruct the wireless environments. In this paper, we propose two practical physical layer security schemes for the MIMO orthogonal frequency-division multiplexing (MIMO-OFDM) systems: the precoding matrix index (PMI)-based secret key generation with rotation matrix (MOPRO) and the channel quantization-based (MOCHA) scheme. The former utilizes PMI and rotated reference signals to prevent the eavesdroppers from learning the secret key information and the latter applies channel quantization in order to extract more secret key bits. It is shown that not only the secure communication but also the MIMO gain can be guaranteed by using the proposed schemes.

Quantum trade-off coding for bosonic communication

The trade-off capacity region of a quantum channel characterizes the optimal net rates at which a sender can communicate classical, quantum, and entangled bits to a receiver by exploiting many independent uses of the channel, along with the help of the same resources. Similarly, one can consider a trade-off capacity region when the noiseless resources are public, private, and secret key bits. In [Phys. Rev. Lett. 108, 140501 (2012)], we identified these trade-off rate regions for the pure-loss bosonic channel and proved that they are optimal provided that a longstanding minimum output entropy conjecture is true. Additionally, we showed that the performance gains of a trade-off coding strategy when compared to a time-sharing strategy can be quite significant. In the present paper, we provide detailed derivations of the results announced there, and we extend the application of these ideas to thermalizing and amplifying bosonic channels. We also derive a "rule of thumb" for trade-off coding, which determines how to allocate photons in a coding strategy if a large mean photon number is available at the channel input. Our results on the amplifying bosonic channel also apply to the "Unruh channel" considered in the context of relativistic quantum information theory.

Exploiting Channel Diversity in Secret Key Generation From Multipath Fading Randomness

We design and analyze a method to extract secret keys from the randomness inherent to wireless channels. We study a channel model for multipath wireless channel and exploit the channel diversity in generating secret key bits. We compare the key extraction methods based both on entire channel state information (CSI) and on single channel parameter such as the received signal strength indicators (RSSI). Due to the reduction in the degree-of-freedom when going from CSI to RSSI, the rate of key extraction based on CSI is far higher than that based on RSSI. This suggests that exploiting channel diversity and making CSI information available to higher layers would greatly benefit the secret key generation. We propose a key generation system based on low-density parity-check (LDPC) codes and describe the design and performance of two systems: one based on binary LDPC codes and the other (useful at higher signal-to-noise ratios) based on four-ary LDPC codes.

Cooperative Secret Key Generation from Phase Estimation in Narrowband Fading Channels

By exploiting multipath fading channels as a source of common randomness, physical layer (PHY) based key generation protocols allow two terminals with correlated observations to generate secret keys with information-theoretical security. The state of the art, however, still suffers from major limitations,e.g., low key generation rate, lower entropy of key bits and a high reliance on node mobility. In this paper, a novel cooperative key generation protocol is developed to facilitate high-rate key generation in narrowband fading channels, where two keying nodes extract the phase randomness of the fading channel with the aid of relay node(s). For the first time, we explicitly consider the effect of estimation methods on the extraction of secret key bits from the underlying fading channels and focus on a popular statistical method - maximum likelihood estimation (MLE). The performance of the cooperative key generation scheme is extensively evaluated theoretically. We successfully establish both a theoretical upper bound on the maximum secret key rate from mutual information of correlated random sources and a more practical upper bound from Cramer-Rao bound (CRB) in estimation theory. Numerical examples and simulation studies are also presented to demonstrate the performance of the cooperative key generation system. The results show that the key rate can be improved by a couple of orders of magnitude compared to the existing approaches.

Counterfactual quantum cryptography based on weak coherent states

In the ``counterfactual quantum cryptography'' scheme [T.-G. Noh, Phys. Rev. Lett. 103, 230501 (2009)], two legitimate distant peers may share secret-key bits even when the information carriers do not travel in the quantum channel. The security of this protocol with an ideal single-photon source has been proved by Yin et al. [Z.-Q. Yin, H. W. Li, W. Chen, Z. F. Han, and G. C. Guo, Phys. Rev. A 82, 042335 (2010)]. In this paper, we prove the security of the counterfactual-quantum-cryptography scheme based on a commonly used weak-coherent-laser source by considering a general collective attack. The basic assumption of this proof is that the efficiency and dark-counting rate of a single-photon detector are consistent for any $n$-photon Fock states. Then through randomizing the phases of the encoding weak coherent states, Eve's ancilla will be transformed into a classical mixture. Finally, the lower bound of the secret-key-bit rate and a performance analysis for the practical implementation are both given.

The Cube Attack on Stream Cipher Trivium and Quadraticity Tests

In 2008 I. Dinur and A. Shamir presented a new type of algebraic attack on symmetric ciphers named cube attack. The method has been applied to reduced variants of stream ciphers Trivium and Grain-128, reduced variants of the block ciphers Serpent and CTC and to a reduced version of the keyed hash function MD6. Previously, a very similar attack named AIDA was introduced by M. Vielhaber, in 2007. In this paper we develop quadraticity tests within the cube attack and apply them to a variant of stream cipher Trivium reduced to 709 initialization rounds. Using this method we obtain the full 80-bit secret key. In this way it eliminates the stage of brute force search of some secret key bits which occured in previous cube attacks.

Correlation power analysis of Trivium

ABSTRACTCorrelation power analysis (CPA) has been a powerful and thoroughly studied threat for implementations of block ciphers and public key algorithms but not yet for stream ciphers. This paper proposes a novel CPA attack on the hardware‐oriented stream cipher Trivium, one of the finally chosen ciphers by the eSTREAM project. Based on the Hamming distance model, the proposed attack exploits the resynchronization phase of Trivium. By choosing proper initial value vectors, the algorithmic noise of the device is completely eliminated. Furthermore, a novel concept of modified correlation coefficients is introduced, which can be used to describe the relation between the hypothetical power consumption values and the measured power consumption values. Through the calculation of modified correlation coefficients, the effect of the electronic noise is significantly decreased and values of the hypotheses can be discriminated uniquely by the highest modified correlation coefficient. According to the recovered hypotheses, many equations on the secret key bits can be obtained, which will be sequentially solved to extract the secret key of Trivium. Compared with Fischer's differential power analysis attack on Trivium, the proposed algorithm is more efficient and robust. Finally, a simulation attack is mounted to confirm the efficiency of the algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

High-Rate Uncorrelated Bit Extraction for Shared Secret Key Generation from Channel Measurements

Secret keys can be generated and shared between two wireless nodes by measuring and encoding radio channel characteristics without ever revealing the secret key to an eavesdropper at a third location. This paper addresses bit extraction, i.e., the extraction of secret key bits from noisy radio channel measurements at two nodes such that the two secret keys reliably agree. Problems include 1) nonsimultaneous directional measurements, 2) correlated bit streams, and 3) low bit rate of secret key generation. This paper introduces high-rate uncorrelated bit extraction (HRUBE), a framework for interpolating, transforming for decorrelation, and encoding channel measurements using a multibit adaptive quantization scheme which allows multiple bits per component. We present an analysis of the probability of bit disagreement in generated secret keys, and we use experimental data to demonstrate the HRUBE scheme and to quantify its experimental performance. As two examples, the implemented HRUBE system can achieve 22 bits per second at a bit disagreement rate of 2.2 percent, or 10 bits per second at a bit disagreement rate of 0.54 percent.

Quantum key distribution protocols with six-photon states against collective noise

Either collective-dephasing noise or collective-rotation noise is considered, two efficient quantum key distribution protocols are presented. With eight product states of three EPR pairs, two bits of secret key can be distributed successfully in each six-photon state. Comparing with the four-photon secret key distribution protocols, the security is also enhanced by using three sets (or more) of measurement bases.

Cryptanalysis of an authentication scheme using truncated polynomials

An attack on a recently proposed authentication scheme of Shpilrain and Ushakov is presented. The public information allows the derivation of a system of polynomial equations for the secret key bits. Our attack uses simple elimination techniques to distill linear equations. For the proposed parameter choice, the attack often finds secret keys or alternative secret keys within minutes with moderate resources.

Secure coherent-state quantum key distribution protocols with efficient reconciliation

We study the equivalence of a realistic quantum key distribution protocol using coherent states and homodyne detection with a formal entanglement purification protocol. Maximally entangled qubit pairs that one can extract in the formal protocol correspond to secret key bits in the realistic protocol. More specifically, we define a qubit encoding scheme that allows the formal protocol to produce more than one entangled qubit pair per entangled oscillator pair or, equivalently for the realistic protocol, more than one secret key bit per coherent state. The entanglement parameters are estimated using quantum tomography. We analyze the properties of the encoding scheme and investigate the resulting secret key rate in the important case of the attenuation channel.

Linear Attack Using Multiple Linear Approximations

SUMMARY One of Kaliski and Robshaw’s algorithms, which is used for the linear attack on block ciphers with multiple linear approximations and introduced as Algorithm 2M in this paper, looks efficient but lacks any theoretical and mathematical description. It means there exists no way to estimate the data complexity required for the attack by the algorithm except experiments of the reduced variants. In this paper we propose a new algorithm using multiple linear approximation. We achieve the theoretical and mathematical analysis of its success probability. The new algorithm needs about 2 40.6 plaintexts to find 12 bits of secret key of 16-round DES

Secure key distribution by swapping quantum entanglement

We report two key distribution schemes achieved by swapping quantum entanglement. Using two Bell states, two bits of secret key can be shared between two distant parties that play symmetric and equal roles. We also address eavesdropping attacks against the schemes.

Cloning and cryptography with quantum continuous variables

The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine that copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely F = 2/3, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this continuous quantum cryptographic scheme is then analyzed for the optimal individual attack. Methods to convert the resulting Gaussian keys into secret key bits are also studied. Finally, the extension of the Gaussian cloner to optimal N-to-M continuous cloners is discussed, and it is shown how to implement these cloners for light modes using a phase-insensitive optical amplifier and beam splitters. In addition, a phase-conjugate input cloner is defined, yielding M clones and M' anticlones from N replicas of a coherent state and N' replicas of its phase-conjugate (with M' - M = N' - N). This novel kind of cloners is shown to outperform the standard N-to-M cloners in some cases.