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相互情報量最大化規範ベクトル量子化を用いた物理層秘密鍵共有方式に関する検討

Tomoyuki Higashide, Shinsuke Ibi, Takumi TAKAHASHI, Hisato Iwai

Published Oct 31, 2021• 0 citations
Publisher

Abstract

Wireless communication is riskier than wired communication due to eavesdrop by unauthorized stations. To deal with this problem, public key cryptosystem and common key cryptosystem are used in general. In contrast, key agreement schemes based on information-theoretically security attract attention. One example is a secret key agreement scheme based on radio wave propagation characteristics. This technique uses channel reciprocity and location dependency of radio wave propagation. Most of the secret key agreement schemes generate keys by scalar quantization. However, secret keys generated by scalar quantization occur key disagreement in higher probability than these by vector quantization. A general quantizer selection scheme selects a quantizer with minimum key disagreement between two authorized stations. An eavesdropper is able to generate keys with this quantizer more easily. This paper assumes correlated MIMO channel, and proposed the quantizer utilizing correlation between authorized stations as key information and the quantizer selection scheme taking key entropies leak to eavesdroppers into consideration. This scheme that reduces information leaks to eavesdropper maintaining key disagreement probability between authorized stations.

DOI
10.14988/00028590

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Wireless communication is riskier than wired communication due to eavesdrop by unauthorized stations. To deal with this problem, public key cryptosystem and common key cryptosystem are used in general. In contrast, key agreement schemes based on information-theoretically security attract attention. One example is a secret key agreement scheme based on radio wave propagation characteristics. This technique uses channel reciprocity and location dependency of radio wave propagation. Most of the secret key agreement schemes generate keys by scalar quantization. However, secret keys generated by scalar quantization occur key disagreement in higher probability than these by vector quantization. A general quantizer selection scheme selects a quantizer with minimum key disagreement between two authorized stations. An eavesdropper is able to generate keys with this quantizer more easily. This paper assumes correlated MIMO channel, and proposed the quantizer utilizing correlation between authorized stations as key information and the quantizer selection scheme taking key entropies leak to eavesdroppers into consideration. This scheme that reduces information leaks to eavesdropper maintaining key disagreement probability between authorized stations.
Information security schemes based on radio propagation property such as secret key agreement and secret data transmission have attracted attention in the current wireless community. For the secret key agreement from common information, a general formula of the secret key capacity is given, but a specific formula of secret key capacity has not present for secret key agreement from Gaussian correlated information, which is typical case in wireless channels. This paper deals with the theoretical analysis on secret key capacity for the mobile communication channel model. The analysis result shows that the upper band of secret key capacity is given with conditional mutual information and that the formulas of upper and lower bands are expressed as functions of the signal-to-noise power ratio and the noise power ratio of eavesdropper to legitimate user. The analysis result also shows that secret key capacity can approximately be given by conditional mutual information in the case that noise power ratio of eavesdropper to legitimate user is large.
Encryption of confidential data with a secret key has become a widespread technique for securing wireless transmissions. However, existing key distribution methods that either deliver the secret key with a key distribution center or exchange the secret key using public-key cryptosystems are unable to establish perfect secret keys necessary for symmetric encryption techniques. This research considers secret key establishment, under the broad research area of information theoretic security, using the reciprocal wireless channel as common randomness for the extraction of perfect secret keys in multiple-input multiple-output (MIMO)communication systems. The presentation discusses the fundamental characteristics of the time-variant MIMO wireless channel and establishes a realistic channel simulation model useful for assessing key establishment algorithms. Computational examples show the accuracy and applicability of the model. The discussion then turns to an investigation of the influence of the spatial and temporal correlation of the channel coefficients on the bound of the key size generated from the common channel, and it is found that a sampling approach exists that can generate a key using the minimum sampling time. A practical key generation protocol is then developed based on an enhancement of a published channel coefficient quantization method that incorporates flexible quantization levels, public transmission of the correlation eigenvector matrix and low-density parity-check (LDPC) coding to improve key agreement. This investigation leads to the development of improved channel quantization techniques that dynamically shift the quantization boundaries at one node based on the information provided by the other node. Analysis based on a closed-form bound for the key error rate (KER) and simulations based on the channel model and measurement data show that the enhanced algorithms are able to dramatically reduce key mismatch and asymptotically approach the KER bound. Finally, other secret key generation algorithms based on channel-encryption rather than quantization are discussed, leading to a new concept for secret key generation using the common wireless channel.
Secret key agreement based on radio propagation characteristics attracts attention as a kind of the wireless physical layer security. However, there are few studies on drop of the secret key capacity by multiple spot eavesdropping. This paper derived theoretical formula of the secret key capacity in secret key agreement based on the complex channel coefficient. This paper also derived theoretical formula of the leakage information by multiple spot eavesdropping and showed that leakage information increased with the increase of the eavesdropping spot number. Validity of these theoretical formulas was confirmed by computer simulation. Then, this paper calculated the coefficient of correlation of the channel coefficient in the simple propagation environment and evaluated security of secret key agreement by calculating leakage information for multiple spot eavesdropping.
Key generation technique generates symmetric keys based on the temporal variation, reciprocity and spatial decorrelation of the wireless channel. Most key generation schemes, however, assume that the eavesdropping channels are independent of the main channel and neglect the influence of the eavesdroppers. In this paper, we analyze the secret key capacity taking into account the information leaked to eavesdroppers, and the security analysis shows the eavesdropping channel correlation will reduce the secret key capacity. Then we propose a security channel estimating (SCE) scheme to resist eavesdroppers and the scheme is shown to be efficient. Finally, we use the Monte Carlo simulation verifies the theoretical analysis results.
Vector quantization schemes are proposed to extract secret keys from correlated wireless fading channels. By assuming that the channel between two terminals are reciprocal, its estimates can be used as the common randomness for generating secret keys at the two terminals. Most schemes in the literature assume that channels are independent over time and utilize scalar quantization on each element of the estimated channel vector to generate secret key bits. These schemes are simple to implement but yield high key disagreement probability (KDP) at low SNR and low key entropy when channels are highly correlated. In this work, two vector quantization schemes, namely, the minimum key disagreement probability (MKDP) and the minimum quadratic distortion (MQD) secret key generation schemes, are proposed to effectively extract secret keys from correlated channel estimates. The vector quantizers are derived using KDP and QD as the respective distortion measures. To further reduce KDP, each channel vector is first pre-multiplied by an appropriately chosen unitary matrix to rotate the vector away from quantization cell boundaries. The MKDP scheme achieves the lowest KDP but requires high complexity whereas the MQD scheme yields lower complexity but at the cost of slightly increased KDP. Computer simulations are provided to demonstrate the effectiveness of the proposed vector quantization schemes.
The inherent randomness of wireless radio channels can be employed to extract secrets, whenever the channel reciprocity holds. Privacy amplification is an ingredient step for removing the redundancy of key, of which, the mount of information leaked to potential eavesdroppers, is often difficult to determine. In this paper, we propose a secret-key generation scheme without privacy amplification, of which the disagreement of key is coordinated through the reconciliation of sample positions as did in the level-crossing scheme. Compared to the level-crossing scheme, the proposed approach accumulates the reliable samples and further employs multi-bit quantization for improving the rate of secret-key generation. The accumulated samples should be decorrelated for generating random keys. Through extensive simulations, we find that the Karhunen-Loève transform for decorrelation is very sensitive in implementation.