Traditional approaches for providing confidentiality of wirelessly transmitted signals are often based on cryptographic techniques. While these techniques ensure that messages are encrypted and secured against eavesdropping, they are not sufficient to protect important transmission attributes at the physical (PHY) layer. Specifically, several elds in the headers of PHY and medium access control (MAC) frames are typically sent unencrypted to maintain proper protocol functionality (e.g., sender/receiver identification). As a result, they leak side-channel information (SCI), including payload size, frequency and phase oset, modulation and coding scheme, identities of communication nodes, frame type, transmission rate, etc. These SCI can be exploited by an adversary to launch various passive (eavesdropping) and active (jamming) attacks. To complement cryptographic techniques used at upper layers and prevent the leakage of SCI at the PHY/MAC layers, PHY-layer security techniques have been introduced. These techniques exploit the characteristics of the wireless channel along with multiple-input multiple-output (MIMO) technologies, in which multiple transmitting and receiving antennas are utilized to prevent information leakage to eavesdroppers and/or avoid jamming attacks. In particular, if the signal-to-interference-plus-noise ratio (SINR) at an adversary is lower than the one at a legitimate receiver, secure communication can be achieved through the so-called wiretap coding. MIMO systems enable the transmitter and/or the receiver to generate artificial noise, called friendly jamming (FJ), so as to reduce the SINR at the adversary without impacting the SINR at the legitimate receiver. In this dissertation, we focus on exploring the security threats to next-generation wireless systems. We develop MIMO-based PHY-layer security methods to achieve reliable and secret communications in these systems. First, we consider a broadcast channel, in which a multi-antenna transmitter (Alice) sends K confidential information signals to K legitimate receivers (Bobs) in the presence of L eavesdropping devices (Eves). Alice uses MIMO precoding to generate the information signals along with her own Tx-based friendly jamming (TxFJ). Interference at each Bob is removed via a technique called MIMO zero-forcing. This TxFJ, however, leaves an eavesdropping \vulnerability region" in the proximity of each Bob, which can be exploited by a nearby Eve. Specically, because of the high correlation in the channel state information (CSI) at a Bob and nearby Eves, the TxFJ becomes less effective in preventing eavesdropping at these Eves. We address this problem by augmenting TxFJ with receiver-based friendly jamming (RxFJ), generated by each Bob. Specifically, we allow each Bob to use self-interference suppression (SIS) techniques to transmit a friendly jamming signal while simultaneously receiving an information signal over the same channel. These SIS techniques exploit circulators to attenuate the self-interference power of RxFJ at Bobs and utilize analog/digital cancellation methods to clean out any remaining residual self-interference. Considering the resulting broadcast channel, we rst study a two-user scenario and develop a secrecy encoding scheme for constructing the signals intended to two Bobs. We characterize the corresponding achievable secrecy sum-rate and formulate an optimization problem to maximize this metric. We then extend our approach to K-user scenarios and study a power minimization problem. Particularly, in our analysis we minimize the powers allocated to information and friendly jamming signals (both TxFJ and RxFJ) while guaranteeing individual secrecy rates for various Bobs. The problem is solved for the cases when the eavesdropper's CSI (ECSI) is known or unknown (but with a known distribution). Simulations show the effectiveness of the proposed solutions. Furthermore, we discuss how to schedule transmissions when the rate requirements need to be satised on average rather than instantaneously. In low and high power regime, a scheduling algorithm that serves only the strongest receivers is shown to outperform the one that schedules all receivers. Next, we consider a single-cell massive MIMO system in which a base station (BS) with a large number of antennas transmits simultaneously to several single antenna users. The BS acquires the CSI for various receivers using uplink pilot transmissions. We demonstrate the vulnerability of the CSI estimation process to a pilot-contamination (PC) attack that aims at minimizing the sum-rate of downlink transmissions by contaminating uplink pilots. We rst study PC attacks for two downlink power allocation strategies under the assumption that the attacker knows the locations of the BS and its users. Later on, we relax this assumption and consider the case when such knowledge is probabilistic. The formulated problems are solved using stochastic optimization, Lagrangian minimization, and game-theoretic methods. A closed-form solution for a special case of the problem is obtained. Furthermore, we analyze the \achievable individual secrecy rates" under PC attacks, and provide an upper-bound on these rates. We also study this scenario without a priori knowledge of user locations at the attacker by introducing chance constraints. Another attack model is considered, where the attacker generates jamming signals in both the CSI estimation and data transmission phases by exploiting inband full-duplex techniques. Our results indicate that such attacks can degrade the throughput of a massive MIMO system by more than 50%, and reduce fairness among users significantly.
Traditional approaches for providing confidentiality of wirelessly transmitted signals are often based on cryptographic techniques. While these techniques ensure that messages are encrypted and secured against eavesdropping, they are not sufficient to protect important transmission attributes at the physical (PHY) layer. Specifically, several elds in the headers of PHY and medium access control (MAC) frames are typically sent unencrypted to maintain proper protocol functionality (e.g., sender/receiver identification). As a result, they leak side-channel information (SCI), including payload size, frequency and phase oset, modulation and coding scheme, identities of communication nodes, frame type, transmission rate, etc. These SCI can be exploited by an adversary to launch various passive (eavesdropping) and active (jamming) attacks. To complement cryptographic techniques used at upper layers and prevent the leakage of SCI at the PHY/MAC layers, PHY-layer security techniques have been introduced. These techniques exploit the characteristics of the wireless channel along with multiple-input multiple-output (MIMO) technologies, in which multiple transmitting and receiving antennas are utilized to prevent information leakage to eavesdroppers and/or avoid jamming attacks. In particular, if the signal-to-interference-plus-noise ratio (SINR) at an adversary is lower than the one at a legitimate receiver, secure communication can be achieved through the so-called wiretap coding. MIMO systems enable the transmitter and/or the receiver to generate artificial noise, called friendly jamming (FJ), so as to reduce the SINR at the adversary without impacting the SINR at the legitimate receiver. In this dissertation, we focus on exploring the security threats to next-generation wireless systems. We develop MIMO-based PHY-layer security methods to achieve reliable and secret communications in these systems. First, we consider a broadcast channel, in which a multi-antenna transmitter (Alice) sends K confidential information signals to K legitimate receivers (Bobs) in the presence of L eavesdropping devices (Eves). Alice uses MIMO precoding to generate the information signals along with her own Tx-based friendly jamming (TxFJ). Interference at each Bob is removed via a technique called MIMO zero-forcing. This TxFJ, however, leaves an eavesdropping \vulnerability region" in the proximity of each Bob, which can be exploited by a nearby Eve. Specically, because of the high correlation in the channel state information (CSI) at a Bob and nearby Eves, the TxFJ becomes less effective in preventing eavesdropping at these Eves. We address this problem by augmenting TxFJ with receiver-based friendly jamming (RxFJ), generated by each Bob. Specifically, we allow each Bob to use self-interference suppression (SIS) techniques to transmit a friendly jamming signal while simultaneously receiving an information signal over the same channel. These SIS techniques exploit circulators to attenuate the self-interference power of RxFJ at Bobs and utilize analog/digital cancellation methods to clean out any remaining residual self-interference. Considering the resulting broadcast channel, we rst study a two-user scenario and develop a secrecy encoding scheme for constructing the signals intended to two Bobs. We characterize the corresponding achievable secrecy sum-rate and formulate an optimization problem to maximize this metric. We then extend our approach to K-user scenarios and study a power minimization problem. Particularly, in our analysis we minimize the powers allocated to information and friendly jamming signals (both TxFJ and RxFJ) while guaranteeing individual secrecy rates for various Bobs. The problem is solved for the cases when the eavesdropper's CSI (ECSI) is known or unknown (but with a known distribution). Simulations show the effectiveness of the proposed solutions. Furthermore, we discuss how to schedule transmissions when the rate requirements need to be satised on average rather than instantaneously. In low and high power regime, a scheduling algorithm that serves only the strongest receivers is shown to outperform the one that schedules all receivers. Next, we consider a single-cell massive MIMO system in which a base station (BS) with a large number of antennas transmits simultaneously to several single antenna users. The BS acquires the CSI for various receivers using uplink pilot transmissions. We demonstrate the vulnerability of the CSI estimation process to a pilot-contamination (PC) attack that aims at minimizing the sum-rate of downlink transmissions by contaminating uplink pilots. We rst study PC attacks for two downlink power allocation strategies under the assumption that the attacker knows the locations of the BS and its users. Later on, we relax this assumption and consider the case when such knowledge is probabilistic. The formulated problems are solved using stochastic optimization, Lagrangian minimization, and game-theoretic methods. A closed-form solution for a special case of the problem is obtained. Furthermore, we analyze the \achievable individual secrecy rates" under PC attacks, and provide an upper-bound on these rates. We also study this scenario without a priori knowledge of user locations at the attacker by introducing chance constraints. Another attack model is considered, where the attacker generates jamming signals in both the CSI estimation and data transmission phases by exploiting inband full-duplex techniques. Our results indicate that such attacks can degrade the throughput of a massive MIMO system by more than 50%, and reduce fairness among users significantly.
Achieving secure transmission in wireless network is a significantly important research topic. Classic cryptography encrypts a confidential message to an unreadable cipher message. Thus only the authentic receiver with correct secrecy key is able to decrypt the message. However, with the growing computational capability of adversaries, the requirement of secrecy key generation and distribution is getting stringent. Another method to achieve wireless security, which has attracted much attention in recent years, is through physical layer processing, named physical layer security. In a typical wiretap channel model consisting of a transmitter, a legal receiver and an adversary (illegal receiver), early works have proven that it is possible to achieve positive secrecy rate using multiple antenna techniques, such as beamforming, at the transmitter. In this thesis, we focus on two types of malicious behaviors of the adversary: passive eavesdropping and active attack. For the passive eavesdropping, we first consider the multi-input-single-output (MISO) wiretap channel, in which the legitimate transmitter utilizes the artificial noise aided precoding strategy to maximize the achievable secrecy rate of the channel. Both scenarios of known and unknown channel state information (CSI) for the eavesdropper channels are considered. By deriving the closed-form expression of ergodic secrecy rate, we prove that there exists an optimal power ratio between the information signal and the artificial noise. We then extend our study to a four-node fading channel model in a wireless relay network, which includes two single-antenna users, one single-antenna eavesdropper and one relay node equipped with multiple antennas. By studying the decode-and-forward (DF) scheme, cooperative jamming (CJ) scheme and one proposed hybrid relay scheme, relay-and-jamming (RJ), we aims to find the optimal relay scheme with the condition that the transmitter and the relay node are under individual power constraints and the CSI of the illegitimate channel is only statistically known. Our analysis shows that the hybrid RJ scheme is optimal when the transmitter has a relatively small power budget and/or the transmitter is far away from the intended receiver. Besides the passive eavesdropping, the adversary could also choose the active attack. The pilot spoofing attack is one active attack conducted by the adversary during the channel estimation phase of the legitimate transmission. In practical systems, the pilot signals are usually known \textit{a priori} and repeatedly used information. In this attack, an intelligent adversary spoofs the transmitter on the estimation of CSI by sending the identical pilot signal as the legitimate receiver. By doing so, the adversary could obtain a larger channel rate in the data transmission phase, and also drastically weaken the strength of the received signal at the legitimate receiver if the adversary utilizes large enough power. Due to the serious consequences caused by such an attack, we first propose an energy ratio detector (ERD) that explores the asymmetry of received signal power levels at the transmitter and the legitimate receiver when the attack occurs. Our analysis shows that the ERD could provide very high probability of detection with certain requirement on the false alarming probability. Furthermore, we design a two-way training based scheme to provide not only attack detection but also secure transmission. The two-way training based detector (TWTD) exploits the intrusive component created by the adversary, followed by a secure beamforming-assisted data transmission. In addition to the good detection performance, our scheme could estimate both legitimate and illegitimate channels, with which the beamforming could be designed for data transmission.
This paper considers a broadcast channel with a multi-antenna transmitter (Alice) sending two independent confidential data streams to two legitimate users (Bob and Charlie) in the presence of a passive eavesdropper (Eve). To enhance their secrecy rates, Bob and Charlie are assumed to be capable of self-interference suppression (SIS). Alice, on the other hand, uses MIMO precoding to generate the two confidential information signals along with its own (Tx-based) friendly jamming. The interfering signals at Bob and Charlie are removed by employing the zero-forcing technique. This, however, leaves ``vulnerability regions'' around Bob and Charlie, which can be exploited by a nearby eavesdropper. We address this problem by augmenting Tx-based friendly jamming with Rx-based friendly jamming, generated by Bob and Charlie. For the resulting broadcast channel, a secrecy encoding scheme is developed to construct the signals intended to Bob and Charlie. The corresponding achievable secrecy sum-rate is characterized, and an optimization problem is formulated. A special case of this problem is investigated. Simulation results show the effectiveness of utilizing (Tx- and/or Rx-based) jamming, and the impact of the degree of SIS on physical-layer security.
This paper considers a broadcast channel with a multi-antenna transmitter (Alice) sending two independent confidential data streams to two legitimate users (Bob and Charlie) in the presence of a passive eavesdropper (Eve). To enhance their secrecy rates, Bob and Charlie are assumed to be capable of self-interference suppression (SIS). Alice, on the other hand, uses MIMO precoding to generate the two confidential information signals along with its own (Tx-based) friendly jamming. The interfering signals at Bob and Charlie are removed by employing the zero-forcing technique. This, however, leaves ``vulnerability regions'' around Bob and Charlie, which can be exploited by a nearby eavesdropper. We address this problem by augmenting Tx-based friendly jamming with Rx-based friendly jamming, generated by Bob and Charlie. For the resulting broadcast channel, a secrecy encoding scheme is developed to construct the signals intended to Bob and Charlie. The corresponding achievable secrecy sum-rate is characterized, and an optimization problem is formulated. A special case of this problem is investigated. Simulation results show the effectiveness of utilizing (Tx- and/or Rx-based) jamming, and the impact of the degree of SIS on physical-layer security.
We consider a broadcast channel in which a multi-antenna transmitter (Alice) sends K confidential information signals to K legitimate users (Bobs) in the presence of L eavesdroppers (Eves). Alice uses multiple-input multiple-output (MIMO) precoding to generate the information signals along with her own (Tx-based) friendly jamming (FJ). Interference at each Bob is removed by MIMO zero-forcing. This, however, leaves a “vulnerability region” around each Bob, which can be exploited by a nearby Eve. We address this problem by augmenting Tx-based FJ (TxFJ) with Rx-based FJ (RxFJ), generated by each Bob. Specifically, each Bob uses self-interference suppression to transmit a friendly jamming signal, while simultaneously receiving an information signal over the same channel. We minimize the powers allocated to the information, TxFJ, and RxFJ signals under given guarantees on the individual secrecy rate for each Bob. The problem is solved for the cases when the eavesdropper's channel state information is known/unknown. Simulations show the effectiveness of the proposed solution. Furthermore, we discuss how to schedule transmissions when the rate requirements need to be satisfied on average rather than instantaneously. Under special cases, a scheduling algorithm that serves only the strongest receivers is shown to outperform the one that schedules all receivers.
Security has become an increasingly significant and urgent issue in wireless networks. The growing computational capability of the eavesdropper (Eve) and more and more complicated secure key management in large scale and heterogeneous networks, pose more and more stringent requirement to the cryptographic protocols. As a new design paradigm, physical layer security has been recognised as a promising solution to enhance the security of wireless links relying on the channel properties and advanced signal processing, and can act as either an alternative or a complementary solution to the conventional cryptographic methods. Without complicated secure key generation and management, physical layer security is quite suitable for the large scale distributed networks. In this thesis, we aim to improve the secrecy performance in emerging wireless communication systems relying on different physical layer security techniques. Firstly, the security of an amplify-and-forward successive relaying network with multiple untrusted relay nodes is investigated, where the conventional detrimental inter-relay interference is exploited to jam the untrusted nodes without assistance of external helpers. Considering different complexity requirements, several relay selection schemes are proposed, and the closed-form expressions of the lower bound of the secrecy outage probability and the maximum secrecy diversity order are derived accordingly. It is shown that the maximum secrecy diversity order of N-1 can be achieved for an N relay nodes network. Secondly, the artificial noise (AN) aided secure transmission strategy for a multiple-input single-output multiple-Eve (MISOME) system with a secure user (Bob) and a normal user (NU) is investigated. The power allocations among Bob, NU and AN, as well as the wiretap code rates, are jointly optimized to maximize the effective secrecy throughput (EST), under the average throughput constraint of NU. An alternative optimization algorithm with guaranteed convergence is proposed to obtain the optimal parameters. It is shown that the EST increases with the transmitting power and the number of transmit antennas, and decreases with the throughput constraint of NU, and the EST can be improved through injecting AN and concurrent transmission of Bob and NU. Thirdly, physical layer security in a multi-antenna small-cell network is investigated, where the multi-antenna base stations (BSs), cellular users, and Eves are all randomly distributed according to independent Poisson point processes. Stochastic geometry is applied to analyze the connection and secrecy outage probabilities and the average achievable secrecy rate. The impact of different parameters, including power allocation, BS and Eve density, and the adaptive eavesdropping or jamming on the secrecy performance is analyzed. It is shown that the average secrecy rate is a quasi-concave function of the power allocation factor and monotonically decreases with the ratio of the Eve-BS density. Finally, we study the physical layer security in a large-scale heterogeneous network consisting of both sub-6 GHz massive multi-input multi-output (MIMO) macro cells and millimeter wave (mmWave) small cells. By considering pilot spoofing attacks from the Eves, the coverage and secrecy probabilities are derived using stochastic geometry and the conditions under which the millimeter wave tier outperforms the sub-6 GHz counterpart are discussed in terms of both coverage and secrecy.It is shown that the mmWave small cell can provide better coverage performance in the high transmission code-rate region, and the secrecy performance of the mmWave system outperforms the sub-6 GHz counterpart in the low redundant rate region, which reveals the advantage of using mmWave for secure communication.
Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective. First, we study the Gaussian multiple-input multiple-output (MIMO) wiretap channel. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner. Next, we study the secure broadcasting problem, where a transmitter wants to have secure communication with multiple legitimate users in the presence of an external eavesdropper. We study several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region. Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message. Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region. Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel. Next, we focus on the multiple access wiretap (MAC-WT) channel whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where each user's link to the legitimate receiver is stronger than its link to the eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable region in an n-letter form. We evaluate a looser version of our outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT. Then, we investigate the effects of user cooperation on the secrecy of broadcast channels by considering the cooperative relay broadcast channel (CRBC). We propose an achievable scheme that combines Marton's coding scheme for broadcast channels and Cover and El Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive secrecy rates, which is not possible for scalar Gaussian broadcast channels without cooperation. We further investigate the effects of user cooperation on secrecy by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC. We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF. Next, we study the two-user one-eavesdropper discrete memoryless compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel, and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users. Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and the transmitter sends a confidential message to each group of legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group. Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading, both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain. Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation. Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme.