On forward secrecy in one-round key exchange

Most one-round key exchange protocols provide only weak forward secrecy at best. Furthermore, one-round protocols with strong forward secrecy often break badly when faced with an adversary who can obtain ephemeral keys. We provide a characterisation of how strong forward secrecy can be achieved in one-round key exchange. Moreover, we show that protocols exist which provide strong forward secrecy and remain secure with weak forward secrecy even when the adversary is allowed to obtain ephemeral keys. We provide a compiler to achieve this for any existing secure protocol with weak forward secrecy.

Towards a provably secure DoS-Resilient key exchange protocol with perfect forward secrecy

Just Fast Keying (JFK) is a simple, efficient and secure key exchange protocol proposed by Aiello et al. (ACM TISSEC, 2004). JFK is well known for its novel design features, notably its resistance to denial-of-service (DoS) attacks. Using Meadows’ cost-based framework, we identify a new DoS vulnerability in JFK. The JFK protocol is claimed secure in the Canetti-Krawczyk model under the Decisional Diffie-Hellman (DDH) assumption. We show that security of the JFK protocol, when reusing ephemeral Diffie-Hellman keys, appears to require the Gap Diffie-Hellman (GDH) assumption in the random oracle model. We propose a new variant of JFK that avoids the identified DoS vulnerability and provides perfect forward secrecy even under the DDH assumption, achieving the full security promised by the JFK protocol.

Decode-and-forward relay beamforming for secrecy with finite-alphabet input

In this letter, we compute the secrecy rate of decode-and-forward (DF) relay beamforming with finite input alphabet of size M. Source and relays operate under a total power constraint. First, we observe that the secrecy rate with finite-alphabet input can go to zero as the total power increases, when we use the source power and the relay weights obtained assuming Gaussian input. This is because the capacity of an eavesdropper can approach the finite-alphabet capacity of 1/2 log(2) M with increasing total power, due to the inability to completely null in the direction of the eavesdropper. We then propose a transmit power control scheme where the optimum source power and relay weights are obtained by carrying out transmit power (source power plus relay power) control on DF with Gaussian input using semi-definite programming, and then obtaining the corresponding source power and relay weights which maximize the secrecy rate for DF with finite-alphabet input. The proposed power control scheme is shown to achieve increasing secrecy rates with increasing total power with a saturation behavior at high total powers.

Decode-and-forward relay beamforming for secrecy with imperfect CSI and multiple eavesdroppers

In this paper, we evaluate secrecy rates in cooperative relay beamforming in the presence of imperfect channel state information (CSI) and multiple eavesdroppers. A source-destination pair aided by.. out of.. relays, 1 <= k <= M, using decode-and-forward relay beamforming is considered. We compute the worst case secrecy rate with imperfect CSI in the presence of multiple eavesdroppers, where the number of eavesdroppers can be more than the number of relays. We solve the optimization problem for all possible relay combinations to find the secrecy rate and optimum source and relay weights subject to a total power constraint. We relax the rank-1 constraint on the complex semi-definite relay weight matrix and use S-procedure to reformulate the optimization problem that can be solved using convex semi-definite programming.

On secrecy above secrecy capacity

We consider secrecy obtained when one transmits on a Gaussian Wiretap channel above the secrecy capacity. Instead of equivocation, we consider probability of error as the criterion of secrecy. The usual channel codes are considered for transmission. The rates obtained can reach the channel capacity. We show that the “confusion” caused to the Eve when the rate of transmission is above capacity of the Eve's channel is similar to the confusion caused by using the wiretap channel codes used below the secrecy capacity.

Achievable secrecy sum-rate in a fading MAC-WT with power control and without CSI of eavesdropper

We consider a two user fading Multiple Access Channel with a wire-tapper (MAC-WT) where the transmitter has the channel state information (CSI) to the intended receiver but not to the eavesdropper (eve). We provide an achievable secrecy sum-rate with optimal power control. We next provide a secrecy sum-rate with optimal power control and cooperative jamming (CJ). We then study an achievable secrecy sum rate by employing an ON/OFF power control scheme which is more easily computable. We also employ CJ over this power control scheme. Results show that CJ boosts the secrecy sum-rate significantly even if we do not know the CSI of the eve's channel. At high SNR, the secrecy sum-rate (with CJ) without CSI of the eve exceeds the secrecy sum-rate (without CJ) with full CSI of the eve.

Joint Scheduling & Jamming for Data Secrecy in Wireless Networks

The broadcast nature of the wireless medium jeopardizes secure transmissions. Cryptographic measures fail to ensure security when eavesdroppers have superior computational capability; however, it can be assured from information theoretic security approaches. We use physical layer security to guarantee non-zero secrecy rate in single source, single destination multi-hop networks with eavesdroppers for two cases: when eavesdropper locations and channel gains are known and when their positions are unknown. We propose a two-phase solution which consists of finding activation sets and then obtaining transmit powers subject to SINR constraints for the case when eavesdropper locations are known. We introduce methods to find activation sets and compare their performance. Necessary but reasonable approximations are made in power minimization formulations for tractability reasons. For scenarios with no eavesdropper location information, we suggest vulnerability region (the area having zero secrecy rate) minimization over the network. Our results show that in the absence of location information average number of eavesdroppers who have access to data is reduced.

Secrecy in the 2-User Symmetric Deterministic Interference Channel with Transmitter Cooperation

This work presents novel achievable schemes for the 2-user symmetric linear deterministic interference channel with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. The proposed achievable scheme consists of a combination of interference cancelation, relaying of the other user's data bits, time sharing, and transmission of random bits, depending on the rate of the cooperative link and the relative strengths of the signal and the interference. The results show, for example, that the proposed scheme achieves the same rate as the capacity without the secrecy constraints, in the initial part of the weak interference regime. Also, sharing random bits through the cooperative link can achieve a higher secrecy rate compared to sharing data bits, in the very high interference regime. The results highlight the importance of limited transmitter cooperation in facilitating secure communications over 2-user interference channels.

Outer Bounds on the Secrecy Rate of the 2-User Symmetric Deterministic Interference Channel with Transmitter Cooperation

This paper derives outer bounds for the 2-user symmetric linear deterministic interference channel (SLDIC) with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. Five outer bounds are derived, under different assumptions of providing side information to receivers and partitioning the encoded message/output depending on the relative strength of the signal and the interference. The usefulness of these outer bounds is shown by comparing the bounds with the inner bound on the achievable secrecy rate derived by the authors in a previous work. Also, the outer bounds help to establish that sharing random bits through the cooperative link can achieve the optimal rate in the very high interference regime.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

Sum Secrecy Rate in Multicarrier DF Relay Beamforming

In this paper, we study sum secrecy rate in multicarrier decode-and-forward relay beamforming. We obtain the optimal source power and relay weights on each subcarrier which maximize the sum secrecy rate. For a given total power on a given subcarrier k, P-0(k), we reformulate the optimization problem by relaxing the rank-1 constraint on the complex positive semidefinite relay weight matrix, and solve using semidefinite programming. We analytically prove that the solution to the relaxed optimization problem is indeed rank 1. We show that the subcarrier secrecy rate, R-s (P-0(k)), is a concave function in total power P-0(k) if R-s (P-0(k)) > 0 for any P-0(k) > 0. Numerical results show that the sum secrecy rate with optimal power allocation across subcarriers is more than the sum secrecy rate with equal power allocation. We also propose a low complexity suboptimal power allocation scheme which outperforms equal power allocation scheme.