Azadeh Sheikholeslami

Liang Mi, Azadeh Sheikholeslami, José Bento

The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of non-metrics can complicate solving them. Multi-marginal OT (MMOT) generalizes OT to simultaneously transporting multiple distributions. It captures important relations that are missed if the transport only involves two distributions. Research on MMOT, however, has been focused on its existence, uniqueness, practical algorithms, and the choice of cost functions. There is a lack of discussion on the metric properties of MMOT, which limits its theoretical and practical use. Here, we prove new generalized metric properties for a family of pairwise MMOTs. We first explain the difficulty of proving this via two negative results. Afterward, we prove the MMOTs' metric properties. Finally, we show that the generalized triangle inequality of this family of MMOTs cannot be improved. We illustrate the superiority of our MMOTs over other generalized metrics, and over non-metrics in both synthetic and real tasks.

Azadeh Sheikholeslami, Majid Ghaderi, Hossein Pishro-Nik et al.

This paper considers secure energy-efficient routing in the presence of multiple passive eavesdroppers. Previous work in this area has considered secure routing assuming probabilistic or exact knowledge of the location and channel-state-information (CSI) of each eavesdropper. In wireless networks, however, the locations and CSIs of passive eavesdroppers are not known, making it challenging to guarantee secrecy for any routing algorithm. We develop an efficient (in terms of energy consumption and computational complexity) routing algorithm that does not rely on any information about the locations and CSIs of the eavesdroppers. Our algorithm guarantees secrecy even in disadvantaged wireless environments, where multiple eavesdroppers try to eavesdrop each message, are equipped with directional antennas, or can get arbitrarily close to the transmitter. The key is to employ additive random jamming to exploit inherent non-idealities of the eavesdropper's receiver, which makes the eavesdroppers incapable of recording the messages. We have simulated our proposed algorithm and compared it with existing secrecy routing algorithms in both single-hop and multi-hop networks. Our results indicate that when the uncertainty in the locations of eavesdroppers is high and/or in disadvantaged wireless environments, our algorithm outperforms existing algorithms in terms of energy consumption and secrecy.

Azadeh Sheikholeslami, Dennis Goeckel, Hossein Pishro-Nik

Secure communication over a wiretap channel is considered in the disadvantaged wireless environment, where the eavesdropper channel is (possibly much) better than the main channel. We present a method to exploit inherent vulnerabilities of the eavesdropper's receiver to obtain everlasting secrecy. Based on an ephemeral cryptographic key pre-shared between the transmitter Alice and the intended recipient Bob, a random jamming signal is added to each symbol. Bob can subtract the jamming signal before recording the signal, while the eavesdropper Eve is forced to perform these non-commutative operations in the opposite order. Thus, information-theoretic secrecy can be obtained, hence achieving the goal of converting the vulnerable "cheap" cryptographic secret key bits into "valuable" information-theoretic (i.e. everlasting) secure bits. We evaluate the achievable secrecy rates for different settings, and show that, even when the eavesdropper has perfect access to the output of the transmitter (albeit through an imperfect analog-to-digital converter), the method can still achieve a positive secrecy rate. Next we consider a wideband system, where Alice and Bob perform frequency hopping in addition to adding the random jamming to the signal, and we show the utility of such an approach even in the face of substantial eavesdropper hardware capabilities.

Azadeh Sheikholeslami, Dennis Goeckel, Hossein Pishro-Nik

Secure communication over a memoryless wiretap channel in the presence of a passive eavesdropper is considered. Traditional information-theoretic security methods require an advantage for the main channel over the eavesdropper channel to achieve a positive secrecy rate, which in general cannot be guaranteed in wireless systems. Here, we exploit the non-linear conversion operation in the eavesdropper's receiver to obtain the desired advantage - even when the eavesdropper has perfect access to the transmitted signal at the input to their receiver. The basic idea is to employ an ephemeral cryptographic key to force the eavesdropper to conduct two operations, at least one of which is non-linear, in a different order than the desired recipient. Since non-linear operations are not necessarily commutative, the desired advantage can be obtained and information-theoretic secrecy achieved even if the eavesdropper is given the cryptographic key immediately upon transmission completion. In essence, the lack of knowledge of the key during the short transmission time inhibits the recording of the signal in such a way that the secret information can never be extracted from it. The achievable secrecy rates for different countermeasures that the eavesdropper might employ are evaluated. It is shown that even in the case of an eavesdropper with uniformly better conditions (channel and receiver quality) than the intended recipient, a positive secure rate can be achieved.