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Communication at the terahertz band is increasingly seen as vital for future short-range very high datarate channels. However, these channels suffer from significant environmental impairments and, as a result, providing coverage in indoor settings requires the use of directional line of sight (LoS) paths to visible users and reflected paths, using smooth metal reflectors, for users in the shadow of an obstruction. Previous work has shown that these types of reflected paths display similar characteristics to LoS paths and we call them R-LoS (reflected LoS). MIMO for LoS and R-LoS channels is feasible at terahertz frequencies and delivers very high capacity at some distances. Unfortunately, channel capacity varies greatly with small changes in distance (the channel matrix fluctuates between full rank and rank 1) which is undesirable for communication systems. In this paper, we utilize diffusive reflectors to create multiple reflections such that the MIMO channel capacity for R-LoS is better behaved. We conduct experiments at 410 GHz for reflections from different artificially created diffuse surfaces. We use measurements to estimate channel capacity for 2×2 MIMO when the only path is the diffuse reflected one. We show that by creating multiple controlled reflections, it is possible to achieve relatively stable capacity up to 13 - 16 bits/sec/Hz at varying distances. We also analyze the phase of the received signals and the beam profile in detail. Overall, our results indicate that by utilizing artificially created reflections, we can maintain a stable MIMO channel at high capacity. 

Abstract In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small degree endomorphism enables polynomial-time path-finding and endomorphism ring computation (in: Love and Boneh, ANTS XIV-Proceedings of the Fourteenth Algorithmic Number Theory Symposium, volume 4 of Open Book Ser. Math. Sci. Publ., Berkeley, 2020). An endomorphism gives an explicit orientation of a supersingular elliptic curve. In this paper, we use the volcano structure of the oriented supersingular isogeny graph to take ascending/descending/horizontal steps on the graph and deduce path-finding algorithms to an initial curve. Each altitude of the volcano corresponds to a unique quadratic order, called the primitive order. We introduce a new hard problem of computing the primitive order given an arbitrary endomorphism on the curve, and we also provide a sub-exponential quantum algorithm for solving it. In concurrent work (in: Wesolowski, Advances in cryptology-EUROCRYPT 2022, volume 13277 of Lecture Notes in Computer Science. Springer, Cham, 2022), it was shown that the endomorphism ring problem in the presence of one endomorphism with known primitive order reduces to a vectorization problem, implying path-finding algorithms. Our path-finding algorithms are more general in the sense that we don’t assume the knowledge of the primitive order associated with the endomorphism. 

Terahertz frequencies are an untapped resource for providing high-speed short-range communications. As a result, it is of interest to study the propagation characteristics of terahertz waves and to develop channel models. In previous work we used a measurement-based approach to develop an accurate channel model for line of sight (LoS) links. In this paper we extend that work by developing channel models for non-line of sight (NLoS) links where the signal suffers one reflection. We study reflections that occur off a metal plate as well as a piece of wood.Our model for received magnitude includes the effects of standing waves that develop between the transmitter and receiver. Measurements show an excellent agreement between empirical data and the model. In addition, we have analyzed the received phase of the reflected signal at frequencies in the range 320-480 GHz. We observed a linear error between the predicted and actual phase and developed a model to accommodate that discrepancy. The final model we have developed for predicting received phase is very accurate for the entire range 320 - 480 GHz and for both materials. 

There is a growing interest in exploiting the terahertz frequency band for future communication systems that demand high data rates. Given the complex propagation behavior of this frequency band, various researchers have developed channel models that can be utilized in the development of communication systems. These models however do not include a crucial aspect of terahertz propagation at short distances – the presence of standing waves. Our measurements show that at specific distances, the effect of standing waves is significant. In this paper, we extend previous terahertz channel models to include the effect of standing waves and show a good fit with our measurements. Our measurements and modeling cover the five most promising terahertz frequency bands – 140, 220, 340, 410, 460 GHz.