Constructing 77-clusters

A set of $n$-lattice points in the plane, no three on a line and no four on a circle, such that all pairwise distances and all coordinates are integral is called an $n$-cluster (in $\mathbb{R}^2$). We determine the smallest existent $7$-cluster with respect to its diameter. Additionally we provide a toolbox of algorithms which allowed us to computationally locate over 1000 different $7$-clusters, some of them having huge integer edge lengths. On the way, we exhaustively determined all Heronian triangles with largest edge length up to $6\cdot 10^6$.Comment: 18 pages, 2 figures, 2 table

Randomness Concerns When Deploying Differential Privacy

The U.S. Census Bureau is using differential privacy (DP) to protect confidential respondent data collected for the 2020 Decennial Census of Population & Housing. The Census Bureau's DP system is implemented in the Disclosure Avoidance System (DAS) and requires a source of random numbers. We estimate that the 2020 Census will require roughly 90TB of random bytes to protect the person and household tables. Although there are critical differences between cryptography and DP, they have similar requirements for randomness. We review the history of random number generation on deterministic computers, including von Neumann's "middle-square" method, Mersenne Twister (MT19937) (previously the default NumPy random number generator, which we conclude is unacceptable for use in production privacy-preserving systems), and the Linux /dev/urandom device. We also review hardware random number generator schemes, including the use of so-called "Lava Lamps" and the Intel Secure Key RDRAND instruction. We finally present our plan for generating random bits in the Amazon Web Services (AWS) environment using AES-CTR-DRBG seeded by mixing bits from /dev/urandom and the Intel Secure Key RDSEED instruction, a compromise of our desire to rely on a trusted hardware implementation, the unease of our external reviewers in trusting a hardware-only implementation, and the need to generate so many random bits.Comment: 12 pages plus 2 pages bibliograph

Improving Actuator-Sensor-Actuator Communication Performance in WSANs using a Multicast Approach based on Bloom Filters

In Wireless Sensor and Actuator Networks (WSANs), to ensure the communication between multiple actuators is an essential issue. In line with this, we propose a multicast routing protocol, named Multicast Border Oriented Forward Routing Protocol (M-BOFP), whose communication between actuators is performed by multicast implemented on top of the network of sensor nodes. The M-BOFP takes advantage of the Bloom filters, a probabilistic data structure with low memory cost, to carry information of multicast groups requiring low and fixed message overhead. This paper presents preliminary results of the comparative analysis between the MBOFP and its precursor the BOFP. For this analysis, we carry out a performance evaluation of the proposed protocol considering different scenarios representing small, moderate and large-scale networks.Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)Fed Univ Sao Paulo UNIFESP, Sao Jose Dos Campos, SP, BrazilFed Univ Sao Paulo UNIFESP, Sao Jose Dos Campos, SP, BrazilFAPESP: 2015/18580-9Web of Scienc