Identity management systems (IDMSs) are widely used to provision user identities while managing authentication, authorization, and data sharing within organizations and on the web. Traditional identity systems typically suffer from single points of failure, lack of interoperability, and privacy issues, such as enabling mass data collection and user tracking. Blockchain technology has the potential to alleviate these concerns: it can support the ability for users to control the custody of their own identifiers and credentials, enabling novel data ownership and governance models with built-in control and consent mechanisms. Hence, blockchain-based IDMSs, which could benefit both users and businesses, are beginning to proliferate. This work categorizes these systems into a taxonomy based on differences in blockchain architectures, governance models, and other salient features. Context is provided for the taxonomy through the description of related terms, emerging standards, and use cases while highlighting relevant security and privacy considerations. Keywords blockchain; data custody; data ownership; decentralized identifier; distributed ledger; identity management; public key infrastructure; self-sovereign identity; smart contract; user-controlled identity wallet; verifiable credential; zero-knowledge proof Disclaimer Any mention of commercial products or reference to commercial organizations is for information only; it does not imply recommendation or endorsement by the National Institute of Standards and Technology (NIST), nor does it imply that the products mentioned are necessarily the best available for the purpose.

A digraph whose degree sequence has a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and their degree sequences, and show these characterizations to be equivalent. Using this result, we obtain a new, short proof of the Fulkerson-Chen theorem on degree sequences of general digraphs.

A sequence π = (d 1 ,. .. , dn) is graphic if there is a simple graph G with vertex set {v 1 ,. .. , vn} such that the degree of v i is d i. We say that graphic sequences π 1 = (d (1) 1 ,. .. , d (1) n) and π 2 = (d (2) 1 ,. .. , d (2) n) pack if there exist edge-disjoint n-vertex graphs G 1 and G 2 such that for j ∈ {1, 2}, d G j (v i) = d (j) i for all i ∈ {1,. .. , n}. Here, we prove several extremal degree sequence packing theorems that parallel central results and open problems from the graph packing literature. Specifically, the main result of this paper implies degree sequence packing analogues to the Bollobás-Eldridge-Catlin graph packing conjecture and the classical graph packing theorem of Sauer and Spencer. In discrete tomography, a branch of discrete imaging science, the goal is to reconstruct discrete objects using data acquired from low-dimensional projections. Specifically, in the k-color discrete tomography problem the goal is to color the entries of an m × n matrix using k colors so that each row and column receives a prescribed number of entries of each color. This problem is equivalent to packing the degree sequences of k bipartite graphs with parts of sizes m and n. Here we also prove several Sauer-Spencer-type theorems with applications to the two-color discrete tomography problem.

Most modern electronic devices can produce a random number. However, it is difficult to see how a group of mutually distrusting entities can have confidence in any such hardware-produced stream of random numbers, since the producer could control the output to their gain. In this work, we use public and immutable cryptocurrency smart contracts, along with a set of potentially malicious randomness providers, to produce a trustworthy stream of timestamped public random numbers. Our contract eliminates the ability of a producer to predict or control the generated random numbers, including the stored history of random numbers. We consider and mitigate the threat of collusion between the randomness providers and miners in a second, more complex contract.