![]() ![]() This proof technique’s algebraic reimagination lifts these hardness of computation results to more complex relativized settings via a new data processing inequality, central to resolving some of the most fundamental problems in computer science and cryptography. The geometric (or combinatorial) interpretation of this proof technique is inherently constructive that is, the proof technique identifies the optimal coin-tossing protocols, which have applications in new isoperimetric inequalities in the product spaces over large alphabets. ![]() In particular, it elaborates on a new proof technique introduced in to simultaneously characterize the optimal coin-tossing protocols and prove lower bounds to the insecurity of any coin-tossing protocol. This survey summarizes the current state-of-the-art of coin-tossing protocols in the full information model and recent advances in this field, settling several long-standing open problems. Furthermore, the research outcomes for this functionality has direct consequences on diverse topics in mathematics and computer science-for example, extremal graph theory, extracting randomness from imperfect sources, cryptography, game theory, circuit representation, distributed protocols, and poisoning and evasion attacks on learning algorithms. These hardness of computation results for the coin-tossing functionality extend to other general functionalities as well. Collective coin-tossing is an elegant functionality providing uncluttered access to the primary bottlenecks of achieving security in a specific adversarial model. In this model, each processor has an unbounded computational power and communicates over a broadcast channel. Collective coin-tossing protocols upgrade the local independent private randomness of each of the processors into shared randomness with which all processors agree. This survey presents one representative application of each of these two perspectives.īen-Or and Linial, in a seminal work, introduced the full information model to study collective coin-tossing protocols. ![]() Furthermore, this proof-technique’s algebraic reimagination resolves several long-standing fundamental hardness-of-computation problems in cryptography. ![]() The combinatorial perspective into this new proof-technique yields new coin-tossing protocols that are more secure than well-known existing coin-tossing protocols, leading to new isoperimetric inequalities over product spaces. In particular, it elaborates on a new proof technique that identifies the minimum insecurity incurred by any coin-tossing protocol and, simultaneously, constructs the coin-tossing protocol achieving that insecurity bound. This survey summarizes the current state-of-the-art of coin-tossing protocols in the full information model and recent advances in this field. Additionally, the research outcomes for this versatile functionality has direct consequences on diverse topics in mathematics and computer science. Collective coin-tossing is an elegant functionality providing uncluttered access to the primary bottlenecks to achieve security in a specific adversarial model. Ben-Or and Linial, in a seminal work, introduced the full information model to study collective coin-tossing protocols. ![]()
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