Peihan Miao

Number of lines in hypergraphs

Abstract Chen and Chvatal introduced the notion of lines in hypergraphs; they proved that every 3 -uniform hypergraph with n vertices either has a line that consists of all n vertices or else has at least log 2 n distinct lines. We improve this lower bound by a factor of 2 − o ( 1 ) .

Laconic Oblivious Transfer and Its Applications

In this work, we introduce a novel technique for secure computation over large inputs. Specifically, we provide a new oblivious transfer (OT) protocol with a laconic receiver. Laconic OT allows a receiver to commit to a large input D (of length M) via a short message. Subsequently, a single short message by a sender allows the receiver to learn \(m_{D[L]}\), where the messages \(m_0, m_1\) and the location \(L \in [M]\) are dynamically chosen by the sender. All prior constructions of OT required the receiver’s outgoing message to grow with D.

Secure Multiparty RAM Computation in Constant Rounds

Secure computation of a random access machine RAM program typically entails that it be first converted into a circuit. This conversion is unimaginable in the context of big-data applications where the size of the circuit can be exponential in the running time of the original RAM program. Realizing these constructions, without relinquishing the efficiency of RAM programs, often poses considerable technical hurdles. Our understanding of these techniques in the multi-party setting is largely limited. Specifically, the round complexity of all known protocols grows linearly in the running time of the program being computed. In this work, we consider the multi-party case and obtain the following results:Semi-honest model: We present a constant-round black-box secure computation protocol for RAM programs. This protocol is obtained by building on the new black-box garbled RAM construction by Garg, Lu, and Ostrovsky [FOCS 2015], and constant-round secure computation protocol for circuits of Beaver, Micali, and Rogaway [STOC 1990]. This construction allows execution of multiple programs on the same persistent database.Malicious model: Next, we show how to extend our semi-honest results to the malicious setting, while ensuring that the new protocol is still constant-round and black-box in nature.

Graph metric with no proper inclusion between lines

In trying to generalize the classic Sylvester-Gallai theorem and De Bruijn-Erd?s theorem in plane geometry, lines and closure lines were previously defined for metric spaces and hypergraphs. Both definitions do not obey the geometric intuition in the sense that two lines (closure lines) may intersect at more than one point, and one line (closure line) might be the proper subset of another. In this work, we study the systems where one or both of the configurations are forbidden. We note that when any two lines intersect in at most one point, the two classic theorems extend in any metric space. We study the metric spaces induced by simple graphs where no line is a proper subset of another, and show that the least number of lines for such a graph with n vertices is between the order of n 4 / 3 and n 4 / 3 ln 2 / 3 n .

Decentralized Anonymous Micropayments

Micropayments (payments worth a few pennies) have numerous potential applications. A challenge in achieving them is that payment networks charge fees that are high compared to “micro” sums of money.

Secretary Markets with Local Information

The secretary model is a popular framework for the analysis of online admission problems beyond the worst case. In many markets, however, decisions about admission have to be made in a decentralized fashion and under competition. We cope with this problem and design algorithms for secretary markets with limited information. In our basic model, there are m firms and each has a job to offer. n applicants arrive iteratively in random order. Upon arrival of an applicant, a value for each job is revealed. Each firm decides whether or not to offer its job to the current applicant without knowing the strategies, actions, or values of other firms. Applicants decide to accept their most preferred offer. We consider the social welfare of the matching and design a decentralized randomized thresholding-based algorithm with ratio

Two-Round Multiparty Secure Computation Minimizing Public Key Operations

O\log n

Obfuscation from Low Noise Multilinear Maps.

that works in a very general sampling model. It can even be used by firms hiring several applicants based on a local matroid. In contrast, even in the basic model we show a lower bound of