The motivation of this post is to provide a concise proof concept that can be used to prove both Hall’s marriage theorem and Kőnig’s theorem, which are two of the most well-known theorems in graph theory. Particularly, the max flow min cut theorem concerning a flow network can be employed.

I. Constructing a flow network for any bipartite graph

Given any bipartite graph G = X ∪ Y, we can construct a flow network as follows.

Recall that there exists a one-to-one correspondence between lattices (in the complex plane) and elliptic curves over C (the field of complex numbers). In fact, the following map involving the Weierstrass elliptic function represents an isomorphism of groups (which is a truly remarkable fact in itself):

In the following set of (side) notes, I shed light on aspects of differential privacy that I believe could benefit from clearer explanations and/or exploration.


0. A Brief Introduction
1. Understanding the Formal Definition
2. Global Model vs Local Model
3. Accuracy Bounds
4. Attacks to Local Differential Privacy
5. Frequency Estimation and Application to Voting

0. A Brief Introduction

While the history of differential privacy (in the form of randomized response which was first proposed by Warner) dates back to 1965, its formal definition was given in 2006 by Dwork, McSherry, Nissim, and Smith, and it is only within the past decade that…

Bitcoin’s white paper

Needless to say, we have seen a countless number of ICOs in the past year in a somewhat frenzied manner, a lot of which ended up successfully raising dozens or hundreds of millions of dollars. Meanwhile, the hype (i.e. the crypto wave) has also attracted a number of sketchy players in the space, leading to multiple fraudulent projects (e.g. Prodeum, Centra, BitConnect, etc.) or more generally projects that are not “supposed” (in the traditional sense) to be raising money with nothing but a white paper.

Yet, new ICOs still emerge every day at the time of writing (see Coinschedule, ICO…

I’m sure you’ve heard of IPO (Initial Public Offering) for companies and ICO (Initial Coin Offering) for blockchain projects. Now, we also have what’s called an IFO (Initial Fork Offering), a means by which miners fork a blockchain and mine new coins due to political, ideological, or economic incentives, with strong enough community support.

There has been a lot of news about Bitcoin’s forks recently, the most notorious of which is Bitcoin Cash orchestrated by Jihan Wu. Additionally, there were Bitcoin Gold and Bitcoin Diamond.

Another Bitcoin fork is coming up according to Bitcoin Diamond’s website. This new fork of Bitcoin is launched by Team EVEY and Team 007, two teams of Bitcoin miners who were not happy with the status quo.

The fork is expected to happen at block height 495866, or approximately 5:00 AM (EST) of Nov. 24, 2017.

Relevant Points of Comparison

  1. Bitcoin Cash (BCH): Block size is 8 MB, as opposed to BTC’s 1 MB. SegWit is NOT activated to allow ASICBoost (which allows faster mining than traditional ASIC and hence more centralized mining).
  2. Bitcoin Gold (BTG): The idea is to decentralize mining again. Hence…

Sure, Ethereum is a platform for smart contracts, intended for developers to write DApps (decentralized applications) using smart contracts and for users to interact with those DApps. The currency Ethereum, or Ether, is used as the network fee in the process.


A smart contract is a piece of code intended to facilitate, automate, and verify the negotiation or performance of a contract. Note two effects: 1. less friction cost (by eliminating the middle man); and 2. more transparency (as the blockchain is a transparent ledger).

A public-key cryptography (or asymmetrical cryptography) is one that uses pairs of keys: 1. public key (open to anyone); and 2. private key (only known to the owner). In the case of Bitcoin which uses such cryptography, then what is the relationship between one’s private key, public key, and public address??

1. Private key

A private key is essentially a randomly generated, 32-byte number.

2. Public key

A public key can be derived from the private key using what’s called Elliptic Curve Cryptography. …

Kevin Choi

Computer Science PhD Student | NYU, Columbia |

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