If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

• x+5
• x^4
• x^3+3x^2+3x+1
• 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

• A(0)+B(0)=C(0)
• A(1)+B(1)=C(1)
• A(2)+B(2)=C(2)
• A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

• 12+1=13
• 10+8=18
• 15+8=23
• 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

• A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
• B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
• C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

After Terra's algorithmic stablecoin collapsed in May, TRON announced a plan to increase the capital backing its own stablecoin.

USDD, a near-carbon copy of Terra's UST, arrived on the TRON blockchain on May 5. TRON founder Justin Sun says USDD will be overcollateralized after initially being pegged algorithmically to the US dollar.

A reserve of cryptocurrencies and stablecoins will be kept at 130 percent of total USDD issuance, he said. TRON described the collateral ratio as "guaranteed" and said it would begin publishing real-time updates on June 5.

Currently, the reserve contains 14,040 bitcoin (around $418 million), 140 million USDT, 1.9 billion TRX, and 8.29 billion TRX in a burning contract.

algorithmic failure

USDD was designed to incentivize arbitrageurs to keep its price pegged to the US dollar by trading TRX, TRON's token, and USDD. Like Terra, TRON signaled its intent to establish a bitcoin and cryptocurrency reserve to support USDD in extreme market conditions.

Still, Terra's UST failed despite these safeguards. The stablecoin veered sharply away from its dollar peg in mid-May, bringing down Terra's LUNA and wiping out $40 billion in value in days. In a frantic attempt to restore the peg, billions of dollars in bitcoin were sold and unprecedented volumes of LUNA were issued.

Sun believes USDD, which has a total circulating supply of $667 million, can be backed up.

"Our reserve backing is diversified." Bitcoin and stablecoins are included. USDC will be a small part of Circle's reserve, he said.

TRON's news release lists the reserve's assets as bitcoin, TRX, USDC, USDT, TUSD, and USDJ.

All Bitcoin addresses will be signed so everyone knows they belong to us, Sun said.

Not giving in

Sun told that the crypto industry needs "decentralized" stablecoins that regulators can't touch.

Sun said the Luna Foundation Guard, a Singapore-based non-profit that raised billions in cryptocurrency to buttress UST, mismanaged the situation by trying to sell to panicked investors.

He said, "We must be ahead of the market." We want to stabilize the market and reduce volatility.

Currently, TRON finances most of its reserve directly, but Sun says the company hopes to add external capital soon.

Before its demise, UST holders could park the stablecoin in Terra's lending platform Anchor Protocol to earn 20% interest, which many deemed unsustainable. TRON's JustLend is similar. Sun hopes to raise annual interest rates from 17.67% to "around 30%."

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This post is a summary. Read full article here

Photo by Juanjo Jaramillo on Unsplash

Calling APIs is the most common thing to do in any modern web application. When it comes to talking with an API then most of the time we need to do a lot of repetitive things like getting data from an API call, handling the success or error case, and so on.

When calling tens of hundreds of API calls we always have to do those tedious tasks. We can handle those things efficiently by putting a higher level of abstraction over those barebone API calls, whereas in some small applications, sometimes we don’t even care.

The problem comes when we start adding new features on top of the existing features without handling the API calls in an efficient and reusable manner. In that case for all of those API calls related repetitions, we end up with a lot of repetitive code across the whole application.

In React, we have different approaches for calling an API. Nowadays mostly we use React hooks. With React hooks, it’s possible to handle API calls in a very clean and consistent way throughout the application in spite of whatever the application size is. So let’s see how we can make a clean and reusable API calling layer using React hooks for a simple web application.

I’m using a code sandbox for this blog which you can get here.

import "./styles.css";
import React, { useEffect, useState } from "react";
import axios from "axios";

export default function App() {
  const [posts, setPosts] = useState(null);
  const [error, setError] = useState("");
  const [loading, setLoading] = useState(false);

  useEffect(() => {
    handlePosts();
  }, []);

  const handlePosts = async () => {
    setLoading(true);
    try {
      const result = await axios.get(
        "https://jsonplaceholder.typicode.com/posts"
      );
      setPosts(result.data);
    } catch (err) {
      setError(err.message || "Unexpected Error!");
    } finally {
      setLoading(false);
    }
  };

  return (
    <div className="App">
      <div>
        <h1>Posts</h1>
        {loading && <p>Posts are loading!</p>}
        {error && <p>{error}</p>}
        <ul>
          {posts?.map((post) => (
            <li key={post.id}>{post.title}</li>
          ))}
        </ul>
      </div>
    </div>
  );
}

I know the example above isn’t the best code but at least it’s working and it’s valid code. I will try to improve that later. For now, we can just focus on the bare minimum things for calling an API.

Here, you can try to get posts data from JsonPlaceholer. Those are the most common steps we follow for calling an API like requesting data, handling loading, success, and error cases.

If we try to call another API from the same component then how that would gonna look? Let’s see.

500: Internal Server Error

Now it’s going insane! For calling two simple APIs we’ve done a lot of duplication. On a top-level view, the component is doing nothing but just making two GET requests and handling the success and error cases. For each request, it’s maintaining three states which will periodically increase later if we’ve more calls.

Let’s refactor to make the code more reusable with fewer repetitions.

Step 1: Create a Hook for the Redundant API Request Codes

Most of the repetitions we have done so far are about requesting data, handing the async things, handling errors, success, and loading states. How about encapsulating those things inside a hook?

The only unique things we are doing inside handleComments and handlePosts are calling different endpoints. The rest of the things are pretty much the same. So we can create a hook that will handle the redundant works for us and from outside we’ll let it know which API to call.

500: Internal Server Error

Here, this request function is identical to what we were doing on the handlePosts and handleComments. The only difference is, it’s calling an async function apiFunc which we will provide as a parameter with this hook. This apiFunc is the only independent thing among any of the API calls we need.

With hooks in action, let’s change our old codes in App component, like this:

500: Internal Server Error

How about the current code? Isn’t it beautiful without any repetitions and duplicate API call handling things?

Let’s continue our journey from the current code. We can make App component more elegant. Now it knows a lot of details about the underlying library for the API call. It shouldn’t know that. So, here’s the next step…

Step 2: One Component Should Take Just One Responsibility

Our App component knows too much about the API calling mechanism. Its responsibility should just request the data. How the data will be requested under the hood, it shouldn’t care about that.

We will extract the API client-related codes from the App component. Also, we will group all the API request-related codes based on the API resource. Now, this is our API client:

import axios from "axios";

const apiClient = axios.create({
  // Later read this URL from an environment variable
  baseURL: "https://jsonplaceholder.typicode.com"
});

export default apiClient;

All API calls for comments resource will be in the following file:

import client from "./client";

const getComments = () => client.get("/comments");

export default {
  getComments
};

All API calls for posts resource are placed in the following file:

import client from "./client";

const getPosts = () => client.get("/posts");

export default {
  getPosts
};

Finally, the App component looks like the following:

import "./styles.css";
import React, { useEffect } from "react";
import commentsApi from "./api/comments";
import postsApi from "./api/posts";
import useApi from "./hooks/useApi";

export default function App() {
  const getPostsApi = useApi(postsApi.getPosts);
  const getCommentsApi = useApi(commentsApi.getComments);

  useEffect(() => {
    getPostsApi.request();
    getCommentsApi.request();
  }, []);

  return (
    <div className="App">
      {/* Post List */}
      <div>
        <h1>Posts</h1>
        {getPostsApi.loading && <p>Posts are loading!</p>}
        {getPostsApi.error && <p>{getPostsApi.error}</p>}
        <ul>
          {getPostsApi.data?.map((post) => (
            <li key={post.id}>{post.title}</li>
          ))}
        </ul>
      </div>
      {/* Comment List */}
      <div>
        <h1>Comments</h1>
        {getCommentsApi.loading && <p>Comments are loading!</p>}
        {getCommentsApi.error && <p>{getCommentsApi.error}</p>}
        <ul>
          {getCommentsApi.data?.map((comment) => (
            <li key={comment.id}>{comment.name}</li>
          ))}
        </ul>
      </div>
    </div>
  );
}

Now it doesn’t know anything about how the APIs get called. Tomorrow if we want to change the API calling library from axios to fetch or anything else, our App component code will not get affected. We can just change the codes form client.js This is the beauty of abstraction.

Apart from the abstraction of API calls, Appcomponent isn’t right the place to show the list of the posts and comments. It’s a high-level component. It shouldn’t handle such low-level data interpolation things.

So we should move this data display-related things to another low-level component. Here I placed those directly in the App component just for the demonstration purpose and not to distract with component composition-related things.

Final Thoughts

The React library gives the flexibility for using any kind of third-party library based on the application’s needs. As it doesn’t have any predefined architecture so different teams/developers adopted different approaches to developing applications with React. There’s nothing good or bad. We choose the development practice based on our needs/choices. One thing that is there beyond any choices is writing clean and maintainable codes.