The Wallet Problem: Slowing Down Cryptocurrency Adoption

Since Bitcoin's inception, one major barrier has consistently hindered the widespread adoption of cryptocurrencies: wallets.

To conduct transactions on any blockchain, users need a wallet. This simple requirement explains why cryptocurrency adoption remains slow. The process of installing a software wallet or browser extension (like MetaMask), and learning how to set it up and use it, presents a significant challenge to many users.

How Are Companies Tackling the Wallet Problem?

Web2 Apps with Web3 Backends: One approach to solving the wallet issue is through the use of familiar Web2 interfaces, supported by Web3 backend features. This is how centralized exchanges like Binance operate. When users buy or sell cryptocurrency on Binance, their wallet balances are updated within a traditional database controlled by Binance. Blockchain interaction only occurs when users make deposits or withdrawals, and the users' funds are secured in smart contracts managed by the exchange.

Shamir’s Secret Sharing: A Breakthrough Solution

Shamir’s Secret Sharing (SSS) offers a promising solution. With SSS, users can maintain full ownership of their wallets without needing third-party applications or browser extensions to manage them. Most importantly, it ensures that no sensitive credentials are shared with any decentralized application (DApp)—a crucial aspect of maintaining security in the world of crypto.

How Shamir’s Secret Sharing (SSS) Works

The core idea of SSS is to protect a private secret, such as a user’s private key, while making it accessible only to its rightful owner.

Private Key Generation

SSS enables the generation of multiple "shares" that can reconstruct the private key. Specifically, a total of N shares are generated, and the key can be recovered using only P of them (where P < N).

Shamir's algorithm is based on Lagrange interpolation polynomials. For any polynomial function F(X), there exists a polynomial in the form:

P(X) = a₀ + a₁X² + a₂X³ + ... + aₙXⁿ

Where a₀, a₁, ... aₙ are real numbers, and n is an integer. This polynomial is known as the Lagrange interpolating polynomial.

A key feature of this polynomial is its evaluation at X = 0, which yields the constant term a₀:

P(0) = a₀.

In this case, a₀ represents the user’s private key.

Creating the Shares

To distribute the secret, we generate several sets of random coefficients—let's call them [b₀, b₁, b₂, ... bₙ], [c₀, c₁, c₂, ... cₙ], and [d₀, d₁, d₂, ... dₙ]. These coefficients are used to construct the Lagrange polynomials B(X), C(X), and D(X).

Next, we generate random values for X: [b₀, b₁, b₂, ... bₙ], and evaluate the polynomial at each of these points:

P(b₀) = y₀
P(b₁) = y₁
...
P(bₙ) = yₙ

Now, we have N points, each belonging to the polynomial P(X). Since P(X) is a polynomial of degree n, these points can be used to recover the original polynomial—and, therefore, the private key.

Conclusion

By leveraging Shamir’s Secret Sharing, we can overcome the wallet barrier that slows down cryptocurrency adoption. This method allows users to maintain control of their wallets without relying on third-party apps or exposing sensitive data. The future of crypto lies in making these advanced security mechanisms seamless and accessible to everyone, empowering more people to engage with decentralized finance securely.