My interest in cryptocurrency started because of trust issues.

I became interested in the concept of trusted computer networks because of a company I invested in during the 2000s. This company was promoting a hardware “root of trust” and was trying to get a trusted computing module onto every device. This microchip would allow a baseline of trust to be established on every device and therefore be an important and foundational component in the chain of trust that would follow.

Fast forward to the late 2010s, and Bitcoin and Ethereum are gaining a lot of attention. The main innovation that these digital ledgers brought into society is the establishment of a root of trust.

At the heart of the root of trust in Distributed Ledger Technologies (DLTs) is the public/private key pair. A private key is a series of numbers and letters that only the owner knows, while a public key is a series of numbers and letters that can be shared with others.

Bitcoin, Ethereum, and Litecoin, among others, use a specific mathematical process or algorithm called Elliptic Curve Cryptography (ECC) to create each pair of cryptographic keys (public and private), which is used to secure and authenticate transactions.

In ECC, the public key is generated from the private key using elliptic curve multiplication. An elliptic curve is a set of points on a graph that satisfies a specific mathematical equation. Elliptic curve multiplication is a mathematical operation that involves combining the private key with a predetermined point on the elliptic curve, known as the generator point, to create a new point on the curve, which becomes the public key.

The generator point is a fixed point on the curve that is agreed upon by all users of the cryptocurrency network. It is typically defined as a specific set of coordinates on the curve. The generator point is selected in such a way that it is mathematically infeasible to determine the private key from the public key. The choice of the generator point is a critical part of the security of ECC.

The multiplication process involves a series of point additions and doublings on the elliptic curve. Each doubling operation takes a point on the curve and finds the point that is symmetrically reflected across the x-axis. Each addition operation takes two points on the curve and finds the point that intersects the curve at a third point. The result of the elliptic curve multiplication is a new point on the curve that represents the public key.

The resulting public key is a pair of coordinates on the elliptic curve, typically encoded in a specific format, such as hexadecimal, to make it easier to use in transactions.

In the context of cryptocurrency, a public key is a unique string of characters that is used to identify a user’s wallet. The public key is generated from the user’s private key, which is a secret string of characters known only to the user.

ECC is an effective cryptographic method that is widely used in various blockchain-based systems. Its security relies on the complexity of the mathematical problems involved in finding the private key from the public key. The large number of possible solutions makes it extremely difficult, if not impossible, to reverse-engineer the private key from the public key.

To send cryptocurrency to someone, the sender creates a transaction that includes the recipient’s public key and the amount of cryptocurrency being sent. The transaction is then verified using the sender’s private key, which ensures that only the sender can authorize the transfer of funds.

Once the transaction is verified, it is broadcast to the network, and nodes on the network validate the transaction by checking that the sender has sufficient funds and that the transaction is associated with the correct public key. Once the transaction is validated, it is added to the blockchain.

ECC is explained well in the following YouTube link https://youtu.be/muIv8I6v1aE

Zero-knowledge proofs (ZKPs) are another powerful tool used to further enhance the security and privacy of cryptocurrency transactions. ZKPs allow someone to prove to another that a particular statement is true, without revealing any additional information beyond the statement itself. In cryptocurrency, ZKPs are used to prove that a transaction is valid, without revealing the amounts or parties involved in the transaction.

The use of ZKPs in cryptocurrency is based on the concept of a zk-SNARK, which stands for “zero-knowledge succinct non-interactive argument of knowledge”. Basically, a zk-SNARK is a way of proving that a statement is true without revealing any additional information beyond the statement itself.

In a cryptocurrency transaction, a zk-SNARK can be used to prove that the transaction is valid, without revealing any details about the sender, recipient, or the amount being transferred. This enhances the privacy and security of the transaction, as it prevents third parties from accessing any sensitive information about the transaction.

ZKPs are based on complex mathematical equations and require significant computational power to execute. Together these mathematical methods are used to establish roots of trust.