Understand Ethereum’s Elliptical Curve Cryptography (ECC)
Cryptography (ECC) or the elliptic curve is a child of cryptography for public keys that uses the property of elliptical curves to secure online transactions. In this article, we will deal with the Details of ECC in Bitcoin and Examine How it is compared to the curve of Ethereum.
Bitcoins Elliptical Curve
The Implementation of ECC by Bitcoin is based on the curve secp256k1 (also Known as an elgamal). This curve is selected for its simplicity and efficiency. Here is an illustration of what a secp256k1 curve could look like:
`
E (2)
/ / \
C (0) ~
\ /
G
`
In this diagram, e representatives the point at infinite in the curve (a special “zero” point), C is the private key (the secret number) and g is the public key (the digital signature). The Equation of the Curve is y^2 = x^3 + px + q, wh andbre ‘(x, y)’ are points on the curve.
Ethereum Elliptical Curve
Like Bitcoin, Ethereum also uses secp256k1 for its ECC implementation. However, The Curve of Ethereum Has A SLIGHTLY DIFERENT OF:
`
E (2)
/ / \
C (0) ~
\ /
G
`
The Main Difference is that the private key C is not explicitly listed in the diagram. Instead, it appears as c = (k x^3 + p y)^-1, wh andbre ‘(x, y)points are on the curve and' k is a constant.
Comparison with Bitcoins Curve
While Both Secp256K1 Curves Have Similar Properties, There Are Some Differences:
* Private Key Order : In Ethereum, The Private Key C Appears in a Certain Order IF IT IT IS “[C, G]”, While in Bitcoin Only G.
* Constant K Value : The Constant Used to Calculate the Public Key in Ethereum Has A Different Value than That Used in Bitcoin.
* Point Display : In Ethereum Diagrams, the Points on the Curve Are Shown by “E (2)”, While It is Simply “G” in Bitcoins Diagram.
Diploma
In Summary, Both Bitcoin and Ethereum use the secp256k1 ECC to implement the cryptography of the elliptical curve. While the curves have Similar Properties, there are some differentences in the way they are constructed and presented. Understanding thesis Differences can provide a Deeper Insight Into the Underlying Mathematics of Cryptographic Systems.
Additional resources
Further Reading via ECC and its Applications:
- The Ethereum WhitePaper (2014) Offers an overview of the ECC Implementation of Ethereum.
- The Bitcoin Green Paper (2009) Contains a description of the ECC Algorithm from Bitcoin.
- Research Work by Prominent Developers Such As Vitalik Buterin and Gavin Wood sacrifice Incoming Analyzes and Insights Into Mathematics Beind ECC.
