The maximum defined value of the equation relates to the key size used. The n is the private key value, which indicates how many times the equation should be run, ending on the final value that is used to encrypt and decrypt data.
This process can be completed n number of times within a defined max value. From here, a line is drawn back to our original point A, creating an intersection at point E. Taking point C and bringing it to the mirrored point on the opposite side of the x-axis produces point D. Multiplying a point on the curve by a number produces another point on the curve (C). But, without knowing the private key and depending on the key size used, getting from B to A is difficult, if not impossible, to achieve.ĮCC is based on the properties of a set of values for which operations can be performed on any two members of the group to produce a third member, which is derived from points where the line intersects the axes as shown with the green line and three blue dots in the below diagram labeled A, B and C. This means that a mathematical equation with a public and private key can be used to easily get from point A to point B. Each of these cryptography mechanisms uses the concept of a one-way, or trapdoor, function. From a cryptographic perspective, the points along the graph can be formulated using the following equation:ĮCC is like most other public key encryption methods, such as the RSA algorithm and Diffie-Hellman. One is a public key that is known to anyone, and the other is a private key that is only known by the sender and receiver of the data.ĮCC generates keys through the properties of an elliptic curve equation instead of the traditional method of generation as the product of large prime numbers.
Public key cryptography systems, like ECC, use a mathematical process to merge two distinct keys and then use the output to encrypt and decrypt data. The curve is completely symmetric, or mirrored, along the x-axis of the graph.
What is elliptical curve cryptography (ECC)?Įlliptical curve cryptography (ECC) is a public key encryption technique based on elliptic curve theory that can be used to create faster, smaller and more efficient cryptographic keys.ĮCC is an alternative to the Rivest-Shamir-Adleman ( RSA) cryptographic algorithm and is most often used for digital signatures in cryptocurrencies, such as Bitcoin and Ethereum, as well as one-way encryption of emails, data and software.Īn elliptic curve is not an ellipse, or oval shape, but it is represented as a looping line intersecting two axes, which are lines on a graph used to indicate the position of a point.
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