What is an elliptical curve code (ECC)?

What is the ellipse curve code? Why is there so much information about this type of cryptography nowadays?

Elliptic curve cryptography (ECC) is a public-key cryptography technique based on the theory of elliptic curves, which makes cryptography faster, smaller and stronger. ECC generates cryptography through the properties of elliptic curve equations instead of the traditional large prime number method. This technology can be used with most public encryption methods such as RSA and Diffie-Hellman.

According to some researchers, ECC reaches a security level of only 164 bits while other systems need 1024 bits to reach the same level. Because ECC helps establish security with computing power and low battery power, it is widely applied to mobile applications.

ECC was developed by Certicom, a provider of electronic business security systems and recently licensed by Hifn, manufacturer of integrated circuits and network security products. RSA is also currently developing its own ECC. A lot of companies including 3COM, Cylink, Motorola, Pitney Bowes, Siemens, TRW and VeriFone have ECC support on their products.

What is an elliptical curve code (ECC)? Picture 1 Equations and graphs of elliptical curves

The properties and functions of elliptical curves have been studied in mathematics for 150 years. Their use as a code was first introduced in 1985 by Neal Koblitz from Washington University and Victor Miller at IBM (these are two independent studies).

The elliptical curve is not ellipse (oval), but is represented as a roundabout at two axes. ECC relies on the properties of a particular type of equation created from a group (set of elements along with a binary operation combining any two elements of the set into a third element). The graph comes from the point where the intersection of the curve and the two axes. Taking that score multiplied by a number to find the next score, but it's hard to know which number to multiply even if the next result and score are given.

The equations of the ellipse curve have a characteristic that is extremely valuable for coding purposes, because they are easy to implement but extremely difficult to reverse.

However, the use of elliptical curves still has some limitations in this industry. Nigel Smart, a Hewlett Packard researcher, found a few holes in this curve that made them very easy to crack. However, Certicom's Philip Deck said that, although these curves are vulnerable, ECC developers know how to classify them for use. He believes that ECC is a unique technological potential that can be exploited globally and used on all devices, According to Deck, 'the only thing that can do that is the ellipse curve'.