**Elliptic Curve Cryptography Encryption Application and Benefits**

Elliptic curve encryption, a popular modern cryptographic system, is faster than most and has a wider appeal. ECC is based upon the elliptic curve theory, which allows for more efficient cryptographic keys. ECC’s asymmetricÂ encryptionÂ is lighter because it has smaller keys.

## Understanding ECC

Public encryption methods such as Diffie-Hellman and RSA generate large numbers that require high computing power. They require large resources to encrypt applications, and they may not be suitable for mobile applications with limited resources. The creation of keys with elliptic curves is faster and more efficient. ECC uses elliptic curve equations to generate complex keys that are mathematically strong and secure. Additionally, elliptical curve cryptography employs shorter keys that offer robust protection and are therefore effective in protecting mobile applications.

## ECC Applications

ECC encryption is one popular method for digital signatures of popular cryptocurrencies such as bitcoin. For cryptography purposes and to sign transactions, cryptocurrencies use the Elliptic Curve Digital Signature Algorithms (ECDSA key). Digital signatures are made using the Elliptic Curve Digital Signature Algorithm (ECDSA) key during key pair or key exchange. Because of its low resource use, ECDSA signing SSL certificates is used in different parts of SSL standards. ECC can also be used for:

- Demonstrating ownership of cryptocurrency like bitcoins
- Secure internal communications and confidential data for the US government
- Users of the TOR project are allowed to keep their anonymity.
- Encryption signatures for Apple’s iMessage communication system
- Secure web browsing

## What makes ECC different from other public-key encryption methods?

ECC cryptographic algorithms are used by organizations for the same reasons that RSA algorithms. ECC and RSA both generate a private key as well as a public key infrastructure that allows two users or devices to securely communicate by exchanging a secret. The ECC public-key encryption techniques offer some advantages over RSA or other encryption methods. A 256-bit ECC key provides nearly the same security level as a 3072 bit RSA key. The elliptic curve cryptography algorithm allows systems with limited resources (e.g. computational power) to use approximately 10% of the bandwidth or storage space required by RSA algorithms.

ECC is based upon the elliptic curve theory and uses the properties that the equation has to generate encryption keys. This approach is different from the traditional method of a generation where public-key cryptography algorithms generate large prime numbers. The ECC encryption technique can also be used by other public-key cryptographic techniques, such as Diffie-Hellman or RSA. Research has shown that ECC cryptographic systems provide encryption and protection with a 164-bit key. Other systems would need a 1,024-bit key to offer the same level. ECC security systems are preferred for protecting mobile apps because they use smaller keys that provide higher protection and lower computing power.

## ECC Trapdoor Function

ECC trapdoor functions are one of the main reasons why the elliptic curve key is more efficient and different from the RSA cryptographic keys. The ECC encryption method uses the trapdoor function as a mathematical algorithm. This algorithm works by calculating the hops required to reach a set of points.

- You start at an arbitrary point on an Elliptic curve. Then, use the dot function for a new point.
- Start at A:
- A dot B = -C (connect points B and A with a line that intersects at the -C).

**Source**Â ArsTechnica

- Reflect from â€“C to C across X-axis, and A dot C= -D (connect A/C with a line that intersects at the -D).

**Source**Â ArsTechnica

- Reflect from â€“D to D across X-axis, and A dot = -E (connect A & D with a line intersecting at -E).

**Source**Â ArsTechnica

- Reflect on the X-axis from -E through E.

This trapdoor function is very useful because it’s easy to find the endpoint if the user knows the starting point (A), and the hops required to get there (E). It is difficult to calculate the number of hops required if only the beginning point and ending points are known. ECC cryptography uses the same approach. The public key cryptography represents the starting EC points A and E, while the private key indicates the number of hops required to get from A or E.

## ECC has many advantages

ECC keys are more efficient than RSA keys and other public cryptographic methods. Therefore, elliptic cryptography with public-key encryption can be easier to use but more difficult to reverse. RSA encryption, on the other hand, is based upon the assumption that a product of multiplication large prime numbers is easy but it is difficult to factor the product back to the original prime number.

The 256-bit ECC keys are equivalent to a key length of 3072 bits. ECC cryptography has an advantage because it uses smaller, more efficient, and simpler ECC keys. ECC cryptography is more efficient than RSA because it uses fewer resources and energy on small mobile devices.

ECC encryption can be used in conjunction with Diffie Hellman to improve performance. ECC encryption doesn’t perform RSA functions of authentication and communication, but it generates an ephemeral DH key with the help of an elliptic curve private key. The ECDHERSA encryption is included in the associated SSL cipher sets. This complements DHE cipher suites.

The main benefit of using elliptic curve cryptography in combination with Diffie-Hellman(ECDHE-RSA), over plain Diffie-Hellman, is that it optimizes performance and provides a similar level of protection, but with fewer keys.

Although there are concerns about ECC certificates being implemented, which provide a source for random numbers to make signatures, the benefits that elliptic curve cryptography offers far outweigh the disadvantages of traditional RSA algorithms. ECC encryption is a viable alternative to traditional public encryption methods due to quantum computing and other emerging technologies.