# Elliptic Curve Photography: What You Need to Know

Elliptic curve cryptography (ECC) is a public key cryptographic algorithm that’s commonly utilized for security purposes, like authentication, encryption, and digital signatures.

It uses the elliptic curve theory for key generation, so unlike other types of cryptography, the basis here is the elliptic curve equation, not factoring in large prime numbers.

In this guide, we’ll discuss how ECC works and its advantages, disadvantages, vulnerabilities, and applications.

## History of Elliptic Curve Cryptography

In 1970, James H. Ellis developed a non-secret encryption method that uses a public key. The method was further developed by Clifford Cocks, which led to the development of the RSA encryption method in 1983.

Then, in 1985, Neal Koblitz of the University of Washington and Victor Miller of IBM separately studied the possibility of using elliptic curves in cryptography. But it wasn’t until later that Certicom, a security provider, developed ECC encryption. The technology was licensed for use by Hifn, an integrated circuitry, and network security manufacturer.

## Components of Elliptic Curve Cryptography

Elliptical curve cryptography consists of 5 key elements:

- Elliptic Curves
- Finite Fields
- The "Generator" Point
- Private and Public Keys
- Elliptic-Curve Discrete Logarithm Problem (ECDLP)

The working principle is the way elliptic curves are structured algebraically over finite fields, which enables the creation of uncrackable keys.

A “Generator” point is defined to generate a point in its subgroup other than the predefined constant elliptic curve point.

The private key is a random integer that’s generated quickly, while the public key is an EC point that consists of a pair of integer coordinates X and Y.

As for The Elliptic-Curve Discrete Logarithm Problem (ECDLP), it’s based on the assumption that it’s impossible to identify a discrete logarithm of a random elliptic curve element in reference to a public base point.

## Elliptic Curve Cryptography Algorithms

The Elliptic-curve Diffie–Hellman (ECDH) is the most widely used protocol in ECC. It’s an agreement between two users, where each of them has an elliptic-curve public–private key pair used to create a secret that can be shared via an unprotected channel. The secret can either serve as a key or derive a different key.

Other algorithms used include ECDSA for classical curves, EdDSA for twisted Edwards curves, and hybrid encryption schemes like ECIES and EEECC (EC-based ElGamal).

## Elliptic Curve Cryptography Vs RSA

The main difference between ECC and RSA is key size. ECC uses smaller keys than RSA without compromising security. For example, a 384-bit ECC key can achieve the same protection as a 7670-bit RSA key. This results in faster key generation and less load on memory for ECC.

It’s also worth noting that ECC uses public and private keys that aren’t equally exchangeable. This is because, in ECC, the private key is an integer, while the public key is represented as a point on the curve.

However, the implementation process of ECC can be more complex and time-consuming than with RSA, but since encryption/decryption and key generation in ECC is much faster than RSA, it’s well worth it.

## Applications of Elliptic Curve Cryptography

These are some of the ways ECC is utilized:

### Real-world Applications

The most notable practical applications of ECC include online banking, email encryption, and online payments.

When you make a payment online, your card’s info is protected with ECC by the vendor. In email applications, ECC is used to encrypt your email so that no one can read it in transit.

Pretty Good Privacy (PGP) is one of the most popular email encryption solutions that serve this purpose.

### Elliptic Curve Digital Signature

An Elliptic Curve Digital Signature Algorithm (ECDSA) secures transactions using ECC keys. It functions similarly to other DSAs, but it uses smaller keys, making it more efficient.

### ECC Keys in Cryptocurrencies

An ECC key pair consists of public and private keys. The public key verifies digital signatures, while the private key is used for signature verification. These keys are heavily used in cryptocurrencies such as Bitcoin, where the ECDSA algorithm is used to sign transactions.

## Security of ECC

ECC is very secure, especially when larger keys are used. A minimum key size of 246 or 384 bits is recommended to ensure security.

However, despite being regarded as secure, ECC vulnerabilities exist. For example, a side-channel attack like simple power attacks, fault analysis, and differential power attacks, may cause leaks. Another type of attack is twist-security attacks. These are used to leak the private key.

Both side-channel and twist security attacks can be prevented with simple countermeasures, like curve choices and parameter validation.

## Conclusion

That was a quick overview of elliptical curve cryptography and its applications.

ECC is fast, efficient, and secure, making it a superior choice to other encryption methods like RSA. It requires a higher level of technical knowledge to be successfully implemented, but its results are exceptionally good.

Future applications will require faster and more secure encryption methods, and further development of ECC is crucial to keep pace.

**Key Takeaways:**

- ECC was developed by Certicom
- ECC’s primary components are elliptical curves, finite fields, Generator points, public and private keys, and the Elliptic-Curve Discrete Logarithm Problem (ECDLP)
- ECC is faster and more efficient than RSA but has a steeper learning curve
- ECC may be vulnerable to side-channel and twist security attacks, but they can be easily countered

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