Elliptic Curve Cryptography (ECC) Algorithm Explained

Cyberattacks have grown significantly in the last few years. Since the pandemic year 2020, the surge in the number of cyberattacks has been huge.

As per recent stats, businesses suffered over 50% cyber attacks per week in 2021. Moreover, 43% of cyberattacks are targeted at small and medium-sized businesses. So, why is this happening? One of the prime factors is the lack of powerful encryption. A powerful yet not that popular way of securing data while transacting online is Elliptic Curve Cryptography. 

Unlike many other encryption techniques, ECC encryption involves a mathematical function that is easy to compute in one direction but is tough to reverse. This is the reason it is preferred, just like the RSA encryption. 

If you aren’t aware of the remarkable ECC cryptography, we have this extensive guide for you! Read and discover more! 

What is Elliptic Curve Cryptography?

Elliptic Curve Cryptography, aka ECC, is a key-based method of encrypting data online. We know that whenever the data is shared on the web, it is encrypted to ensure security. 

ECC does this by using a pair of public and private keys for both encryption and decryption. It is often compared to the RSA (Rivest–Shamir–Adleman) algorithm, as the RSA algorithm follows the same approach but with prime numbers. 

Unlike RSA, ECC uses the concept of elliptic curves to generate security between key pairs. 

Read More on ECC Vs RSA Difference: Decoding the Difference

How does ECC work?

Elliptic Curve Cryptography (ECC) is a contemporary method of securing data communication and digital signatures through the use of geometrical concepts, namely; elliptic curves over finite fields.

ECC starts with the determination of a private key which is a random whole number usually in the range of 256 – 512 bits. The related public key is formed by multiplying the private key by a special point of the curve—generator point under elliptic curve multiplication.

This operation gives a point on the curve which serves as the public key. In ECC, the plaintext is converted to a point on the elliptic curve and through a set of mathematical operations such as point multiplication as well as point addition/subtraction produces the ciphertext.

Thus, the efficiency of ECC is in the combination of high security with the use of keys of significantly smaller sizes compared to the use of traditional cryptographic methods;

This approach is especially useful for mobile devices and IoT devices, where energy efficiency and high levels of security are critical.

Advantages of ECC

Enhanced Security with Smaller Key Sizes

ECC offers the same level of security as those regular algorithms such as RSA but with compressed keys. For instance, a 256-bit ECC key provides equivalent security to a 3072-bit RSA key.

This also implies that ECC can support high security without the need to rely on very large keys thereby mitigating the key compromise problem. These additional securities make ECC one of the effective tools to safeguard data against modern-day complex cyber threats.

Improved Performance and Efficiency

The ECC is faster than the other two types because the key sizes are smaller and consume less power. It results in faster encryption and decryption, making ECC most appropriate to be used where high performance demands encompass mobile devices and IoT devices.

The necessity of using ECC is because it can guarantee that secure messages and payment can be made without much delay, thus making it convenient for users.

Reduced Bandwidth and Storage Requirements

This makes sense because ECC keys, because of their shorter length, also consume less bandwidth in their transmission and take less storage space.

This advantage is vital especially in cases when bandwidth or storage space is a concern or when numerous keys are utilized.

For example, in a large scale system like cloud services or data centers, the overhead consumption can bring notable savings in cost and enhance performance of the system.

Scalability and Flexibility

The smaller key sizes and fast computation necessary for ECC make it customizable for large networks, including communications in large networks.

It is also versatile for application in a variety of cryptographic protocols and standards to make it versatile in as many security applications as possible.

This scalability also allows ECC to accommodate organizations of all sizes, from direct sellers to multinational companies that have different security needs and systems.

Enhanced Security for Future-Proofing

There is also a possibility that with the increase in computational power and time, the existing algorithms with more significant key sizes can be cracked by brute force.

This feature is achieved through ECC’s key sizes which are smaller than that of the traditional RSA but protect against more advanced threats than current ones without the need for exponentially larger key size.

This progressive attitude of safeguarding ensures that the related systems using ECC stays protected as technology evolves.

Disadvantages of ECC

Complex Implementation

ECC can sometimes be harder to implement compared to other standard algorithms such as RSA and DSA. Some of the mathematical concepts which have been used in the ECC such as elliptic curve arithmetic are complex and sensitive.

This can create implementation errors if not managed, which might endanger security. ECC may require investment in specialized expertise and resources to enhance accuracy and security of the implementations.

Patent and Licensing Issues

Traditionally, ECC has been restricted by several patents and licensing issues, which may affect its implementation. Even though some of these patents have long since expired, licensing problems continue to affect its application in some jurisdictions and fields.

This can add legal and financial complexities that may hinder organizations from implementing ECC especially the small businesses.

Compatibility and Interoperability

However, it should be noted that ECC is not supported by all the systems and protocols in use today. There are concerns about interconnectivity, as some older systems and software may not work with ECC.

This may reduce its applicability where interoperability with the pre-existing systems is crucial. Companies may have to support two systems simultaneously or invest time and money in integration, which also poses challenges.

Performance Overhead in Specific Use Cases

ECC is considered highly effective, but there are particular scenarios where its productivity may be low.

For example, in applications where there is a lot of computation or real-time interaction, the overhead of performing elliptic curve operations may well cancel out the advantages of smaller keys.

It can thus be considerably slower than other cryptographic algorithms in some cases, which makes it important to consider if it is appropriate for particular applications or not.

Limited Expertise and Resources

As it is relatively new compared to older algorithms such as RSA, there could be fewer experts equipped with knowledge in the field of ECC. This lack of knowledge can make it difficult for organizations to hire the right talent for implementation and support.

This issue can be addressed through training and development of in-house expertise but this takes time and investment.

Why is Elliptic Curve Cryptography Algorithm better than RSA? 

Ok, we know that elliptical cryptography uses the mathematical concept of elliptical curves to ensure safe data transfer over the web. So does RSA, then how is ECC encryption better? 

Smaller Key Size 

Encryption is not an easy process. Creating random security keys every time, storing them safely, and applying them to plaintext is a process that is tough. But, as it is done by a machine, we don’t have to worry, but if the keys are long, it can affect the system resources. As the storage space required is more for longer keys, ECC can help here. 

One of the key benefits of Elliptic Curves Cryptography over RSA is the key size. Unlike RSA, the key size of ECC encryption is significantly smaller. Here is an example! 

For the same level of security, the key length of an RSA key and ECC keys are mentioned below:

ECC Key (in bits)	RSA Key (in bits)
160	1024
224	2048
256	3072
384	7680
521	15360

Faster Key Creation

One of the ideal features of the Elliptic curve cryptography algorithm is that it generates keys super fast. For example, the generation of a private key in ECC is just like generating a random integer which is faster and more efficient. On top of speed, any key in the range of the function is a valid private key. 

Lower Computing Power

The ECC algorithm in cryptography is useful for encryption while generating smaller keys. But, this is not it. The ECC encryption algorithm also uses lower computing power and battery than the RSA. Hence, saving resources for other processes. 

It can be scaled

Again, let’s bring in the concept of the keys here. We know that the keys produced by ECC are smaller in length and faster to generate. The smaller length of the keys makes ECC easily scalable. On the other hand, when RSA keys reach the length of 3072-bits or over, ECC performs over 100% faster.

Ideal for low-powered Devices

The ECC encryption uses smaller keys that are directly related to the efficient use of resources. As the computing power required is less, ECC is ideal to be used on mobile and IoT devices. 

Is Elliptic Curve Cryptography Algorithm Secure?

Well, the basic thing that distinguishes ECC from other encryption methods is the key size. So, even if you are using a bigger key size to encrypt the data, it will be smaller as compared to other methods.

Moreover, the security will be more than other methods. On top of this, the internal efficiencies that this method has are what makes it secure. 

Various ECC Algorithms

Based on the mathematics of elliptic curves over finite fields, ECC can provide various algorithms! 

ECC Digital Signature Algorithm

The Elliptic Curve Digital Signature Algorithm (ECDSA) is used by cryptocurrencies like Bitcoin and Ethereum. The security features of ECC enable cryptocurrencies to sign the transactions securely. ECDSA is used for classical curves, and the Edwards-curve Digital Signature Algorithm (EdDSA) is used for twisted Edward curves. 

ECC Key Agreement Algorithms

The ECC key agreement algorithms allow for secure key exchanges over an insecure channel. They are of various types like ECDH, FHMQV, and X25519. 

ECC Encryption Algorithms

ECC encryption algorithms like ECIES and EECC allow for semantic security. 

Is ECC Best for you?

Elliptic curve cryptography is used in various organizations today, such as Facebook, Cloudflare, etc. So, is it ideal for you? 

As per the current scenario, RSA is the most widely used cryptosystem. It is used by over 90% of SSL certificates, while ECC is used by 8%. Now, by statistics, it may seem like it is not for you. But, trust us, the adoption of ECC is on the rise. 

If you have a website that requires powerful security and is complex, ECC could be the perfect match for you. However, note that the use of ECC requires implementation, and it needs to be handled carefully. 

Wrapping Up!

As per the current web security scenario, ECC SSL is one of the best alternatives to RSA in SSL encryption. Therefore, it is best to plan ahead and be future-ready to adopt it. ECC may not be dominant today, but it will surely be in the future, not to forget the rising use of mobiles for which it is an indispensable choice.