ECC Vs RSA Certificate Difference: Decoding the Cryptographic Algorithm

When discussing securing online communications, ECC and RSA are both encryption algorithms that are inevitable to mention. These algorithms are typically used in SSL/TLS certificates to ensure communication security in the digital space. So naturally, ECC vs. RSA might confuse many.

While buying an SSL certificate, the dilemma of ECC vs. RSA confuses website owners. They would want to make an informed decision to ensure maximum safety for their end users.

So, how does one choose between encryption algorithms when buying an SSL certificate? Let’s discuss.

What is RSA?

RSA stands for Rivest Shamir Adleman, and these are the names of the inventors of this cryptographic algorithm. Though it came into existence in 1977, in today’s time, RSA is widely used for encrypting emails, software, website data, etc. Its principle is based on the prime factorization method for one-way data encryption.

The process involved taking two large random prime numbers and multiplying them together to develop a public key. It is known as the modulus, and though it is made public, one cannot determine the message or piece of data as the two prime numbers are kept private.

Also Read: What is Sectigo RSA Domain Validation Secure Server CA?

Here is a Mathematical Representation of How RSA Works:

RSA encryption uses the principles of number theory and mathematical trapdoor functions to encrypt and decrypt data.

The encryption process begins by selecting two large prime numbers: p and q. These two prime numbers are multiplied to create a modulus, n = pq.

A public exponent, which is usually denoted as e, is then chosen. This number should be relatively prime to n, which is calculated as: (p-1)(q-1).

The private key is then generated using the modulus, n, and another number, d, which is chosen such that (ed) mod (p-1)(q-1) = 1.

To encrypt a message sender m raises it to the power of e mod n. To decrypt the message, the receiver raises the ciphertext to the power of d mod n. This process then results in the original message.

Also Read: RSA vs. AES Encryption: Key Differences Explained

How difficult could it be to get hold of these two prime numbers, you might think? Even if you think of trillions, it is too small of a number to represent them precisely.

The difficulty is so much that it would take 1500+ years of computing time for sieving 768-bit, 232-digit RSA modulus using a ‘single core 2.2 GHz AMD Opteron processor with 2 GB RAM.’ Today, most SSL certificates employ a 2048-bit private key for RSA certificates.

What is responsible for making this encryption algorithm is its simple nature. Derived from a simple mathematical principle, it is highly suitable for ensuring data security on the Internet.

As a result, it is widely used in various applications, including secure communication, online banking and shopping, and electronic signature schemes. One of the advantages of RSA is that it can be relatively fast, mainly when used with shorter key lengths.

Features of RSA

• Asymmetric Encryption: RSA uses two keys, one for encryption and one for decryption. As the encryption key is made public and the decryption key is kept private, it helps establish secure communication between two parties.

• Key Size: RSA keys can be generated with key sizes of 512, 1024, 2048, and 3072 bit. The larger its size, the more secure the encryption is.

• High Security: RSA is considered one of the most secure encryption algorithms based on the difficulty of getting two large and random prime numbers. So, without a private key, no one can decrypt the data.

• Digital Signatures: RSA is also used to create digital signatures, which are used to prove the authenticity of a message or document.

Now, let us understand ECC.

What is ECC?

ECC stands for Elliptical curve cryptography. As the name suggests, it is a form of an asymmetric cryptographic algorithm developed based on applying the elliptic curve’s algebraic structure over finite fields. The algorithm came into use when Neal Koblitz and Victor S in the 1980s suggested the application of elliptical curves in cryptography. However, ECC came into the limelight in 2004.

As it functions on the elliptic curve discrete logarithm problem (ECDLP), it is tough to crack since. Also, there has been no known solution to the mathematical problem given by the equation producing the elliptical curve in a graph. Intruders can only launch an attack through a brute-force attack or a trial-and-error approach.

Structurally, ECC is more secure than RSA as it provides an optimum amount of security with a short key length, resulting in less computing power and network load. This translates into a better user experience.

In ECC, encryption and decryption are done using the points on the elliptic curve. The equation y²=x³ + ax + b defines an elliptic curve. It is a mathematical construct used in this cryptography. A set of points on the curve are chosen as a public key, and a private key is chosen as a point on the curve.

Different values of a and b can be used to create different curves, each with different properties, which can be used for different encryption purposes.

The point ‘a’ and ‘b’ are coefficients of the curve, and x and y are coordinates on the curve. The curve is defined over a finite field, and all points on the curve must satisfy this equation. The curve is also symmetric over the x-axis.

It means that any point on the curve can be mirrored over the x-axis, and the curve will remain the same. Additionally, any non-vertical line will intersect the curve in three points or fewer.

In the encryption process, a point on the curve called the public key and a second point called the private key are selected. Then a series of mathematical operations, such as point multiplication and addition, is done on the public key and the plaintext message. This is done to produce a ciphertext.

The decryption process involves the same mathematical operations on the ciphertext and the private key. It helps in retrieving the original plaintext message. The security of ECC is based on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP).

One of the advantages of ECC is that it can provide an equivalent level of security to other algorithms, such as RSA, with shorter key lengths. This makes it more resistant to specific attacks and more suitable for resource-constrained environments.

Overall, ECC is a widely used and trusted encryption algorithm well-suited for various applications, including secure communication, online banking and shopping, and the IoT. It is known for its efficiency and scalability,

Features of ECC:

• Smaller Key Size: As ECC employs a small key size, it is quite efficient in memory usage & processing power.

• Same Level of Security: With a minor key size of 256-bit, ECC provides the same security as RSA’s 2048 key length.

• Faster Performance: ECC is faster than RSA, which is more suited for device applications.

• Digital Signature: The places where digital signatures, such as digital documents and financial transactions, use ECC due to its faster computational speed. Moreover, they exhibit strong resistance to quantum computing attacks.

ECC is used in various protocols, including SSL/TLS, SSH, S/MIME, and IPSec.

This was all about ECC. Now is the time to compare them based on different parameters and decide which is better or are both of them at par with each other. So let’s get started with elliptic curve cryptography vs. RSA.

RSA Vs. ECC: Difference Decoded

These are some of the differences of the elliptic curve vs. RSA.

Key Length: ECC 256 vs RSA 2048

The key length of RSA is measured in bits, typically ranging from 1024 to 4096 bits. The longer the key length, the stronger the encryption. For RSA, a key length of 2048 bits is considered the standard that is secure enough for most applications.

When compared to RSA, ECC has a more minor key length compared to RSA. It is measured in terms of the size of the prime modulus, which typically ranges from 160 to 521 bits. For ECC, A key length of 256 bits is considered the standard.

Security (in Bits)	Key Length of RSA	Key Length of ECC
80	1024	160-223
112	2048	224-255
128	3072	256-383
192	7680	384-511

Performance

The performance of ECC and RSA can differ in several ways:

• Encryption/Decryption: ECC encryption and decryption operations are faster than RSA due to elliptic curve mathematics.

• Digital Signatures: ECC digital signatures are faster than RSA due to the application of elliptic curve mathematics.

• Bandwidth: The demand for bandwidth is less with ECC compared to RSA when transmitting data over a network.

• Power Consumption: ECC drains less power than RSA, making it more suitable for devices with limited power resources.

If we have to give you a number- RSA can respond to 450 requests per second with a 150-millisecond average response time, but ECC takes only 75 milliseconds to respond to the same number of requests per second.

Key Generation

ECC key generation is faster and more computationally efficient than RSA key generation. This is because ECC key generation involves choosing a random elliptic curve over a finite field and selecting a random point as the public key.

On the other hand, RSA key generation involves selecting two large prime numbers and performing mathematical operations on them to generate the public and private keys.

Applications

ECC is used in various protocols, including SSL/TLS, SSH, S/MIME, and IPSec, whereas RSA is mainly used in SSL/TLS and SSH.

These are some of the major differences between RSA and ECC. Here is a table for your better understanding.

Rivest-Shamir-Adleman (RSA)	Elliptic Curve Cryptography (ECC)
RSA is one of the oldest and well-established public-key cryptography methods.	ECC is comparatively a newer public-key cryptography method.
Works on the principle of the prime factorization method.	Works on the mathematical representation of elliptic curves.
RSA runs faster as it is a simple algorithm.	As it is complex in nature, ECC takes more time to run.
Due to a lack of scalability, RSA has started becoming vulnerable.	ECC is more secure thanks to its adaptive phase. Its application might scale up in the future.
For implementing encryption, RSA demands bigger key lengths.	Compared to RSA, ECC demands shorter key lengths.
Standard Key length- 2,048 bits	Standard Key length- 256 bits
It supports all the platforms.	It exhibits compatibility with new browsers and OS (some platforms like cPanel are not supported)

ECC vs RSA Certificates: Which Is Better?

Both ECC and RSA certificates are secure. However, the choice between the two should be based on your organization’s needs and requirements.

Regarding ECC Encryption VS RSA, the former is generally considered more secure than the latter for the abovementioned reasons.

On the other hand, RSA certificates have been widely used for decades and are considered more widely supported by older systems. So it ultimately comes down to your website requirements and system compatibility.