Elliptic Curve Cryptography (ECC) is a method of encoding data that allows only certain persons to decrypt it. It's like a secret note to a friend in class, but much more advanced (and with fewer checkboxes asking if someone likes you).
Compared to RSA, ECC is a significantly more robust cryptographic approach. Using the mathematics of elliptic curves, public-key encryption can be made more secure for different key pairs.
Although RSA uses prime integers to achieve the same goal, ECC is becoming increasingly popular due to its reduced key size and continued reliability. The ability of devices to maintain security has been pushed to the limit due to the increase in key size, and this trend is expected to continue as manufacturers seek to meet this growing demand. Therefore, it is important to have some prior knowledge of setting up ECC.
Unlike RSA, which uses factorization of prime numbers, ECC's approach to public-key cryptography is based on an algebraic structure over finite fields. Therefore, keys generated by ECC are more difficult to crack numerically. The existing RSA public key encryption standard is vulnerable to attack, so an ECC certificate is seen as a more secure alternative.
The use of ECC is the next natural step to ensure high quality, performance and security for the foreseeable future. This is because it is becoming increasingly popular as companies look to protect their customers' personal data online, as well as improve the usability of their website on mobile devices. As more and more businesses use ECC to protect sensitive data, there is a growing need for a brief introduction to the technology.
History of Elliptic Curve Cryptography
The history of ECC dates back to the 1980s. In 1985, two mathematicians named Neil Koblitz and Victor S. Miller independently proposed the idea of using elliptic curves in cryptography.
The idea of using these curves for cryptography was a game-changer. Prior to ECC, most encryption methods relied on factoring large numbers, which is a fancy way to break large numbers into smaller ones. But ECC was different: the properties of these curves were used to create a unique and more efficient encryption method.
The idea of using these curves for cryptography was a game-changer. Prior to ECC, most encryption methods relied on factoring large numbers, which is a fancy way to break large numbers into smaller ones. But ECC was different: the properties of these curves were used to create a unique and more efficient encryption method.
ECC Algorithm
ECC provides several different groups of algorithms depending on their use cases, defined on an elliptic curve over limb fields.
- Digital signatures: ECC provides algorithms for digital signatures, such as the elliptic curve digital signature algorithm ECDSA and EdDSA;
- Encryption: ECC provides message encryption algorithms, namely ECIES and EEECC;
- Key Convention: ECC provides algorithms such as ECDH and FHMQV for the key convention.
All of these algorithms use elliptic curves, such as secp256K1, Curve25519, and P251, to calculate keys and ciphers. In addition, they rely on the discrete elliptic curve logarithm task to ensure that these algorithms are difficult to crack and thereby ensure the security of the network.
Why use ECC?
ECC is based on the same "complex" problems as classical public key cryptography based on integers. This means that ECC algorithms will also be cracked when quantum computing makes Shor's algorithm usable.
However, ECC has several advantages over public key cryptography based on integers. The first of these is the length of the key. ECC requires much shorter key lengths to achieve the same level of security as RSA and the Diffie-Hellman protocol. Although symmetric cryptography requires even shorter keys (and is more quantum-resistant), it does not have the same functionality as asymmetric cryptography.
This shorter key length makes ECC more efficient than its integer counterparts. The ECC algorithm has lower memory and power requirements than other classic public key encryption methods, making it a better choice for resource-constrained devices such as smartphones and IoT devices.
Safe use of ECC
At the algorithm level, ECC is as secure as RSA, Diffie-Hellman, and similar algorithms because it is based on the same "complex" problems. Unless a non-quantum algorithm is found that effectively solves factorization or discrete logarithm problems, these algorithms are safe until sufficiently large quantum computers become available.
If ECC can be tricky, it's choosing a curve. There are many different elliptic curves, some of which are safer than others. When implementing ECC, it is important to choose a well-studied curve that has no known drawbacks.
Applications of Elliptic Curve Cryptography
Today, ECC is used in a wide range of applications, from securing online transactions to protecting sensitive data stored on mobile devices. Here are a few of the most common uses of ECC:
SSL/TLS
ECC is widely used in SSL/TLS protocols, which are used to secure online transactions. Many websites now support ECC-based SSL/TLS certificates, which provide a higher level of security than traditional RSA-based certificates.
Digital signatures
ECC is also used for digital signatures, which are used to verify the authenticity of digital documents. Digital signatures are widely used in industries such as banking, healthcare, and law, where it is important to have a secure and reliable way to verify the authenticity of documents.
Mobile devices
ECC is also widely used in mobile devices, where it is important to have an easy and effective encryption method. Many mobile devices now support ECC-based encryption, which provides a higher level of security while consuming less battery power and computing resources.
Internet of Things
In the IoT industry, it is crucial to have a simple and effective encryption method. ECC is well suited for IoT devices, which often have limited resources, processing power, and battery life.
Key Benefits of ESS
The following are some of the benefits of using ECC certificates:
Shorter key lengths
ECC provides a higher level of security with a shorter key size. The energy required to crack the RSA-generated key 3072 is equal to the same amount of energy required to crack the ECC-generated key 256. This shows that a key of length 256 generated using ECC is as cryptographically strong as a key length 3072 generated using RSA encryption.
Less processing power
Because key sizes are shorter, encrypting and decrypting data is cheaper.
Fast key generation
The key generation process is relatively simple and less computationally expensive because it involves safely generating a random integer within a given range. This makes it extremely fast compared to the RSA encryption algorithm.
Quick Signatures
ECC uses ECDSA, which generates a digital signature extremely quickly because it involves a simple step of multiplying a point on the curve.
Disadvantages of ESS
The disadvantages of ECC are as follows:
Complexity
ECC is quite difficult to implement, making it more prone to errors. This compromises the overall security of the system if it is not implemented properly.
Random Number Generator
The security of the system is compromised if a broken random number generator is used during private key selection.
Patents
This is one of the main factors limiting the widespread use of the ECC algorithm. Some of the main patents are held by Certicom and the National Security Agency (NSA).
Signature verification
Although the signature creation process is fast, the verification process takes some time due to time-consuming calculations.
Backdoor
Fears are growing that the NSA may have injected a backdoor into the ECC algorithms, allowing them to monitor encrypted messages being sent.
ECC is an adaptation of classical integer asymmetric cryptography. Because it is more efficient in terms of key length and power consumption, it is a useful alternative to integer algorithms.