What is RSA and how does it work?
RSA (Rivest-Shamir-Adleman) is an asymmetric encryption algorithm that uses prime number factorization to create a secure channel for data transfer. Since its creation in 1977, RSA has become a fundamental part of SSL/TLS protocols and, to this day, is supported by a large number of programming languages. Applications within various fields use RSA, including cryptocurrencies, email encryption, key exchange, and digital signatures.
The RSA encryption process involves multiplying two large prime numbers (p and q) to get a composite number (n), which is used to create public and private cryptographic keys. The security of RSA encryption is built on the idea that it’s virtually impossible to factor the compound number back to its prime numbers — it’s simply too large.
However, because RSA operates with excessively large numbers, it needs to generate a key that’s at least 3072 bits in length to match the 128-bit security standard.
Types of RSA keys
The RSA uses two types of cryptographic keys – public and private. Both keys are the results of advanced mathematical equations. If you’re into numbers, here’s a rough explanation of how each of the keys is calculated:
- The RSA public key comprises the composite number (n) and a public exponent (e). The public exponent is a number that has to satisfy two conditions. First, It must be a comprime to ϕ(n) when ϕ(n) is (p−1)(q−1). Second, the public exponent should be a small number, such as 65537.
- The RSA private key consists of the composite number (n) and a private component (d). The private component (d) is chosen so that it would leave a remainder of 1 when it is multiplied by the public exponent (e) and divided by ϕ(n).
Both public and private keys in the RSA algorithm include the composite number (n) — an element connecting the two. This element allows RSA to function as an asymmetric algorithm, making the keys interdependent but not interchangeable: whatever is encrypted with the public key can only be decrypted by the private key.
What is ECDSA and how does it work?
The elliptic curve digital signature algorithm (ECDSA) is a cryptographic algorithm that creates its cryptographic key pair by using the concepts of the older DSA algorithm and applying them to an elliptic curve cryptography (ECC). Developed in 1992, ECDSA is mainly used for digital signatures and cryptographic key exchange.
ECDSA works on a foundation of the discrete logarithm problem (DLP), which is computationally infeasible to solve. In essence, a point P is randomly chosen within the ECDSA’s elliptic curve (E). Then, another point – Q – is selected from within the same curve, resulting from P multiplied by k times. The difficulty of his mathematical problem is that P and Q are large numbers, and it’s extremely hard to find a scalar k that would satisfy the equation.
Even though ECDSA uses large keys, they are significantly smaller than in the case of RSA. For ECDSA to reach the 128-bit security standard, it’s enough to use 256-bit keys. In comparison, RSA needs at least 3072-bit keys to match the same standard. Regardless of the smaller keys in use, ECDSA provides the same level of security as RSA. The smaller key size also makes ECDSA a perfect algorithm for mobile applications because they require less bandwidth.
Types of ECDSA keys
The ECDSA is made out of two cryptographic keys — public and private. Each of the keys stands for a particular element from the DLP equation (Q=kP):
- The ECDSA private key stands for the randomly selected integer (k), which doesn’t change as long as the cryptographic key pair is used.
- The ECDSA public key represents point Q and is derived from the private key (k) when it’s used in the equation Q=kP. Here, P stands for the predefined point within the elliptic curve.
The key generation in ECDSA involves much more advanced mathematical calculations than the provided simplified version of the DLP equation (Q=kP). However, this simplification helps to illustrate that the public key in ECDSA is derived from the private key and how the two are connected.
Comparing RSA and ECDSA
Both the older RSA and the more recent ECDSA algorithms can provide a matching level of security that today’s hacking tools can barely break. However, they have their differences when it comes to specific features, including key size, speed, security, and complexity.
Key size
The RSA algorithm uses significantly larger cryptographic keys than ECDSA. To reach 128-bit security, RSA needs to use keys that are at least 3072 bits in length. Meanwhile, it’s sufficient for ECDSA to generate public keys twice the size of the desired 128-bit security to reach this standard.
Speed and efficiency
The larger cryptographic keys used in RSA make it a slower algorithm compared to ECDSA. Because both algorithms carry out complex mathematical calculations, their key lengths become the most significant factor in determining the algorithms' speed and performance. While using smaller keys, ECDSA also requires way less memory than the RSA.
Security
Both RSA and ECDSA can be configured to provide equal security levels. However, ECDSA requires significantly shorter private and public keys to achieve the same level of security that RSA can provide with long keys. Because of that, ECDSA keys demand smaller network loads and computing power compared to RSA.
Complexity
RSA is based on prime factorization, which takes a relatively simple mathematical approach to generating public and private keys. This makes RSA stand out among other asymmetric cryptography algorithms for its simplicity. It’s entirely another story with ECDSA, which uses DLP and elliptic curves to create its key pairs and is much more difficult to implement. This complexity may lead to security failures if the algorithm is not implemented correctly.
| RSA | ECDSA |
|---|---|
| Uses the prime factorization method to generate cryptographic keys | Uses elliptical curve representation to generate cryptographic keys |
| Simple implementation | Complicated implementation compared to RSA |
| Uses long cryptographic keys | Uses shorter cryptographic keys compared to RSA |
| Slower performance | Faster performance |
| Widely adopted in various fields | Adopted in particular fields |
Which one should you choose?
One of the essential things when deciding which one of the two – RSA or ECDSA – algorithms to choose is what you want to secure with their cryptography. Each of the algorithms works best in specific environments.
RSA use cases
When it comes to specific scenarios, RSA is mainly used in:
- Encrypting data and digital signatures. RSA can encrypt small amounts of data and secure symmetric encryption keys in bulk encryption.
- SSL/TLS certificates. Because RSA is integrated into many cryptographic libraries, it’s a popular choice for server certificates and is often used to secure websites.
- Key exchange. RSA can securely exchange cryptographic keys over an unsecured network.
- Software distribution. With the help of RSA signatures, you can check if the software downloads are genuine and authentic and if they haven’t been tampered with since the developer released them.
ECDSA use cases
Though a more recent cryptographic algorithm, ECDSA is prevalently used in:
- Digital signatures. In fact, digital signatures are currently the primary use case for ECDSA, given that its shorter key length makes the signing process fast and efficient.
- Cryptocurrencies and blockchain. ECDSA’s small key sizes make the algorithm a preferred choice for blockchain technology. It can handle digital signatures efficiently and quickly without requiring extensive storage space.
- Mobile applications. Because of their size, ECDSA keys don’t require much storage and offer faster processing. These features are especially valued in mobile applications because they provide good performance without sacrificing security.
- Internet of Things devices (IoT). IoT devices typically have lower computational capacity than a more demanding algorithm, such as RSA, would require. ECDSA is an optimal solution for securing connections and data exchange with IoT devices.
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