Elliptic Curve Cryptography Explained

Public key infrastructure (PKI) relies on two different cryptographic keys, a public key and a private key, to encrypt and decrypt data. These complex algorithms use mathematical formulas to generate digital certificates with unique digital identities to secure information.

Elliptic Curve Cryptography (ECC) is one method of generating these key pairs that has proven to be an effective way to secure data. The National Institute of Standards and Technology (NIST) has endorsed ECC as a recommended algorithm for secure key exchange with standards for digital signatures.

ECC keys have a shorter key length and require less power, which is significant for use in embedded systems, such as mobile or IoT devices, and for faster load times.

What Is Elliptic Curve Cryptography?

The name says it all. Elliptic Curve Cryptography (ECC) is a type of cryptography using public and private key encryption based on elliptic curve theory. This creates smaller, but more efficient encryption keys for security.

ECC cryptography is growing in popularity relative to the Rivest-Shamir-Adelman (RSA) public-key encryption methodology used to secure data in transit. While the RSA algorithm provides encryption of email or data using prime number factoring, ECC cryptography bases public keys on the looping lines on intersecting axis points on a graph.

The lines are symmetrical across the x-axis and non-vertical lines intersect the curve in three or fewer locations. Elliptic curve cryptography explained as a simplified formula would look like this:

Elliptic Curve Equation

Y² = x³ + ax + b

Pros and Cons of This Algorithm

ECC Pros

One of the reasons for the growing popularity of ECC cryptography is that the keys themselves are considerably smaller in size for the same effective encryption strength. For example, an ECC cryptography key of 256 bits would have the same level of security as an RSA key of 3072-bit size. There’s also not a direct line between the sizes and security. For example, an ECC key of 521 bits would require an RSA key length of 15360-bits to provide the same level of encryption.

ECC-based systems provide a higher security level in comparison to other methods and have been proven to withstand le

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