{"id":16434,"date":"2023-12-21T20:41:37","date_gmt":"2023-12-21T20:41:37","guid":{"rendered":"https:\/\/businessyield.com\/tech\/?p=16434"},"modified":"2024-01-04T20:42:33","modified_gmt":"2024-01-04T20:42:33","slug":"elliptic-curve-cryptography","status":"publish","type":"post","link":"https:\/\/businessyield.com\/tech\/technology\/elliptic-curve-cryptography\/","title":{"rendered":"Elliptic Curve Cryptography: What Is It & How Does It Work?","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"\n
Elliptic curve cryptography (ECC) is a cryptographic algorithm that utilizes public key encryption to carry out essential security operations such as encryption, authentication, and digital signatures. The basis of ECC is in the theory of elliptic curves, which utilizes the peculiarities of the elliptic curve equation to produce keys. Read more to find out how elliptic curve cryptography works and more about cryptography algorithms and certificates.<\/p>\n\n\n\n
Elliptic Curve Cryptography (ECC) is a cryptographic method that uses keys to encrypt data. ECC primarily concerns the utilization of public and private key pairs to facilitate the encryption and decryption of internet data. The Rivest-Shamir-Adleman (RSA) cryptographic algorithm is often associated with discussions about ECC. RSA employs prime factorization to achieve unidirectional encryption of various entities, such as emails, data, and software. <\/p>\n\n\n\n
An equation in the form of y2 = x3 + ax + b may describe an elliptic curve, which is a two-dimensional curve. A and b are fixed values, while x and y are symbols that can take on different values. Elliptic curves possess numerous intriguing mathematical characteristics that render them highly suitable for cryptographic purposes. The property being referred to is known as “point addition” and is visually depicted in the following illustration. <\/p>\n\n\n\n
Another benefit of encryption is “point-doubling.” We can find 2P on an elliptic curve by adding P to itself: P + P = 2P. <\/p>\n\n\n\n
We can duplicate points indefinitely until we reach “the infinity point,” O. This occurs when the distance between points P and 2P approaches 0 without limits.<\/p>\n\n\n\n
Thus, except at infinity (O), we can add and double on an elliptic curve endlessly without getting the same result.<\/p>\n\n\n\n
Adding and doubling each point P on an elliptic curve, including infinity (O), generates an infinite number of points. Thus, elliptic curves can create limitless keys.<\/p>\n\n\n\n
Having explored elliptic curves and their functionality, let us now examine their application in cryptography. Elliptic curve cryptography commonly depends on the Elliptic Curve Discrete Logarithm Problem (ECDLP), which asserts that finding x is difficult given y = g^x mod p, where g is a known integer and p is a prime number. <\/p>\n\n\n\n
This problem is complicated because there is no solution to efficiently calculate x from y without trial and error.<\/p>\n\n\n\n
Solving for y in the equation x = g^y mod p is as challenging as resolving the DDL problem. Without knowing the confidential exponent y, it would be difficult to calculate y from x without excessive trial and error.<\/p>\n\n\n\n
Thus, by choosing g and p carefully, it becomes difficult for someone without the secret exponent x to compute x from y (or vice versa).<\/p>\n\n\n\n
Elliptic curve cryptographic algorithms can be used for things like digital signatures and key agreement protocols, as long as it is hard enough to figure out the secret exponent x from y (or the other way around).<\/p>\n\n\n\n
Public-key cryptography operates by employing methods that are computationally efficient in one direction and computationally challenging in the opposite direction. \u00a0RSA cryptography uses the fact that multiplying prime numbers yields a larger number, while factoring huge numbers back into primes is computationally difficult.<\/p>\n\n\n\n
Nevertheless, to maintain a high level of security, RSA requires keys that are at least 2048 bits in length. \u00a0This results in a sluggish process and underscores the significance of key sizes.\u00a0<\/p>\n\n\n\n
The size of elliptic curve encryption is a significant benefit, resulting in increased computational capabilities for smaller, portable devices. Factoring is a simpler and less energy-intensive process compared to solving for an elliptic curve with discrete logarithms. Therefore, when considering two keys of equal size, RSA’s encryption that relies on factoring is more susceptible to vulnerabilities. <\/p>\n\n\n\n