# CISSP Elliptic Curve Cryptosystems

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Elliptic curves are excellent mathematical schemes that have demonstrated effectiveness in several various kinds of operations. An elliptic curve cryptosystem (ECC) gives you a lot of the same functions RSA offers: digital signatures, secure key distribution, and encryption. One major advantage is the efficiency of ECC. It is more effective compared to RSA and various other asymmetric algorithms.

On this particular subject of mathematics, a group is actually made up of structured patterns which are points on the curve. All these points are the values to process the ECC’s mathematical formulas used in encryption and decryption. The algorithm calculates different logarithms of elliptical shapes, which happens to be distinct from computing various logarithms in a set field (this is what El Gamal and Diffie-Hellman utilize).

Certain products have limited handling capability, storage space, source of power, and bandwidth, similar to wireless devices and smart phones. With such kinds of products, effectiveness of resource utilization is critical. ECC delivers encryption capability, demanding a minimal amount of the resources necessary for RSA as well as other algorithms, therefore it is used in these kinds of products.

In many instances, if the key is longer, the more security it provides, however ECC can give the same degree of protection with a shorter length of key compared to what RSA needs. Mainly because longer keys demand a lot more resources to carry out mathematical steps, the smaller keys utilized in ECC will need lesser resources from the device.

This algorithm is dependent on “Lucas sequences” and performs a discrete logarithm in a limited field, however through the use of the Lucas sequences; calculation usually takes place a lot quicker.

Zero Knowledge Proof

Whenever military personnel are briefing the news stations regarding certain significant world event, they actually have one objective into consideration: to share the information that the public ought to know and nothing more. You should not offer additional information that an individual can use to consider more details than they are required to know. The military bears this objective mainly because it recognizes that not just the good guys are paying attention to CNN. This is an illustration of zero knowledge proof. You inform an individual merely the information they should know without “giving up the property.”

Zero knowledge proof is commonly employed in cryptography as well. In the event that I encrypt a specific thing with my personal key, it is possible to confirm my personal key was utilized by decrypting the data with my shared key. By encrypting a specific thing with my personal key, I am demonstrating to you I possess my personal key-but I actually do not present or show you my personal key. I do not “give up the property” by revealing my personal key. In a zero knowledge proof, the verifier are unable to prove to yet another entity that this confirmation is authentic, since he does not possess the personal key to confirm it. Therefore, simply the owner of the personal key can prove he bears possession of the key.

Knapsack

Through the years, various variations of knapsack algorithms have developed. The very first to have been developed was Merkle-Hellman and this could be utilized exclusively for encryption, but it was afterwards enhanced to offer digital signature functionality. These particular algorithms are based upon the “knapsack problem,” a mathematical challenge that presents the following:

In case you have a number of different objects, each one possessing its own weight, will you be able to add these objects to a knapsack so that the knapsack bears a certain weight?

This algorithm was found to be unstable and is not at present applied in cryptosystems.

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