Cooper_Assignment #3

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Cooper: Assignment 3 Zachary Cooper Cryptography Concepts: ISSC266 Doctor Leonard Simon April 23, 2023

2 Assignment 3 Larger key size often brings a need for my computing power and slower encryption capabilities. When using a mobile application, it can often be difficult to quickly encrypt and decrypt data while remaining secure. Quicker speeds often negate the security when discussing encryption. Elliptic Curve Cryptography is the solution for this issue. Elliptic Curve Cryptography uses a smaller key size to provide the equivalent level of security as RSA (Froehlich, 2022). Elliptic Curve Cryptography is like RSA. Both forms of cryptography use a public-key and a private-key. One key is used to encrypt the data while the other is used decrypt that data. Elliptic Curve Cryptography utilizes a trapdoor function that allows getting from one point to another easy but going back almost impossible. For example, the trapdoor function makes going from point A to point B easy. Going from point B to point A, however, is what is difficult (DevCentral, 2015). These forms of cryptography rely on a math equations and Elliptic Curve Cryptography bases its equation on a mirrored across the x-axis elliptical curve. The graphic from Techtarget shows an example of an elliptical curve and two lines going through it. The top line is the original and uses a method known as a “dot notation.” For example, A ‘dot’ B will yield C. Next, C will move down the y-axis to the mirrored elliptical to get point D. Point D will connect to the original point, A. This connection will yield E and the process can repeat where a mirrored point across from E will connect to A and continue. This process done a

3 Assignment 3 specific number of times, which will be what the private-key is based off (DevCentral, 2015). The formula for the elliptical curve is y²=x³ + ax + b. The key size relates to the maximum defined value of the equations (Froehlich, 2022). Due to the difficulty in doing the process backward, a lower key size provides plenty of security. Without the private-key, breaking the code is near impossible and there is one reported instance of Elliptic Curve Cryptography being broken in 2009. In the example case, 200 PlayStation 3 game consoles were clustered and managed to break into an Elliptic Curve Cryptography of 112-bits. This took over three months to complete (Bos, 2009). Elliptic Curve Cryptography level of security is why the United States Government has stated this method is used for Top Secret information (DevCentral, 2015).

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4 Assignment 3 References Bos, J. (2009). PlayStation 3 computing breaks 260 barrier. https://web.archive.org/web/20090715060838/http://lacal.epfl.ch/page81774.html DevCentral. (2015). YouTube. Elliptic Curve Cryptography Overview. https://www.youtube.com/watch?v=dCvB-mhkT0w Froehlich, A. (2022). elliptical curve cryptography (ECC). https://www.techtarget.com/searchsecurity/definition/elliptical-curve-cryptography

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