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elliptical_curves [2021/07/26 17:53] (current)
spencer created
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 +====== Elliptical Curves ======
  
 +===== INTRO =====
 +
 +
 +An elliptical curve is a cubic curve equation whose solutions create a shape known as a torus (or a doughnut-
 +shaped three-dimensional figure with a hole in the center and a smooth surface which could be spread out as a
 +rectangle in two dimensions). While elliptical curves are generally thought of in terms of this mathematical
 +construct, the use of elliptical curve equations in public key cryptography generates one of the strongest forms of
 +encryption.
 +===== A MORE MATHEMATICAL EXPLANATION =====
 +
 +In maths, an elliptical curve can be considered a set of elements that are part of an abelian group (or numbers
 +which have a binary operation ‘ · ’, which can be connected to an ordered pair). This goes hand in hand with five
 +axiomatic properties which will be constant: closure, associative, identity element, inverse element, and
 +commutative. These things together are used in concert in order to create the public key exchange. Elliptical
 +curves can be used in conjunction with other public key cryptography algorithms, such as a Diffe-Hellman
 +exchange. In this scenario, the key itself would be created by an exponentiation over the group (or the process of
 +creating an exponent), where the exponentiation itself is a multiplication operation.
 +===== QUANTUM CONCERNS =====
 +
 +This particular set of algorithms is supported by NIST in Suite B, which is was originally used for both
 +unclassified and classified information. However as of 2015, due to the concerns about quantum computing,
 +the NSA has announced it’s intent to replace elliptical curve cryptography in use.
 +===== IN USE =====
 +
 +One well-known example of this algorithm in action is the dual elliptic curve known as PRNG (DEC PRNG),
 +which is recommended in the ANSI standard X9.82, ISO standard 18031, NIST standard SP 800-90.
elliptical_curves.txt · Last modified: 2021/07/26 17:53 by spencer