Document Type

Student Presentation

Publication Date



Cryptography is a constantly evolving field – elliptic curve groups have been a major part of this field since 1987 when Koblitz and Miller separately proposed their use in cryptosystems such as RSA.

  • Elliptic Curve: A curve defined by the equation: where A and B are less than a prime p, and where the discriminant is not equal to zero. We are concerned with the curves where A = 0.
  • Elliptic Curve Group (ECG): A group whose elements are defined by the elliptic curve and the operation in question. Elliptic curves naturally qualify as groups due simply to their nature.
  • Elliptic Pair of Primes: Two primes (p,q) such that an ECG defined by the following equation has an order q, and the ECG defined by a different equation mod q has the order p. These pairs are the main topic of our study, and learning more about them and their effects on RSA security is our primary goal.
  • Discrete Log Problem (DLP): Solving for x in the equation:

NOTE: Operations such as addition and multiplication are defined differently when used in terms of an ECG operation. An example can be found below.

Faculty Sponsor

Dr. Liljana Babinkostova

Included in

Mathematics Commons