The mathematics of elliptic curves has been studied since ancient times. These mathematical structures have found applications in varied fields. More recently, there has been a growing interest in applying these structures to cryptography. Various such applications have been proposed. Elliptic curve based cryptographic algorithms have been shown to provide greater security with shorter key sizes than the conventional RSA based cryptosystems, making them more memory e cient and less processor intensive. One of the fundamental requirements of all such elliptic curve cryptographic algorithms is that the order of the group of points satisfying the elliptic curve meet a certain set of requirements. However, finding the group order is not a trivial task. There are numerous special cases of elliptic curves where determining the group order is trivial. This thesis however, deals with the study of general point counting algorithms and their performances, which are applicable to all the curves. Possible improvements to the algorithms are provided where possible.
Library of Congress Subject Headings
Curves, Elliptic; Cryptography--Data processing
Department, Program, or Center
Computer Science (GCCIS)
Sundriyal, Suresh, "Counting points on elliptic curves over Zp" (2008). Thesis. Rochester Institute of Technology. Accessed from
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