Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves
نویسنده
چکیده
Ezra (Bud) Brown ([email protected]) has degrees from Rice and Louisiana State, and has been at Virginia Tech since the first Nixon Administration. His research interests include graph theory, the combinatorics of finite sets, and number theory—especially elliptic curves. In 1999, he received the MAA MD-DC-VA Section Award for Outstanding Teaching, and he loves to talk about mathematics and its history to anyone, especially students.
منابع مشابه
Semi-magic Squares and Elliptic Curves
We show that, for all odd natural numbers N , the N-torsion points on an elliptic curve may be placed in an N × N grid such that the sum of each column and each row is the point at infinity.
متن کاملEfficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کاملCubic Curves, Finite Geometry and Cryptography
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9, 3, 1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a ‘shared secret’ related to the group law. ...
متن کاملOn the elliptic curves of the form $ y^2=x^3-3px $
By the Mordell-Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. There is no known algorithm for finding the rank of this group. This paper computes the rank of the family $ E_p:y^2=x^3-3px $ of elliptic curves, where p is a prime.
متن کاملOn the Elliptic Curves of the Form $y^2 = x^3 − pqx$
By the Mordell- Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves, where p and q are distinct primes. We give infinite families of elliptic curves of the form y2=x3-pqx with rank two, three and four, assuming a conjecture of Schinzel ...
متن کامل