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Primitive Divisors of Certain Elliptic Divisibility Sequences
Elliptic curve Elliptic divisibility sequence Primitive diviso Canonical height
2010/11/30
We establish conditions necessary for the n-th element of any elliptic divisibility sequence generated by points on Ea : y2 = x3+ax to not have a primitive divisor. As a consequence of this, along wit...
Elliptic divisibility sequences and the elliptic curve discrete logarithm problem
elliptic divisibility sequences elliptic curve cryptography elliptic curve discrete logarithm problem
2009/6/9
We use properties of the division polynomials of an elliptic
curve E over a finite field Fq together with a pure result about elliptic
divisibility sequences from the 1940s to construct a very simpl...
The elliptic curve discrete logarithm problem and equivalent hard problems for elliptic divisibility sequences
elliptic curve discrete logarithm problem equivalent hard problems elliptic divisibility sequences
2009/6/3
We define three hard problems in the theory of elliptic divisibility
sequences (EDS Association, EDS Residue and EDS Discrete
Log), each of which is solvable in sub-exponential time if and only if t...