TY - JOUR
T1 - Distribution of elliptic twin primes in isogeny and isomorphism classes
AU - Shparlinski, Igor E.
AU - Sutantyo, Daniel
PY - 2014/4
Y1 - 2014/4
N2 - Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which groups of points on an elliptic curve over a finite field and its quadratic twist are both of prime order. We obtain a heuristic asymptotic formula for the number of isogeny and isomorphism classes of such curves and present some supporting computational results.
AB - Motivated by a recent application to hash functions suggested by O. Chevassut, P.-A. Fouque, P. Gaudry and D. Pointcheval, we study the frequency with which groups of points on an elliptic curve over a finite field and its quadratic twist are both of prime order. We obtain a heuristic asymptotic formula for the number of isogeny and isomorphism classes of such curves and present some supporting computational results.
UR - http://www.scopus.com/inward/record.url?scp=84890809887&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2013.10.018
DO - 10.1016/j.jnt.2013.10.018
M3 - Article
AN - SCOPUS:84890809887
VL - 137
SP - 1
EP - 15
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -