ZHANG Li-jun, WANG Kun-peng. Group Law of Elliptic Curves over Zn and Its Application in Paillier Schemes[J]. Acta Electronica Sinica, 2011, 39(8): 1733-1738.
ZHANG Li-jun, WANG Kun-peng. Group Law of Elliptic Curves over Zn and Its Application in Paillier Schemes[J]. Acta Electronica Sinica, 2011, 39(8): 1733-1738.DOI：
and application of this group law are studied in this paper.We present explicit addition formulae to make
E
(
Z
n
) an abelian group.This solves the problem that some points addition can not be defined using other addition laws in the literature.For the convenient cryptographic application of such elliptic curves
we give the group structure of
E
(
Z
n
) under our addition law.We propose a remedy for the original elliptic curves Paillier schemes which have security defectiveness.
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