Elliptic curve Paillier schemes (Q1601824)

This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schemes are not secure. A more natural generalisation of Paillier's scheme to elliptic curves is given.