Efficient Modular Division Implementation: ECC over GF(p) Affine Coordinates Application

Elliptic Curve Public Key Cryptosystems (ECPKC) are becoming increasingly popular for use in mobile appliances where bandwidth and chip area are strongly constrained. For the same level of security, ECPKC use much smaller key length than the commonly used RSA. The underlying operation of affine coordinates elliptic curve point multiplication requires modular multiplication, division/inversion and addition/substraction. To avoid the critical division/inversion operation, other coordinate systems may be chosen, but this implies more operations and a strong increase in memory requirements. So, in area and memory constrained devices, affine coordinates should be preferred, especially over GF(p).

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