- 期刊
Montgomery Algorithm Based on Co_Z Operation on Edwards Curves over Prime Field
摘要
Based on the formula of point addition and point doubling on the Edwards elliptic curve on the prime field, combined with the method of calculating only y coordinate, the formula in the affine coordinate system was deduced, and Montgomery Ladder Algorithm Using Only-y-Coordinate has been given in combination with Lopez- Dahab's ideas. To reduce the inversion operation, we proposed transforming affine coordinate into standard projective coordinates and designing a Co_Z Montgomery Algorithm 5 to improve the Edwards elliptic curve. At the same time, a new algorithm, four based on the Markov chain, is proposed. Theoretical analysis shows that Co_Z Algorithm 5 is 21.4% faster than Yu W Weierstrass-form Elliptic Curves Montgomery algorithm. Algorithm 4 is 35.9% faster than Yu W Algorithm 3. The efficiency of the two algorithms is improved remarkably. The theoretical analysis is supported by elliptic curve experiments in the different binary prime fields.