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This paper gives a comprehensive method to do Elliptic Curve Scalar Multiplication with only x-coordinate. Explicit point operation formulae for all types of defining equations of the curves are derived. For each type of curve, the performance is analyzed. The formulae are applied in Montgomery Ladder to get scalar mul- tiplication algorithm operated with only x-coordinate. The new sca- lar multiplication has the same security level and computation amount with protected binary scalar multiplication (PBSM) against side channel attack, and has the advantages of higher security and little memory needed.
This paper gives a comprehensive method to do Elliptic Curve Scalar Multiplication with only x-coordinate. Explicit point operation formulae for all types of defining equations of the curves are derived. For each type of curve, the performance is analyzed. The formulae are applied in Montgomery Ladder to get scalar mul- tiplication algorithm operated with only x-coordinate. The new sca- lar multiplication has the same security level and computation amount with protected binary scalar multiplication (PBSM) against side channel attack, and has the advantages of higher security and little memory needed.