The fundamental operation for generating a finite abelian group over an elliptic curve is the addition of two points on it. If point P on EC is added to itself (k-1) times then we obtain a new point kP on elliptic curve and kP is termed as the scalar multiplication of point P by scalar k. Source: http://www.ijcsi.org/papers/IJCSI-8-1-131-137.pdf
Scalar point multiplication is the major building block of all elliptic curve cryptosystems, an operation of the form where k is a positive integer and P is a point on the elliptic curve. Calculating gives the result of adding the point P to itself for exact k-1 times, which results in another point Q on the elliptic curve. AND ALSO Scalar point multiplication is one of the major buildings of ECC block. An operation of form where is a positive integer, P is a point on the curve. The idea is adding the point P to itself k - 1 times to get the resulted point Q. Source: http://www.ijser.org/paper/Make-a-Secure-Connection-Using-Elliptic-Curve-Digital-Signature.html
Cryptographic schemes based on ECC rely on scalar multiplication of elliptic curve points. As before given an integer k and a point P... scalar multiplication is the process of adding P to itself k times. Source: http://www.secg.org/collateral/sec1.pdf
Let k be a positive integer and P a point on an elliptic curve. Then elliptic curve scalar multiplication is the operation that computes the multiple Q = kP, defined as the point resulting of adding P to itself k times. Source: http://cacr.uwaterloo.ca/techreports/2011/cacr2011-07.pdf
So which definition of scalar multiplication on elliptic curves is right and why?
Jonathan Crabtree Mathematics Researcher Melbourne Australia (Currently over at http://bit.ly/Vrrx9Q)
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Message was edited by: Jonathan Crabtree to include a P.S.