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Addressing 152282

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Andreas M. Antonopoulos 2015-02-23 20:08:58 -05:00
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@ -170,7 +170,7 @@ In some cases (i.e., if P~1~ and P~2~ have the same x values but different y val
If P~1~ is the "point at infinity," then the sum P~1~ + P~2~ = P~2~. Similary, if P~2~ is the point at infinity, then P~1~ + P~2~ = P~1~. This shows how the point at infinity plays the role of 0. If P~1~ is the "point at infinity," then the sum P~1~ + P~2~ = P~2~. Similary, if P~2~ is the point at infinity, then P~1~ + P~2~ = P~1~. This shows how the point at infinity plays the role of 0.
It turns out that pass:[+] is associative, which means that (A+B)+C = A+(B+C). That means we can write A+B+C without parentheses without any ambiguity. It turns out that pass:[+] is associative, which means that (A pass:[+] B) pass:[+] C = A pass:[+] (B pass:[+] C). That means we can write A pass:[+] B pass:[+] C without parentheses without any ambiguity.
Now that we have defined addition, we can define multiplication in the standard way that extends addition. For a point P on the elliptic curve, if k is a whole number, then kP = P + P + P + ... + P (k times). Note that k is sometimes confusingly called an "exponent" in this case.(((range="endofrange", startref="ix_ch04-asciidoc5")))(((range="endofrange", startref="ix_ch04-asciidoc4"))) Now that we have defined addition, we can define multiplication in the standard way that extends addition. For a point P on the elliptic curve, if k is a whole number, then kP = P + P + P + ... + P (k times). Note that k is sometimes confusingly called an "exponent" in this case.(((range="endofrange", startref="ix_ch04-asciidoc5")))(((range="endofrange", startref="ix_ch04-asciidoc4")))