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judymcconville@roadrunner.com 2017-04-28 10:25:32 -07:00
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@ -115,7 +115,7 @@ Elliptic curve multiplication is a type of function that cryptographers call a "
[[elliptic_curve]] [[elliptic_curve]]
==== Elliptic Curve Cryptography Explained ==== Elliptic Curve Cryptography Explained
((("keys and addresses", "overview of", "elliptic curve cryptography")))((("elliptic curve cryptography")))Elliptic curve cryptography is a type of asymmetric or public-key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve. ((("keys and addresses", "overview of", "elliptic curve cryptography")))((("elliptic curve cryptography", id="eliptic04")))Elliptic curve cryptography is a type of asymmetric or public-key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve.
<<ecc-curve>> is an example of an elliptic curve, similar to that used by bitcoin. <<ecc-curve>> is an example of an elliptic curve, similar to that used by bitcoin.
@ -189,7 +189,7 @@ If P~1~ is the "point at infinity," then the sum P~1~ + P~2~ = P~2~. Similary, i
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. 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. 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.((("", startref="eliptic04")))
[[public_key_derivation]] [[public_key_derivation]]
==== Generating a Public Key ==== Generating a Public Key