Update for 31-01-22 15:00
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math/Eliptic_Curve.wiki
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9
math/Eliptic_Curve.wiki
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= eliptic Curve =
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An eliptic curve is a curve of form:
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```
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y^2 = x^3 + ax + b
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```
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They often curve around the origin
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@ -10,7 +10,4 @@ alpha^3 mod q = x,,3,,
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alpha^q-1 mod 1 = x,,(q-1),,
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```
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Where x,,n,, is
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```
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1, 2, 3, 4, etc
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```
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Where x,,n,, is *the set of values from 1 through q-1*
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@ -9,5 +9,28 @@ created between two parties via an unsecure channel.
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== algorithm ==
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1) For some prime `q`
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2) Select some `alpha` such that `alpha < q` and `alpha` is a [[../math/primative_root]] of
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`q`
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2) Select some `alpha` such that `alpha < q` and `alpha` is a
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[[../math/primative_root|Primative root]] of `q`
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* known as global elements
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3) X,,a,, and X,,b,, are the private keys of alice and bob respectively
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* known as private elements/keys
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4) Y,,a,, is `alpha^x,,a,, mod q`
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* Same for Y,,b,,
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* Known as public elements/keys
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5) Both parties then calculate the shared secret via
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`K,,a,, = Y,,b,,^X,,a,, mod q`
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* same for K,,b,,
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* K,,a,, should be same as K,,b,,
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== example ==
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```
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q = 7
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alpha = 5
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X,,a,, = 3
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Y,,a,, = 5^3 mod 7 = 6
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X,,b,, = 4
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Y,,b,, = 5^4 mod 7 = 2
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```
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@ -1 +1,11 @@
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= Eliptic Curve Cryptography =
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ECC is an algorithm that solves the same problem as [[RSA]], but with smaller
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key sizes. It is asymetric and based on [[../math/Eliptic_Curve]]s and based on
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the difficulty of inding a curve given points on said curve.
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== algorithm ==
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@ -49,3 +49,7 @@ For example Encrypt B
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Decrypt value
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`4^11 mod 14 = 2` or our original `B`
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== Also see ==
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* [[Eliptic_Curve]]
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