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Tiny spacing edits
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vEnhance committed Jul 9, 2024
1 parent c6281b8 commit fa7a2f8
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2 changes: 1 addition & 1 deletion easy/src/ec.typ
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Expand Up @@ -100,7 +100,7 @@ However, right now it only has the structure of a set.

The beauty of elliptic curves
is that it's possible to define an *addition* operation on the curve;
this is called the #cite(https://en.wikipedia.org/wiki/Elliptic_curve#The_group_law"", "group law on the elliptic curve").
this is called the #cite("https://en.wikipedia.org/wiki/Elliptic_curve#The_group_law", "group law on the elliptic curve").
This addition will make $E(FF_p)$ into an abelian group whose identity element
is the point at infinity $O$. This addition can be formalized as a _group law_, which is an equation that points on the curve must follow.

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2 changes: 2 additions & 0 deletions easy/src/kzg.typ
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Expand Up @@ -52,6 +52,8 @@ Then anyone in the world can use the resulting sequence for KZG commitments.
is if all the "trusted parties" collaborate.
]

#pagebreak() // TODO manual pagebreak for printed easy; stopgap hack

== The KZG commitment scheme

Peggy has a polynomial $P(X) in FF_p [X]$.
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3 changes: 2 additions & 1 deletion easy/src/plonk.typ
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Expand Up @@ -229,9 +229,10 @@ Now, what do the gate constraints amount to?
Peggy is trying to convince Victor that the equation
#eqn[
$ Q_L (x) A (x) + Q_R (x) B (x) + Q_O (x) C (x) & \
+ Q_M (x) A (x) B (x) + Q_C (x) & = 0 $
#hide[0] + Q_M (x) A (x) B (x) + Q_C (x) & = 0 $
<plonk-gate>
]
// stopgap: #hide[0] equivalent to latex phantom for plus sign spacing
is true for the $n$ numbers $x = omega, omega^2, ..., omega^n$.

However, Peggy has committed $A$, $B$, $C$ already,
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