Skip to content

Commit

Permalink
Groth edits
Browse files Browse the repository at this point in the history
  • Loading branch information
tideofwords committed May 28, 2024
1 parent e062705 commit fba899b
Showing 1 changed file with 14 additions and 4 deletions.
18 changes: 14 additions & 4 deletions src/groth16.typ
Original file line number Diff line number Diff line change
Expand Up @@ -120,7 +120,7 @@ so let's get back to a simple toy example.
which Peggy knows how to multiply by $gamma$,
and $h$ must be the same linear combination
of $[gamma], Com(gamma U_1), dots, Com(gamma U_n)$.
]
] <groth-motiv-1>

#example[
Here's a more complicated challenge,
Expand All @@ -141,12 +141,22 @@ so let's get back to a simple toy example.

To do this, Trent does the same trusted setup thing.
Trent chooses two constants $alpha$ and $beta$
and publishes
and publishes $[alpha]$, $[beta]$, and
$ alpha Com(U_i) + beta Com(V_i), $
for $1 lt.eq i lt.eq n$.



In addition to $g_1$ and $g_2$,
Peggy now also publishes
$ h = sum_(i=1)^n a_i (alpha Com(U_i) + beta Com(V_i) ). $
Victor needs to verify that
$ h = alpha g_1 + beta g_2; $
if this equality holds, then $g_1$ and $g_2$ must
have the correct form,
just like in @groth-motiv-1.

So Victor checks the equality of pairings
$ pair(h, [1]) = pair(g_1, [alpha]) + pair(g_2, [beta]), $
and the proof is complete.
]

#todo[Deal with trusted setup]
Expand Down

0 comments on commit fba899b

Please sign in to comment.