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Add missing dates

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arnaucube 1 year ago
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e8f76efae6
7 changed files with 5 additions and 5 deletions
  1. BIN
      notes_bls-sig.pdf
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    -3
      notes_bls-sig.tex
  3. BIN
      notes_halo.pdf
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    -1
      notes_halo.tex
  5. BIN
      notes_sonic.pdf
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    -1
      notes_sonic.tex
  7. BIN
      sigma-or-notes.pdf

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notes_bls-sig.pdf


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notes_bls-sig.tex

@ -25,7 +25,7 @@
\title{Notes on BLS Signatures} \title{Notes on BLS Signatures}
\author{arnaucube} \author{arnaucube}
\date{}
\date{July 2022}
\begin{document} \begin{document}
@ -70,13 +70,13 @@ Identical to verification of a normal signature as long as we use the same corre
$$e(g_1, \sigma_{aggr})==e(pk_{aggr}, H(m))$$ $$e(g_1, \sigma_{aggr})==e(pk_{aggr}, H(m))$$
Unfold: Unfold:
$$\fbox{e(pk_{aggr}, H(m))}= e(pk_1 + pk_2 + \ldots + pk_n, H(m)) =$$
$$e(pk_{aggr}, H(m))= e(pk_1 + pk_2 + \ldots + pk_n, H(m)) =$$
$$=e([sk_1] \cdot g_1 + [sk_2] \cdot g_1 + \ldots + [sk_n] \cdot g_1, H(m))=$$ $$=e([sk_1] \cdot g_1 + [sk_2] \cdot g_1 + \ldots + [sk_n] \cdot g_1, H(m))=$$
$$=e([sk_1 + sk_2 + \ldots + sk_n] \cdot g_1, H(m))=$$ $$=e([sk_1 + sk_2 + \ldots + sk_n] \cdot g_1, H(m))=$$
$$=[sk_1 + sk_2 + \ldots + sk_n]~\cdot~e(g_1, H(m))=$$ $$=[sk_1 + sk_2 + \ldots + sk_n]~\cdot~e(g_1, H(m))=$$
$$=e(g_1, [sk_1 + sk_2 + \ldots + sk_n] \cdot H(m))=$$ $$=e(g_1, [sk_1 + sk_2 + \ldots + sk_n] \cdot H(m))=$$
$$=e(g_1, [sk_1] \cdot H(m) + [sk_2] \cdot H(m) + \ldots + [sk_n] \cdot H(m))=$$ $$=e(g_1, [sk_1] \cdot H(m) + [sk_2] \cdot H(m) + \ldots + [sk_n] \cdot H(m))=$$
$$=e(g_1, \sigma_1 + \sigma_2 + \ldots + \sigma_n)= \fbox{e(g_1, \sigma_{aggr})}$$
$$=e(g_1, \sigma_1 + \sigma_2 + \ldots + \sigma_n)= e(g_1, \sigma_{aggr})$$
Note: in the current notes $pk \in G_1$ and $\sigma, H(m) \in G_2$, but we could use $\sigma, H(m) \in G_1$ and $pk \in G_2$. Note: in the current notes $pk \in G_1$ and $\sigma, H(m) \in G_2$, but we could use $\sigma, H(m) \in G_1$ and $pk \in G_2$.

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notes_halo.pdf


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notes_halo.tex

@ -25,7 +25,7 @@
\title{Notes on Halo} \title{Notes on Halo}
\author{arnaucube} \author{arnaucube}
\date{}
\date{July 2022}
\begin{document} \begin{document}

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notes_sonic.pdf


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notes_sonic.tex

@ -25,7 +25,7 @@
\title{Notes on Sonic} \title{Notes on Sonic}
\author{arnaucube} \author{arnaucube}
\date{}
\date{April 2022}
\begin{document} \begin{document}

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sigma-or-notes.pdf


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