diff --git a/notes_bls-sig.pdf b/notes_bls-sig.pdf index 524afbb..772c788 100644 Binary files a/notes_bls-sig.pdf and b/notes_bls-sig.pdf differ diff --git a/notes_bls-sig.tex b/notes_bls-sig.tex index 257c558..41c3420 100644 --- a/notes_bls-sig.tex +++ b/notes_bls-sig.tex @@ -25,7 +25,7 @@ \title{Notes on BLS Signatures} \author{arnaucube} -\date{} +\date{July 2022} \begin{document} @@ -70,13 +70,13 @@ Identical to verification of a normal signature as long as we use the same corre $$e(g_1, \sigma_{aggr})==e(pk_{aggr}, H(m))$$ Unfold: -$$\fbox{e(pk_{aggr}, H(m))}= e(pk_1 + pk_2 + \ldots + pk_n, H(m)) =$$ +$$e(pk_{aggr}, H(m))= e(pk_1 + pk_2 + \ldots + pk_n, H(m)) =$$ $$=e([sk_1] \cdot g_1 + [sk_2] \cdot g_1 + \ldots + [sk_n] \cdot g_1, H(m))=$$ $$=e([sk_1 + sk_2 + \ldots + sk_n] \cdot g_1, H(m))=$$ $$=[sk_1 + sk_2 + \ldots + sk_n]~\cdot~e(g_1, H(m))=$$ $$=e(g_1, [sk_1 + sk_2 + \ldots + sk_n] \cdot H(m))=$$ $$=e(g_1, [sk_1] \cdot H(m) + [sk_2] \cdot H(m) + \ldots + [sk_n] \cdot H(m))=$$ -$$=e(g_1, \sigma_1 + \sigma_2 + \ldots + \sigma_n)= \fbox{e(g_1, \sigma_{aggr})}$$ +$$=e(g_1, \sigma_1 + \sigma_2 + \ldots + \sigma_n)= e(g_1, \sigma_{aggr})$$ 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 $pk \in G_2$. diff --git a/notes_halo.pdf b/notes_halo.pdf index a30b457..93b5e27 100644 Binary files a/notes_halo.pdf and b/notes_halo.pdf differ diff --git a/notes_halo.tex b/notes_halo.tex index 698efa8..3d5a47f 100644 --- a/notes_halo.tex +++ b/notes_halo.tex @@ -25,7 +25,7 @@ \title{Notes on Halo} \author{arnaucube} -\date{} +\date{July 2022} \begin{document} diff --git a/notes_sonic.pdf b/notes_sonic.pdf index 194a304..1a678d4 100644 Binary files a/notes_sonic.pdf and b/notes_sonic.pdf differ diff --git a/notes_sonic.tex b/notes_sonic.tex index 03c0cf8..c48257a 100644 --- a/notes_sonic.tex +++ b/notes_sonic.tex @@ -25,7 +25,7 @@ \title{Notes on Sonic} \author{arnaucube} -\date{} +\date{April 2022} \begin{document} diff --git a/sigma-or-notes.pdf b/sigma-or-notes.pdf index 6481642..c96968e 100644 Binary files a/sigma-or-notes.pdf and b/sigma-or-notes.pdf differ