arnaucube
arnaucube/mathPublic Self-hosted repository
Add missing dates
arnaucube root@arnaucube.com
Sat, 21 Jan 2023 16:02:30 +0100
commit

e8f76efae6d7de57b1eb5cfe4d300cb04f36b28e

parent

ff2c5fa9b3dbdd1caa1a4f0528cb9f6b5c929d5e

M notes_bls-sig.tex → 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 corresponding aggregated public key:

$$e(g_1, \sigma_{aggr})==e(pk_{aggr}, H(m))$$ 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 $pk \in G_2$.
M notes_halo.tex → notes_halo.tex

@@ -25,7 +25,7 @@

\title{Notes on Halo} \author{arnaucube} -\date{} +\date{July 2022} \begin{document}
M notes_sonic.tex → notes_sonic.tex

@@ -25,7 +25,7 @@

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