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Add pairings initial notes

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arnaucube
2022-08-26 10:24:32 +02:00
parent 6b8b9e764b
commit 11e7cc5613
10 changed files with 158 additions and 21 deletions
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notes_bls-sig.tex
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@@ -73,7 +73,7 @@ Unfold:
$$\fbox{e(pk_{aggr}, H(m))}= e(pk_1 + pk_2 + \ldots + pk_n, H(m)) =$$
$$=e([sk_1] \cdot g_1 + [sk_2] \cdot g_1 + \ldots + [sk_n] \cdot g_1, H(m))=$$
$$=e([sk_1 + sk_2 + \ldots + sk_n] \cdot g_1, H(m))=$$
$$=e(g_1, H(m))^{(sk_1 + sk_2 + \ldots + sk_n)}=$$
$$=[sk_1 + sk_2 + \ldots + sk_n]~\cdot~e(g_1, H(m))=$$
$$=e(g_1, [sk_1 + sk_2 + \ldots + sk_n] \cdot H(m))=$$
$$=e(g_1, [sk_1] \cdot H(m) + [sk_2] \cdot H(m) + \ldots + [sk_n] \cdot H(m))=$$
$$=e(g_1, \sigma_1 + \sigma_2 + \ldots + \sigma_n)= \fbox{e(g_1, \sigma_{aggr})}$$