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Merge pull request #1 from tlsnotary/ghash-mac-remark

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Added remark to GHASH MAC section
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Dan
2022-10-17 17:46:20 +00:00
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src/protocol/2pc/mac.md
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@@ -119,6 +119,10 @@ Suppose that the ciphertext consists of 9 blocks \\( \small{ X_1, ..., X_9 } \\)
Naively, the parties could use `Mul_2PC` to compute their shares of \\( \small{ H^5, H^7, H^9 } \\) using 3 invocations of `Mul_2PC`. We now show how this can be done with 2 invocations of `Mul_2PC`.
<span style="color:red">In the following \\( \small{H^n_x} \\) always refers to a sharing of \\( \small{H^n} \\) for party \\( \small{x} \\), and not
a sharing of \\( \small{H} \\) raised to the \\( \small{n} \\)th power, i.e. we deal with sharings of powers of \\( \small{H} \\) and not powers of
sharings of \\( \small{H} \\).</span>
Recalling that:
\\( \small{ H^5•X_5 = (H^4_n + H^4_u)(H_n + H_u)X_5 = H^4_nH_nX_5 + \color{blue}{H^4_nH_uX_5} + \color{blue}{H^4_uH_nX_5} + H^4_uH_uX_5 } \\)