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I've been reading the following document describing Galois Counter Mode: The Galois/Counter Mode of Operation

On page 7 of the document, the following diagram describes the GHASH function used to authenticate data. GHASH is defined as GHASH(H, A, C) where H is a 128-bit unsigned integer and A and C are two bit strings representing the authenticated data $A$ and ciphertext $C$. $m$ and $n$ are used to represent the number of 128 bit blocks of data in $A$ and $C$ respectively.

GCM GHASH

Equation 4 and 5 look incorrect to me. Is $C_i$ correct on line 4? Won't $i$ already be larger than $m$ and thus this won't include the correct blocks of $C$? Shouldn't this be $C_{i-m}$?

And the fifth equation, is this meant to be $C^{*}_{n}$ and not $C^{*}_{m}$?

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Examining the document, it seems that you are correct on both equations. Thus

$$ C_i ~~\textrm{should be}~~C_{i-m}, $$

and

$$ C_m^* ~~\textrm{should be }C_n^*. $$

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