This question is similar to Can XEX or XTS modes be used with only one tweak? except I am interested to know if one can instead use

$X = E_{k}(0) \otimes \alpha^j \\ C = E_{k}(P \oplus X) \oplus X$

in order to simply do a finite field multiplication and an aes operation per block rather than two aes operations per block (unlike the original question) for large amount of data.

  • $\begingroup$ Note that the standard computation strategy for these modes is to compute the $E_k(I)$ once per sector and then compute $\alpha^j$ per-block which is a single multiplication of $\alpha^{j-1}\otimes \alpha$ with the left side being from the previous block. $\endgroup$
    – SEJPM
    Oct 21, 2020 at 21:26
  • $\begingroup$ @SEJPM in this instance you would compute $E_k(I)$ once per filesystem. Assuming 512-byte sectors, in order to access the 4th block of the 3rd sector you would have a j of 100 and an I of 0. $\endgroup$ Oct 21, 2020 at 23:01


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