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Fix accidental sub/super scripting
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martinthomson committed Jul 9, 2024
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10 changes: 5 additions & 5 deletions draft-thomson-ppm-prss.md
Original file line number Diff line number Diff line change
Expand Up @@ -280,12 +280,12 @@ identifier will produce the same randomness.

A randomness context is produced by invoking the `Expand()` function of the
chosen KDF, passing the shared entropy generated in {{extract}} as the `prk`
input, the byte sequence that identifies the context (`ctx_id`) as the `info`
input, the byte sequence that identifies the context (`ctx\_id`) as the `info`
input, and the PRF parameter `Nk` as the `L` input (see {{prf}}), as follows:

~~~ pseudocode
def context = Context.new(kdf, prf, extracted, ctx_id):
context = kdf.Expand(prk = extracted, info = ctx_id, L = prf.Nk)
def context = Context.new(kdf, prf, extracted, ctx\_id):
context = kdf.Expand(prk = extracted, info = ctx\_id, L = prf.Nk)
~~~

The expanded entropy produced by this process is the only information that is
Expand Down Expand Up @@ -560,7 +560,7 @@ p <= 2^{b-(k+a)/2-2}

We use this first component to bound the value of `q` for the second component.
If advantage is equally divided between each component we can bound `q` to be at
most `2^((k-a)/2)`, where `a` is the desired attacker advantage in bits (that
most `2\^((k-a)/2)`, where `a` is the desired attacker advantage in bits (that
is, advantage is at most 2<sup>-a</sup>).

Using that value for `q` and an advantage of `(2^a)/2` for the second component
Expand All @@ -574,7 +574,7 @@ AES-256 having the same 128-bit block size as AES-128. Consequently, increasing
`q` only reduces the value of `p`.

On this basis, the same `q` value can be used for AES-256 as for AES-128. The
usage limit for AES-256 can be doubled to `2^(b-(k+a)/2-1)` (2<sup>43</sup> for
usage limit for AES-256 can be doubled to `2\^(b-(k+a)/2-1)` (2<sup>43</sup> for
40 bits of security; the first component is a negligible 2<sup>-169</sup>).

This analysis models AES as an ideal pseudorandom permutation.
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