[Cryptography] Exotic Operations in Primitive Construction

[Phillip Hallam-Baker]

On Tue, Sep 29, 2020 at 12:56 AM Sid Spry <sid at aeam.us> wrote:

> Hello,
>
> I noticed the other day that bit shifts and rotates are very popular in
> primitive construction. Why is this the case? Intuitively it seems to me
> like
> these operations are some of the most irregular that a computer has to
> offer.
> Bit shifting is related to division, but bit rotation does not seem closely
> related to any other easy to analyze operation. But I have no explanation
> for
> why it feels this way.
>

The reason we get rotate is that it is cheap: It is in essence a
combination of a Left shift and a right shift.

Besides division, they are used for multiplication. Pretty much every
modern FPU has a big barrel shifter in the middle of the data path.

One somewhat strange fact is that pretty much every CPU in use today
supports 80 bit floating point arithmetic but no commonly used programming
language I am aware of makes that accessible to the user except through
specialized libraries.

There is of course no reason that a strong cipher couldn't be created using
FPU operations. But implementation would be very hazardous and likely to
raise numerous incompatibilities between chips.
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