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Can a modulo function be linearized or alternatively expressed?

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David Jonsson

In order to try to simplify or alternatively express cryptographic functions I wonder if the modulo function can be alternatively expressed. Could for example a Fourier series of a sawtooth wave or its discretization be useful? What would that look like for a given range and precision?

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fgrieu avatar
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fgrieu
When the modulus is a power of two, $x\bmod n$ reduces to $x\&(n-1)$, where $\&$ is [bitwise AND](https://en.wikipedia.org/wiki/Bitwise_operation#AND). That generalizes to $n$ of the form $b^k$, by expressing $x$ in base $b$ and keeping the $k$ low-order digits. That applies to any $n$ by expressing $x$ in base $n$, but is not much useful.
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kodlu avatar
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kodlu
do you mean the function $x \mapsto x \pmod n,$ for some $n$? If yes, the above comment answers it.
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