Score:2

Cyclical Redundancy Check and bijections

cn flag

Let $F_M(n)=\operatorname{CRC32}(M|n)$, where $M$ is an arbitrary length prefix message, $n$ is a 32 bit integer (whether little or big-endian encoded is unimportant) and "|" is simply concatenation of data.

Is $F_M(n)$ injective in $[0,2^{32}−1]$?

fgrieu avatar
ng flag
That depends on the definition of CRC32, but for most proper/usual definitions, yes. Hint: write the definition of CRC32 and conclude.
Fractalice avatar
in flag
You can also add an arbitrary suffix: $F(n) = \text{CRC32}(A|n|B)$. Inverting $F$ is also not difficult.
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