What is special about $2^{32}/\phi$ in cryptography? In the Tiny Encryption Algorithm:


  Different multiples of a magic constant are used to prevent simple attacks based on the symmetry of the rounds. The magic constant, 2654435769 or 9E3779B916 is chosen to be $2^{32}/ \phi$, where ϕ is the golden ratio.


Which properties does $2^{32}/ \phi$ have that makes it useful in this context?
One reason that $\varphi$ makes a particularly useful 'magic number' in this context is that the multiples $n\varphi$ are guaranteed to be 'maximally far' from integers (this has to do with the lack of large terms in the continued fraction for $\varphi$), and thus the sequence $\{n\varphi\}$ (or more accurately, its initial segments) is more uniformly distributed mod 1 than the sequence $\{n\alpha\}$ for any other irrational $\alpha$.

To give an example: suppose we choose a magic constant $C_\pi = \lfloor {2^{32}/\pi}\rfloor = 1367130551$.  Then $(355C_\pi)\mod {2^{32}} = 41157$, an unexpectedly small result for such a small multiple of our magic constant.  By contrast, if we use the magic constant $C_\varphi = \lfloor {2^{32}/\varphi}\rfloor = 2654435769$, then the smallest $n$ for which $|(nC_\varphi)\mod {2^{32}}| \leq 2^{16}$ (abusing notation a bit) is $n=28657$.  In practice, this can conceivably lead to things like unexpectedly large correlations between the values $X_n$ and $X_{n+k}$ of a linear congruential random number generator for some smallish $k$; for the most part, though, it's folkloreish black magic, based more on the intuition that 'small multiples of this number being small mod $2^{32}$ will be bad' than on any specific theoretical results.