Pseudo-Hadamard transform

The pseudo-Hadamard transform is a reversible transformation of a bit string that provides cryptographic diffusion. See Hadamard transform.

The bit string must be of even length so that it can be split into two bit strings a and b of equal lengths, each of n bits. To compute the transform for Twofish algorithm, a' and b', from these we use the equations:

${\displaystyle a'=a+b\,{\pmod {2^{n}}}}$

${\displaystyle b'=a+2b\,{\pmod {2^{n}}}}$

To reverse this, clearly:

${\displaystyle b=b'-a'\,{\pmod {2^{n}}}}$

${\displaystyle a=2a'-b'\,{\pmod {2^{n}}}}$

On the other hand, the transformation for SAFER+ encryption is as follows:

${\displaystyle a'=2a+b\,{\pmod {2^{n}}}}$

${\displaystyle b'=a+b\,{\pmod {2^{n}}}}$