# One-way hashing using singular matrices?

In matrix encoding, we convert our message into some numerical value and then create a matrix out of those numbers.
The matrice encryption is based on the fact that a matrix multiplied by its inverse is a unity matrix, so, if we pre-multiply a marix by some encoding matrix $X$ it will get encrypted and will be decoded only by pre-multiplying the encrypted matrix with $X^{-1}$.
But, what will be the case if the encoding matrix is singular ie. $|X|=0$, Then $X^{-1}$ does not exist because $X^{-1}=\frac{1}{|X|}adj(x)$.
So, it wouldn't be possible to get original matrix even if we know the encoding matrix.

Does it mean that the message is encrypted forever. If not, How to decode it? and if yes, Is it universal hashing?

• This sounds like a very bad linear hashing scheme. Almost as bad as a linear congruential random number generator. – Nayuki Jun 18 '18 at 17:00