# GMR (cryptography)

GMR is a digital signature scheme, which is named after its inventors Shafi Goldwasser, Silvio Micali, and Ronald L. Rivest.

As RSA is based on the GMR factoring assumption that there are bijective functions, which are to be calculated quickly, but where the calculation of the inverse function is very complicated. In contrast to RSA, it can be proved that it is not possible even with an adaptive active attack to forge even a new signature for GMR, however.

## The process in detail

You need a collision- resistant Permutationspaar with secret with the domain of definition. The owner of the secret can compute the inverse functions and easy. For all other is the hard.

Must To sign a single message, a reference from randomly select and publish authentic transmitter. To sign an n -bit long message, it calculates the signature. The receiver can calculate the inverse function thereof, and compare the result with the reference.

Obviously, the problem is to publish a new reference for each message. This is realized by reference trees.