Abstract The GW-hypergroupoids are defined as generalization of the Wall hypergroupoids. The authors introduce a system to obtain a ciphertext using a GW-hypergroupoid. Conditions are given on the GW-hypergroupoid to univocally decipher a given ciphertext and to protect the original message and the key. The measure of security is defined as number of different cleartexts corresponding to the same ciphertext. The case is considered that an eavesdropper intercept only once the ciphertext and the corresponding clear-text and so he try to determine the key. In this case the measure of the security is defined as the number of different key by which the same ciphertext can be obtained from a given cleartext. Examples are given and the measure of security is calculated.