New communications paradigms such as wirelesscommunications for handheld devices have increasedrequirements for operating speed of relevant securitymechanisms, such as encryption for confidentiality,hashing for message integrity and combined hashingand public key encryption for digital signature.Existing secure services have traditionally beenimplemented by employing hybrid cryptographicprotocols, i.e. combinations of symmetric andasymmetric (public key) algorithms to handle botheffective key management and cryptographicperformance. These solutions are in increasing degreebecoming obsolete by the trend to connect end userswith terminals with limited storage and processingpower via wireless networks, sometimes established ina totally ad hoc fashion, with little or no centralizedmanagement to organize user authorization for accessto secured services. New, lightweight protocols are inincreasing demand, and the cryptographic primitivesnecessary for implementation of such protocols alsoneed to be adapted to these new user scenarios.At NTNU/Q2S, research in this area has beenongoing for a period of time resulting in a number ofnew solutions adapted to the new paradigmencompassing mobile users of distributedcommunication services. In this talk, some of thegeneral features of the new cryptographic primitiveswill be described. The designs are mainly based onnew insight into the characteristics of quasigroups andquasigroup string operations.