New communications paradigms such as wireless communications for handheld devices have increased requirements for operating speed of relevant security mechanisms, such as encryption for confidentiality, hashing for message integrity and combined hashing and public key encryption for digital signature. Existing secure services have traditionally been implemented by employing hybrid cryptographic protocols, i.e. combinations of symmetric and asymmetric (public key) algorithms to handle both effective key management and cryptographic performance. These solutions are in increasing degree becoming obsolete by the trend to connect end users with terminals with limited storage and processing power via wireless networks, sometimes established in a totally ad hoc fashion, with little or no centralized management to organize user authorization for access to secured services. New, lightweight protocols are in increasing demand, and the cryptographic primitives necessary for implementation of such protocols also need to be adapted to these new user scenarios.At NTNU/Q2S, research in this area has been ongoing for a period of time resulting in a number of new solutions adapted to the new paradigm encompassing mobile users of distributed communication services. In this talk, some of the general features of the new cryptographic primitives will be described. The designs are mainly based on new insight into the characteristics of quasigroups and quasi group string operations.