In the context of mobile devices, speaker recognition engines may suffer from ergonomic constraints and limited amount of computing resources. Even if they prove their efficiency in classical contexts, GMM/UBM systems show their limitations when restricting the quantity of speech data. In contrast, the proposed GMM/UBM extension addresses situations characterised by limited enrolment data and only the computing power typically found on modern mobile devices. A key contribution comes from the harnessing of the temporal structure of speech using client-customised pass-phrases and new Markov model structures. Additional temporal information is then used to enhance discrimination with Viterbi decoding, increasing the gap between client and imposter scores. Experiments on the MyIdea database are presented with a standard GMM/UBM configuration acting as a benchmark. When imposters do not know the client pass-phrase, a relative gain of up to 65% in terms of EER is achieved over the GMM/UBM baseline configuration. The results clearly highlight the potential of this new approach, with a good balance between complexity and recognition accuracy.