[en] Context: Detecting the presence of circumstellar dust around nearby solar-type main sequence stars is an important pre-requisite for the design of future life-finding space missions such as ESA's Darwin or NASA's Terrestrial Planet Finder (TPF). The high Antarctic plateau may provide appropriate conditions to perform such a survey from the ground. Aims: We investigate the performance of a nulling interferometer optimised for the detection of exozodiacal discs at Dome C, on the high Antarctic plateau, and compare it to the expected performance of similar instruments at temperate sites. Methods: Based on the currently available measurements of the atmospheric turbulence characteristics at Dome C, we adapt the GENIEsim software (Absil et al. 2006, A&A, 448, 787) to simulate the performance of a nulling interferometer on the high Antarctic plateau. To feed a realistic instrumental configuration into the simulator, we propose a conceptual design for ALADDIN, the Antarctic L-band Astrophysics Discovery Demonstrator for Interferometric Nulling. We assume that this instrument can be placed above the 30-m thick boundary layer, where most of the atmospheric turbulence originates. Results: We show that an optimised nulling interferometer operating on a pair of 1-m class telescopes located 30 m above the ground could achieve a better sensitivity than a similar instrument working with two 8-m class telescopes at a temperate site such as Cerro Paranal. The detection of circumstellar discs about 20 times as dense as our local zodiacal cloud seems within reach for typical Darwin/TPF targets in an integration time of a few hours. Moreover, the exceptional turbulence conditions significantly relax the requirements on real-time control loops, which has favourable consequences on the feasibility of the nulling instrument. Conclusions: The perspectives for high dynamic range, high angular resolution infrared astronomy on the high Antarctic plateau look very promising.