In this paper we propose a novel approach to joint radar-communication waveform design with low probability of intercept characteristics. The data are encoded onto a certain parameter of a particular random distribution; using this distribution, random sequences are generated, which become amplitude weights for the orthogonal frequency division multiplexing (OFDM) sub-carriers. We assume and describe a worst-case scenario, in which an interceptor possesses a certain amount of knowledge about our approach and attempts to reconstruct the data from intercepted radar/communication signals - we then show, via simulations, that with more than 32 OFDM sub-carriers used in signal design, the interceptor cannot improve upon its bit error rate (BER) even with increasing number of intercepts.