Differential frequency hopping (DFH) technique is widely used in wireless communications by exploiting its capabilities of mitigating tracking interference and confidentiality. However, electronic attacks in wireless systems become more and more rigorous, which imposes a lot of challenges on the DFH sequences designed based on the linear congruence theory, fuzzy and chaotic theory, etc. In this article, we investigate the sequence design in DFH systems by exploiting the equivalence principle between the G-function algorithm and the encryption algorithm, in order to achieve high security. In more details, first, the novel G-function is proposed with the aid of the Government Standard algorithm and the Rivest–Shamir–Adleman algorithm. Then, two sequence design algorithms are proposed, namely, the G-function-assisted sequence generation algorithm, which takes the full advantages of the symmetric and asymmetric encryption algorithms, and the high-order G-function-aided sequence generation algorithm, which is capable of enhancing the correlation of the elements in a DFH sequence. Moreover, the security and ergodicity performance of the proposed algorithms are analyzed. Our studies and results show that the DFH sequences generated by the proposed algorithms significantly outperform the sequences generated by the reversible hash algorithm and affine transformation in terms of the uniformity, randomness, complexity, and the security.