A Generalized Takagi-Cryptosystem with a modulus of the form prqs

In this paper, we propose a generalized Takagi-Cryptosystem with a modulus of the form pr qs. We've studied for the optimal choice for r, s that gives the best efficiency while maintaining a prescribed security level, and we show that the choice of either pr qr+1, pr-1 qr+1, or pr-2qr+2 depending on the value r + s is the optimal. We also present comparison tables for the efficiency of RSA, the multiprime technology, Takagi's scheme, and our proposed scheme.