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We propose a methodology based on genetic programming to automatically generate data-flow based specifications for hardware designs of public-key cryptosystems such as RSA encryption system. We aim at evolving minimal hardware specifications for modular multiplication and exponentiation, which minimise both space (i.e. required gate number) and time (i.e. encryption and decryption time). We show that the evolved designs are shielded against side-channel leakage. We compare our results against existing and well-known designs, which were produced by human designers.