Comparison of selected cryptosystems using single-scale and poly-scale measures

This paper presents useful measures for comparison of distinct cryptosystems, including (i) the public-key cryptography RSA algorithm, (ii) the elliptic-curve cryptography ElGamal algorithm, (iii) a cryptosystem based on radio background noise (RBN), and (iv) a new cryptosystem based on chaos phenomena in cellular automata. The comparison is based on (i) a single-scale measure (i.e., the marginal probability mass functions (mpmf), and (ii) a poly-scale measure (i.e., the finite-sense stationarity, FSS10). Both comparison approaches use the same plaintext and computational power when testing the four cryptosystems. This paper shows experimentally that the chaos based modular dynamical cryptosystem is (i) strong to single-scale statistical cryptanalysis by leaving no patterns in the ciphertexts, (ii) strong to poly-scale cryptanalysis by having a smaller stationarity window than the alternative cryptosystems, and (iii) faster than the selected algorithms from RSA, ElGamal, and natural sources of randomness (RBN).