Abstract
An ElGamal public-key cryptosystem based on Chebyshev maps has recently been proposed, where one can maximize the benefits of the property of Chebyshev polynomials of degree p, Tp(·), i.e. commutativity. However, we have to confront the following two disadvantages of commutativity in using such a real-valued chaotic cryptosystem: (1) Commutativity gives a set of public keys (xi, yi = Ts(xi)) for an integer i from a public key (x, y = Ts(x)) with a private key s. This set constitutes a pair of empirical distributions of (fX(x), fY(y) = PTs{fX(x)}), where PTs is the Perron-Frobenius operator of Ts(·). (2) The resonance property of Tp(·) enables us to take a statistical approach to find the private key s based on prime factorization of integer.
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