Solvable 2-dimensional rational chaotic map defined by Jacobian elliptic functions

Cryptanalysis needs a great deal of pseudo-random numbers. The Jacobian elliptic Chebyshev rational map and its associated binary function have been introduced for generating a sequence of independent and identically distributed (i.i.d.) binary random variables. We have shown that the derivative of an elliptic function induces an elliptic curve and a 2-dimensional rational map. Such a rational map is shown to give a solvable piecewise-monotonic on to a 1-dimensional map with respect to each coordinate. These maps can generate a sequence of i.i.d. binary random vectors.