This paper proposes a class of new mappings called piecewisesquareroot mappings to design feedback stream ciphers.Such mappings can generate chaotic analogue signals that have uniform distribution function

like autocorrelation function

and can be further quantized into 01 sequence with secure statistical properties by a class of special transofrmation.Compared with Zhou & Lings piecewiselinear mappings

piecewisesquareroot mappings provide enhanced security in that they can maintain the original perfect statistical properties

as well as overcome the defect of piecewiselinearity and expand the key space.