Digit sequence encryption

One can consider using as encrypting sequences the digit sequences of numbers obtained from standard mathematical functions. As discussed on page139 such digit sequences often seem locally very random. But in many cases one can immediately tell how a sequence was made just by globally applying appropriate mathematical functions. Thus, for example, given the digit sequence of√s one can retrieve the keys just by squaring the number obtained from early digits in the sequence. Whenever a numberx is known to satisfySum[a[i] f[i][x], {i, n}] 0 with fixedf[i] one can take the early digits ofx and useLatticeReduce to find integer solutions for thea[i]. Withf[i_] = #ⁱ & this method allows algebraic numbers to be recognized. If no linear equation is satisfied by any combination of known functions ofx, however, the method fails, and it seems quite likely that in such cases secure encrypting sequences can be generated, albeit less efficiently than with systems like cellular automata.